Farm Household Production Efficiency Analysis in Ethiopia: The Case of Dessie Zuria District

Transcription

1 Farm Household Production Efficiency Analysis in Ethiopia: The Case of Dessie Zuria District Ali, Beshir Melkaw Registration number: Supervisor: Prof. dr. ir. Alfons Oude Lansink MSc Thesis Business Economics: BEC Number of credits: 36 ECTS Study program: Master Organic Agriculture (MOA) 1 April 2014 Wageningen

2 Acknowledgment First and foremost I offer my sincerest gratitude to my supervisor, Prof.dr.ir. Alfons Oude Lansink, whose guidance, comments, support and encouragement from the initial to the final level enabled me to complete this study. Deepest gratitude is also due to Dr. Hassen Beshir for providing his data set for this study. I would also like to convey thanks to NUFFIC for providing the financial supports to accomplish this study. I would like to express my love and gratitude to my beloved families; for their understanding & endless love, through the duration of my studies. Lastly, I offer my regards and blessings to all of those who supported me in any respect during the completion of the project. i

3 Abstract The aim of the study was to investigate farm households production efficiency using empirical data from a sample of 118 households from Dessie Zuria district, Ethiopia. Farm level and household level technical efficiency (TE), allocative efficiency (AE), economic efficiency (EE) and scale efficiency (SE) scores were estimated using an output oriented bootstrapping DEA method of Simar and Wilson (1998; 2007). At farm level, the mean bias-corrected EE, original AE, original SE and bias-corrected TE scores are 36.3%, 60.4%, 88.4% and 55.9%, respectively. At household level, the corresponding efficiency scores are 37.6%, 58.3%, 88.9% and 60.4%, respectively. The second stage regression analyses of determinants of farm households production efficiency were estimated using a truncated bootstrap technique as proposed by Simar and Wilson (2007). The results demonstrated that age of the household head, total household asset and expenditure, number of plots and extension services are among the important determinants of farm households production efficiency in the region. Arrangement of offfarm activities, farming facilities and materials, extension services, and empowering women are among the areas of interventions to improve production efficiency of farmers. Keywords: Efficiency, Data envelopment analysis, Bootstrap, Truncated regression. ii

4 Table of contents Acknowledgment... i Abstract... ii List of tables... v List of acronyms... vi 1. Introduction Background of the study Statement of the problem Objective of the study Organization of the thesis Theoretical Framework Agricultural household model Farm level versus household level analyses Measures of production efficiency Data and Methods Data Description of the study area Data source and collection Description of variables Methods of frontier estimation Output oriented DEA Output oriented bootstrapping DEA Returns to Scale Tests Second stage regression analyses of determinants of efficiency Results Farm level efficiency measures Household level efficiency measures Efficiency differences between different groups Second stage regression analyses of determinants of efficiency Determinants of technical efficiency Determinants of economic efficiency Determinants of allocative efficiency iii

5 4.4.4 Determinants of scale efficiency Discussions, Conclusions and Policy Implications Discussions Conclusions Policy implications References iv

6 List of tables TABLE 1: DESCRIPTIVE STATISTICS OF INPUTS, OUTPUTS AND PRICES (N=118) TABLE 2: DESCRIPTIVE STATISTICS OF THE EXPLANATORY VARIABLES (N=118) TABLE 3: MEAN FARM LEVEL EFFICIENCY SCORE ESTIMATES AND BOOTSTRAPPING RESULTS TABLE 4: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES AND BOOTSTRAPPING RESULTS TABLE 5: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES FOR MALE VS FEMALE HEADED HOUSEHOLDS TABLE 6: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES FOR LABOR INTENSIVE VS LESS INTENSIVE FARMS TABLE 7: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES FOR SMALL VS LARGE FARMS TABLE 8: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: BIAS-CORR. TE) TABLE 9: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: BIAS CORR. EE) TABLE 10: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL AE) TABLE 11: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL SE) TABLE 12: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL SE-IRS) TABLE 13: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL SE-DRS) v

7 List of acronyms AE CI CRS CSA DAP DEA DGP DMU DRS EE ETB FEAR GDP IRS Allocative Efficiency Confidence Interval Constant Returns to Scale Central Statistical Agency Diammonium Phosphate Data Envelopment Analysis Data Generating Process Decision Making Units Decreasing Returns to Scale Economic Efficiency Ethiopian Birr Frontier Efficiency Analysis with R Gross Domestic Product Increasing Returns to Scale MoFED Ministry of Finance and Economic Development PA SD SE SFA TE Peasant Association Standard Déviation Scale Efficiency Stochastic Frontier Analysis Technical Efficiency UNDP United Nations Development Program VRS WFP Variable Returns to Scale World Food Program vi

8 1. Introduction 1.1 Background of the study Agriculture is the backbone of Ethiopian economy. It accounts for more than 44% of gross domestic product (MoFED, 2012), 80% and 85% of exports and employments respectively (MoFED, 2010). The livelihood of the growing population is directly related with the performance of the sector. Although the country managed to achieve rapid and consecutive economic growth since 1998, Ethiopia ranked 173 out of 187 countries in the 2012 United Nations Human Development Index (UNDP, 2013); and 80 out of 84 in the Global Hunger Index (WFP, 2011). Moreover, while 29% of Ethiopian households live below poverty line (MoFED, 2012); chronic food insecurity has been a defining characteristic of the poverty that has affected millions of Ethiopians of which the vast majority of these poor households live in rural areas that are heavily dependent on subsistence rain-fed agriculture (Subbarao & Smith, 2003; Mussa et al., 2012). Despite its multidimensional importance, the performance of the agricultural sector has remained very poor for several decades. According to Abera (2008), severe weather fluctuations, inappropriate economic policies, low adoption of improved agricultural technologies, prolonged civil unrest and production inefficiency were the main reasons for the low growth rate of agricultural productivity and GDP. The agricultural sector is subsistence and dominated by smallholders on fragmented plots of land. Particularly, Ethiopian highland agriculture is characterized by heavy dependence on rainfall, traditional technology, high population pressure, and severe land degradation (Medhin & Kohlin, 2008). In spite of the government s policy to expand crop production for universal food security, domestic consumption and exports (MoFED, 2006), low productivity levels have been reported by different studies. Until 2005, the government mainly used emergency appeals for food aid on a near annual basis to tackle poverty and hunger (Gilligan et al., 2009). However, through time the government established the New Coalition for Food Security strategy, like the Productive Safety Net Programs (Work for Food Program) to achieve food security (World Bank, 2011; Mussa et al. 2012). However, as Ajibefun (2002) noted, poverty alleviation objectives among smallholder farmers require improvement in the productivity and efficiency of resource use to increase income, attain better standard of living and reduce environmental degradation. According to Asogwa et al. (2011), in order to alleviate poverty and to achieve sustainable development, resources must be used efficiently by giving attention to the elimination of waste. Generally, the achievement of broad based economic growth depends mainly on the ability of an economy in utilizing available resources efficiently. Thus, raising production efficiency in smallholder agriculture could be the basis for achieving universal food security and alleviating poverty particularly among the rural households in Ethiopia. In order to improve production and productivity, an efficient use of production inputs has to be adopted by smallholder farmers. Hence, there is a need to know the actual situation of resource utilization to 1

9 design and implement appropriate policies to raise efficiency. As Msuya et al. (2008) noted an understanding of the relationships between productivity, efficiency, policy indicators and farm-specific practices would provide policy makers with information to design programs that can contribute to increasing food production potential among smallholder farmers. 1.2 Statement of the problem The measurement of economic efficiency of agricultural production has become an increasingly important field of investigation following Farrell s seminal work in He categorized the efficiency of a firm into two components: technical Efficiency (TE) and Allocative Efficiency (AE). He developed the concept of technical efficiency based on the relationships between inputs and outputs. TE measures the ability of a farm to produce maximal potential output from a given set of inputs while AE refers to the ability of a firm to utilize the inputs in optimal proportions, given their respective prices and available technology. AE holds when resource allocation decisions minimize cost, maximize revenue, or more generally maximize profit. The product of the two measures is economic efficiency (Coelli, 1996). As Chavas et al. (2005) noted, despite many researchers investigated the economic efficiency of farm households, almost all have focused on the efficiency of farm activities by ignoring off-farm activities. However, off-farm activities contribute to significant improvements in the welfare of agricultural households. Different studies showed the importance of off-farm income in improving the welfare of agricultural households. In Africa, as Reardon (1997) reported, estimates of nonfarm income as a share of total household income ranges from 22% to 93%, with an average of 45%; and in Ethiopia being 36%. According to studies (Haggblade et al., 1989; Hazell and Hojjati, 1995; Woldehanna, 1997) considerable income diversification between farm and off-farm activities in developing countries may be seen as a response to poorly functioning capital markets; where the cash from nonfarm earnings can help stimulate farm investments and improve agricultural productivity. Joachim (2011) found that non-farm income is positively related with farm expenditures and investments particularly with livestock and equipment investments in Northern Ethiopia. According to the study, access to non-farm income has alleviated farmers credit constraints. A study by Woldehanna (2002) showed that off-farm income accounts 43% of total income (35% off-farm labor income and 8% off-farm non-labor income) in Tigray (Northern Ethiopia) and concluded a positive effect on farm activities. Moreover, an economic analysis of the impact of off-farm activities on farm productivity and output was also conducted in an earlier study by the same researcher in 1997 (Woldehanna, 1997). According to this study, on average, when off-farm income increases by 1 percent, agricultural productivity increases by 0.34 percent. According to him this could be due to households learn managerial skills through experiences in different activities reduce soil mining and initiate better farming practices. This implies that farm and off farm activities are related (i.e. existence of a joint technology). Similar evidences of linkages between off-farm and farm activities were found in Kenya by Kimenye (2002) and in Ghana by Al-Hassen and Egyir (2002). 2

10 Since very poor households often lack access to nonfarm income (Reardon et al., 1992), labor market imperfections can contribute both to inefficient labor allocation in rural households and to a more unequal distribution of income (Chavas et al., 2005). According to Chavas et al. (2005), these rigidities in the labor market and/or jointness 1 between farm and nonfarm activities are sufficient to invalidate efficiency measures conducted solely at the farm level. This stresses the need to include off-farm activities (as a separate index of output) in the analysis of farm household efficiency, particularly for poor African rural households where incomes are low and small inefficiencies can have large impacts on income and welfare. Different researches have been conducted on farm production efficiency in Ethiopia including Hassen et al. (2012), Mussa et al. (2012), Seyoum et al. (1998), Alene (2003), etc. However, none of these researches did consider off-farm activities (as a separate activity) which are highly linked with farm activities particularly for villages surrounding city centers. Specially, in dry seasons farmers used to engage in commercial activities, construction activities, work for food programs, supplying daily labor in the nearby urban centers, etc. They often use off-farm earnings to finance their farm activities such as purchasing of fertilizers and other farm inputs. In other words, previous studies assumed a wellfunctioning and complete labor market, and separation of technologies between farm and off farm activities. However, like in other developing countries, the labor market in Ethiopia is also imperfect; and farm and off farm activities are highly liked as different studies indicated. Moreover, previous studies that applied non-parametric approaches in analyzing efficiency have methodological problems. As Simar and Wilson (2007) noted, studies that followed the two stage nonparametric approaches like DEA, where efficiency scores are calculated in the first stage, and then the estimated efficiencies are regressed on environmental variables in the second stage, failed to describe a coherent data-generating process. As a result, they are invalid due to the complicated nature of serial correlations among the estimated DEA efficiencies. Therefore, the purpose of this study is to analyze production efficiency of farm households by accounting off-farm activities (as a separate index of output) and serial correlations of DEA estimates in the second stage of the analysis. 1.3 Objective of the study The general objective of the study is to assess the production efficiency (technical, allocative, economic and scale efficiencies) of smallholder farms at household and farm levels. The specific objectives include: a. To estimate technical, allocative, economic and scale efficiencies at household and farm levels, b. To investigate efficiency differences between different groups of farm households such as female headed versus male headed households, labor intensive versus less intensive farms, and small versus large farms, and finally c. To analyze the determinants of technical, allocative, economic and scale efficiencies of farm households. 1 Jointness refers to cases where off-farm activities are linked with (and contribute to) farm activities. 3

11 1.4 Organization of the thesis The thesis is organized into five sections. The second section discusses the theoretical framework of the study. It briefly presents the rationale behind household level production efficiency analyses instead of the traditional farm focus analyses. It also introduces the output oriented Farrell s (1957) measure of efficiency. Section three presents the data and methods that the study employed. After presenting the data, it briefly introduces the bootstrapping DEA as a method of computing output oriented efficiency scores so as to improve statistical efficiency and consistency in non-parametrical approaches. Moreover, it also introduces the truncated bootstrap method for estimating the second stage regression. Section four presents data analyses and discussion of results. It presents the farm and household level efficiency measures, efficiency differences between different groups of farm households and the second stage regression analyses of the determinants of production efficiency. Finally, section five presents discussion and summary of results in line with other studies, and policy implications of the findings. 4

12 2. Theoretical Framework In order to analyze production efficiency of farm households at household level, this study adopted the model used by Chavas et al. (2005). The basis of production efficiency analysis of farms at household level is the agricultural household model. As Chavas et al. (2005) argued in the presence of labor market rigidities and/or joint technology of farm and nonfarm activities, the appropriate level of analysis is the household. According to them, measuring production efficiency at the farm level is invalid and misleading. The following sections discuss how the agricultural household model can be used for production efficiency analysis at household level; and how labor market rigidities and joint technology of farm and nonfarm activities invalidate efficiency analyses at farm level. Once efficiency scores (technical, allocative, economic and scale efficiency scores) are estimated at household level by accounting the serial correlations, the truncated bootstrapping regression of Simar and Wilson (2007) will be applied to identify the significant determinants of each measures of efficiency. 2.1 Agricultural household model An agricultural household model is a model that incorporates the production, consumption and the labor supply decisions of a farm household into a single unit (Singh et. al., 1986; Woldehanna, 2000). Suppose that a farm household has family members who make production, consumption, and labor allocation decisions together during a specific time period (assuming a unilateral household model 2 ). Then, each member of the household allocates his/her labor time for farm and/or off-farm activities, and for leisure so as to maximize his/her utility. Let ( ) is the amount of family labor used for farm activities. Assume that the household employs family labor, hired labor, and nonlabor inputs (like land, seed, fertilizer, oxen, etc.) to produce a vector of farm outputs. Let ( ) be the amount of family labor allocated for off-farm activities to generate a non-farm income 3. Let be the feasible set of technology facing the household, such that inputs ( ) can feasibly produce outputs ( ) and written as ( ). Let ( ) be the total amount of time endowment of each family member over a given period of time. Thus, each family member allocate his/her time between leisure activities ( ), on-farm activities ( ), and off-farm activities ( ), subject to the total amount of time constraint which can be stated as: ( ) 2 The unitary models in general represent a household as it is a single individual and as a unit of decision making in the consumption, production and labor allocation decisions (refer Tassew (2000) for detail). 3 Prices will be normalized such that the price of off-farm output is equal to 1. As a result, N is both a measure of off-farm income and an index of off-farm output. 5

13 Suppose that the output market is a perfectively competitive market 4, and let is the price vector for farm outputs, is the price vector for non-labor inputs, and is the wage rate for hired labor. Suppose the household consumes a vector of basket of commodities, whose market prices are. Then, consumption decisions are made subject to the budget constraint which states that consumption expenditure ( ) cannot exceed farm revenue ( ) minus farm production cost ( ) plus nonfarm income (R). This constraint can be written as: The goal of the household is to maximize its utility derived from the consumption of commodities and leisure. Based on the unitary model, let ( ), defined over ( ), is a household utility function. Moreover, assume that that the utility function ( ) is non-satiated 5 and quasi-concave in the ( ) plane. Mathematically, the utility maximization problem of the household can be stated as: ( ) ( ) ( ) The budget constraint expressed in (2) is necessarily binding following the assumption of non-satiation of the utility function ( ). The optimization problem (3) can be decomposed into two stages: first, choose ( ) that maximize the profit of the household; and second, choose ( ) that maximize household utility. The first stage optimization with respect to ( ) implies a profit maximization problem and can be written as: ( ) ( ) Where ( ) is the amount of time that the family members spend working either on farm activities or off-farm activities. Equation (4) establishes profit maximization with respect to the household choice of ( ), with ( ) being the indirect profit function conditional on ( ). Therefore, a household utility maximization (3) implies profit maximization (4). This is because for a given ( ), a failure to maximize profit would reduce household income, which would restrict consumer expenditure (equation 2). Following the assumption of non-satiation, this would make the household worse-off. Therefore, a failure to maximize profit is inconsistent with household utility maximization. As can be seen above, equation 4 includes farm and nonfarm activities, both in terms of labor allocation ( ) and income ( ) at the household level. It involves the general technology, allowing for joint household decisions between farm and nonfarm activities. 4 In this study, the outputs markets are assumed to be perfect while the factor markets are supposed to be imperfect. 5 The assumption of non-satiation implies always more is better. 6

14 Equation (4) implies that the profit function ( ) and production decisions are related since both depend on the amount of time allocated to work, ( ). However, production decisions are not related with consumption decisions. This is because, the profit function ( ) and the production decisions do not depend on. Since appears only in the utility function, they are not arguments of the technology. Therefore, production decisions are separable from consumption decisions. Equation 3 being the first stage of optimization, the second stage optimization is a utility maximization subject to the household budget constraint. It can be stated as: ( ) ( ) ( ) As Chavas et al. (2005) argued the relevant framework to analyze production efficiency at the household level is Equation 4 (which implies profit maximization). According to them, since households do not or cannot respond to economic incentives in the presence of factor market imperfections and/or poor managerial skills, households may not behave in a way consistent with Equation 4. Therefore, efficiency analyses based on Equation 4 can provide useful insights into the nature and causes of economic inefficiency. 2.2 Farm level versus household level analyses According to Chavas et al. (2005), if farm and off-farm activities are related (i.e., existence of joint technology between them) and/or if the labor market is imperfect, then farm level analyses would be inappropriate. Farm focus analysis may be appropriate only if there is no jointness in the technologies underlying farm and nonfarm activities, and the labor market is perfect. Under non-jointness, suppose the farm and off-farm production technologies of the household are given by ( ) and ( ), respectively. It means that the household technology is expressed completely in terms of two separate technologies for a given time endowment as stated in equation 1. In this case, the profit maximization problem of the household equivalent to equation 4 can be stated as: ( ) ( ) ( ) Where ( ) ( ) is the production frontier boundary of the off-farm technology. Equation 6 implies that since farm and off-farm activities are not related, the profit maximization problem requires maximizing farm profit for a given level of off-farm income. In this case, farm level analysis would be appropriate. 7

15 Now, consider the case of labor market rigidity. Suppose that ( ) is a linear function in given as: ( ), where is the wage rate received by the family member from off-farm activities. At farm level, the household aims to maximize its profit given as: ( ) ( ) The overall profit of the household is ( ) ( ). Equation 7 implies that the wage rate measures the opportunity cost of farm labour for each family member. Therefore, farm and off-farm activities are separable. Equation 7 to hold requires a perfect labor market which is not the case in developing countries. Generally, the assumptions of both nonjointness between farm and off-farm technologies (equation 6) and perfectly competitive labor market (equation 7) are not realistic in developing countries which are the bases for farm level analysis. Therefore, equation 4 is the appropriate formulation for production efficiency analysis at household level. It provides the appropriate framework to investigate the efficiency of both farm and off-farm activities. Having the appropriate framework for household efficiency analysis, the following section discusses the different methods of measuring production efficiency. 2.3 Measures of production efficiency Modern efficiency measures begin following Farrell s 1957 work. He categorized measures of efficiency into technical efficiency and allocative (price) efficiency. Technical efficiency refers to the ability of a firm to obtain maximum output from a given set of inputs while allocative efficiency reflects the ability of the firm to use inputs in optimal proportions, given their respective prices. The product of the two measures provides economic or overall efficiency (Coelli, 1995). Furthermore, measures of technical efficiency are decomposed into purely technical (PTE) and scale efficiency (SE). SE measures the optimality of the firm s size (Forsund et al., 1980). A firm displaying increasing returns to scale (IRS) is too small for its scale of operation. In contrast, a firm with decreasing returns to scale (DRS) is too large for the volume of activities that it conducts. Based on the work of Farrell (1957), efficiency measures can be broadly categorized into input oriented and output oriented DEA measures. In order to estimate production efficiency scores of farms at household level, this study used an outputoriented DEA as justified in section 2.2 above. Since the input market is imperfect, input oriented DEA is not appropriate. Moreover, since family labor and land are the two most important inputs for subsistence agriculture, input-oriented DEA (proportional contraction of inputs for a given level of output) does not make sense. Therefore, output-oriented DEA (proportional expansion of outputs for a given set of inputs) is the appropriate way of efficiency scores calculation for smallholders. An output-oriented measure implies the ability of a firm to maximize output/production, given the current level of employment of inputs. It refers to the ability of a firm to increase the quantities of output proportionally while keeping input employment constant (Coelli, 1996). For example, suppose 8

16 firms produce two outputs (Y1 and Y2) by using an input (X) assuming constant returns to scale. The production possibility frontier ZZ is defined by the fully-efficient firms relative to other firms. Therefore, firms operating on the frontier are 100% efficient technically while firms operating within the frontier are inefficient. The following figure (Figure 1) depicts the case. Figure 1: Technical and allocative efficiency (output-oriented) According to Farrell (1957), point A corresponds to an inefficient firm, and the distance AB represents its technical inefficiency. This implies the amount of output that could be increased without requiring extra input. The output oriented technical efficiency of firm A is measured as: ( ) Given the ratio of prices of outputs as defined by the line DD in Figure 1 above, the allocative efficiency of a firm operating at point A is given by the ratio: ( ) The distance BC represents the increment in revenue that would achieve if production were to occur at the allocatively (and technically) efficient point B, instead of at the technically efficient, but allocatively inefficient, point B. The overall or economic efficiency of a firm operating at point A is given by: ( ) The distance AC can be interpreted in terms of revenue increments. 9

17 3. Data and Methods This section briefly presents the data used, and the methods employed to analyze the data. It introduces the output oriented DEA to obtain consistent DEA estimates, and the truncated bootstrap regression to improve statistical efficiency in the second stage regression. 3.1 Data The following three sections present the study area, the data sources and methods of collection, and a description of the variables used in the study Description of the study area The study is conducted in Desie Zuria district of South Wollo which is located in the North Eastern highlands of Ethiopia. It has 20 administrative districts of which two are towns (Kombolcha and Dessie). From the rural districts, Dessie Zuria (a district surrounding the major town Dessie) is selected purposively for this study due to availability of a survey data. According to the Central Statistical Agency s (CSA) census data, in 2007 the total population of South Wollo was 2,519,450 of which 50.5% were females and 88% were rural residents (CSA, 2008). The total land area of South Wollo is 1,773,681 hectares of which 180,100 hectares belong to Dessie Zuria district Data source and collection To achieve the stated objectives, secondary data sources were used. Secondary data is obtained from a household survey by Hassen 6 in He used multistage random sampling method for the selection of the sample respondents. First, he selected three Peasant Associations (PAs) randomly from a total of 27 PAs using simple random sampling procedure. Second, a total of 126 farmers were selected using probability proportional to sample size sampling technique. However, complete data is available for only 118 farmers, which is used in this study. Additional data is gathered and extracted from Central Statistical Agency (CSA) Description of variables This section presents the input, output and price variables which are used in the DEA efficiency score calculations, and the explanatory variables used in the second stage regression. 6 Assistant professor at Wollo University, Department of Agricultural Economics, P.O. Box 1145, Ethiopia. hassenhussien@gmail.com. 10

18 Inputs In producing crops, livestock and livestock products, the households employed the following resources. Land (X1): total amount of cultivated land (including grazing land) in hectares. Farm labor (X2): farm labor refers to the total amount of labor employed in farm activities (crops and livestock production units) in man days. It consists of family and hired labors. Off-farm labor (X3): amount of labor allocated for off-farm activities in man days. Ox days (X4): the number of days that the household employed oxen (two oxen) for cultivation of land in oxen days. Other costs (X5): consist of the values of artificial fertilizers (DAP and UREA), manure and compost applied for crop production in Ethiopian Birr (ETB); cost of seeds for crop productions; cost of feed (grass and straw fed to cattle, sheep and goats; and grains to hens in ETB), and veterinary expenses (the values of veterinary medicines and services used for cattle and hens in ETB). Outputs Since the farmers practiced mixed crop-livestock farming together with off-farm activities, the following are the list of outputs. Crops (Y1): the households produced crops such as teff, barley, wheat, horse bean, chickpea, field pea, linseed, fenugreek, carrot, garlic, grass pea, potato, sorghum, maize, lentil and oat. The households in the sample produced a combination of some of these crops (i.e., a crop produced by some of the farmers might not be produced by other farmers). As a result, the aggregate values of the crops are computed using the market prices of each crop. Then, by using the prices of crops in 2006 as a base (CSA, 2008), the price index is computed. By using the price index (P1), the aggregate value of the crops is deflated to find the quantity index (for the purpose of efficiency score calculations). Livestock products (Y2): it consists of the values of milk, sheep, goat and egg produced during that year. Like the crop products, the values of livestock products are indexed using the 2006 prices (CSA, 2008). The aggregate index of quantity of livestock products is computed using the livestock product price index (P2). Off-farm income (Y3): consists of labor income, non-labor income and remittance in ETB. The value of off-farm income is supposed to be equal to off-farm quantity assuming that the price of off-farm output is 1 ETB. On average, the share of off-farm income from the total household income is about 18%. 11

19 For farm level analyses, inputs X1, X2, X4 and X5, and outputs Y1 and Y2 with their respective prices were used to compute the efficiency scores. At household level, inputs X1, X2+X3, X4 and X5, and outputs Y1, Y2 and Y3 with their respective prices were used to compute the efficiency scores. The summary of descriptive statistics (mean, standard deviations, minimum and maximum) of input, output and price variables is presented in Table 1 below. Table 1: Descriptive statistics of inputs, outputs and prices (N=118) Variables Denotations Mean Std. Dev. Min. Max. Land X Farm labor X Off-farm labor X Ox days X Other costs X Crops (index) Y Livestock products (index) Y Off-farm income Y Crop products price index P Livestock products price index P Second stage regression variables These are the explanatory variables used in the second stage regression. The explanatory variables are external factors (excluding the input-output variables used in the first stage efficiency calculations) that are supposed to explain efficiency differences among farm households. The following factors are expected to capture farm household production efficiency differences. Sex (Z1): refers to the sex of the household head. It is a dummy variable defined by 1 if the household head is male and 0 otherwise. About 83.9% of the household heads are male. In gender efficiency differential researches, most studies concluded that both female and male are equally efficient (Quisumbing, 1996) while some others concluded males are more efficient than females and vice-versa (Udry, 1996; Mussa et al., 2012). Since female headed households are poorer than male headed households, female headed households are expected to be less efficient in the study area. Age (Z2): refers to the age of the household head. It is included to capture the effect of farming experience. More experienced farmers are expected to be more efficient. However, the old aged farmers are also less educated compared to young farmers. Therefore, there it is expected to have a contradicting effect on efficiency. Education level of the household head (Z3): refers to the number of years of schooling. It is expected that educated farmers are less risk averters and willing to adopt new technologies like improved seeds, breeds, fertilizers, etc. As a result, education is expected to affect production efficiency positively. 12

20 Number of plots (Z4): refers to the number of plots that the household cultivated during the production year. One of the constraints of agricultural development in developing countries is the fragmented nature of farming plots. It makes difficult the use of modern technologies. Therefore, it is expected to a negative effect on efficiency. Total household asset (Z5): refers to the sum of the current values of livestock, furniture, farming materials and equipment owned by the household. The more the household asset, the more the household is expected to be efficient. Capital is one of the constraining factors for smallholders. Since livestock is a store of wealth, farmers are expected to more efficient with more capital (livestock). Total household expenditure (Z6): refers to the total yearly consumption expenditure of household on goods and services. Credit (Z7): refers to the amount of credit the household borrowed during that production year in ETB. Since finance is a limiting factor in developing countries for agricultural households, access to credit is expected to raise production efficiency. Distance (Z8): refers to the distance between the home of the household and the nearest market in kilometers. Access to market is also one of the problems of farmers. Therefore, the shorter the distance, the better the infrastructure and information that a household will access. It is expected to affect production efficiency negatively. Extension service (Z9): It is approximated by the number of development agents (DA) visit. The consultancy services of the extension workers are expected to raise production efficiency. Formal training (Z10): refers to a dummy variable defined by 1 if the household attend a formal training and 0 otherwise. About 37% of the households attended formal training during that production year. The training is expected to raise production efficiency. The summary of descriptive statistics (mean, standard deviations, minimum and maximum) of the explanatory variables (for the continuous variables) is presented in Table 2 below. Table 2: Descriptive statistics of the explanatory variables (N=118) Variables Mean Std. Dev. Min. Max. Sex (Z1) Male (83.9%) & Female (16.1%) Age (Z2) Education (Z3) Number of plots (Z4) Total household asset (Z5) Total household expenditure (Z6) Credit (Z7) Distance (Z8) Extension service (Z9) Formal training (Z10) Attended (37%) & Didn t attend (63%) 13

21 3.2 Methods of frontier estimation Output oriented DEA Both the input and output oriented measures assume that the production function of the fully efficient firms is known, while in practice it is not. Farrell (1957) suggested the estimation of the production function from sample data by using either parametric or non-parametric methods. The commonly applied methods are data envelopment analysis (DEA) from non-parametric methods and stochastic frontier analysis (SFA) from parametric methods. The following section presents how the output oriented DEA scores are computed. DEA is a technique based on the non-parametric mathematical programming approach to frontier estimation. It measures the efficiency of a decision making unit (DMU), or in this case a household, relative to the efficiency of all other households. The DEA methodology was formally developed by Charnes et al. (1978), where efficiency was defined as the weighted sum of outputs over a weighted sum of inputs, where the weight structure is calculated by the means of mathematical programming assuming constant returns to scale (CRS). However, Banker et al. (1984) extended the model to include variable returns to scale (VRS) which allowed for optimization of farms based on size. Following the works of Simar and Wilson (2007), it is possible to conduct statistical tests like hypothesis testing, construct confidence intervals and make inference from DEA results using bootstrapping. Suppose there are farm households that employ inputs to produce outputs. For the household these are represented by the column vectors, respectively. The input matrix,, and the output matrix, represent the data for all firms.then, the output maximization process of Banker et al. (1984) to measure technical efficiency for each household can be expressed as: + (11) Where is a vector of outputs of household i (including off-farm output as an index: ), is a vector representing the inputs used by household i ( ), is a vector representing peer weights for household, is the proportional increase in outputs that could be achieved by the household with the input quantities held constant if the inputs were efficiently utilized and 14 is the technical efficiency score which varies between zero and one. When technical efficiency is one ( ), the household is producing on the production frontier and is said to be technically efficient, while implies that the farm is not technically efficient and lies below the frontier (refer Figure 1 above for graphical illustration).

22 There are two ways of computing allocative efficiency. These are: from a cost minimizing perspective and from a revenue maximization perspective. This study employed a revenue maximization perspective for two reasons. Firstly, a cost minimizing perspective requires perfectly competitive factor markets which are assumed to be imperfect in this study. Secondly, since this study used an output oriented DEA, a revenue maximization perspective will be simple for computation. The profit maximization problem (stated in equation 4) implies a revenue maximization problem conditional on inputs ( ) given by: ( ) (12) In a linear programming framework, following Zhang (2010), equation (12) can be rewritten to calculate the allocative efficiency score of household as: + ( ) (13) Where is the revenue-maximizing vector of output quantities for the household (including off farm output) given the output prices and total input level. These vectors of output quantities are allocatively efficient. This revenue maximization problem assumes a well-functioning (perfectly competitive) output markets. Therefore, the objective of the household is to maximize its revenue for given output price levels conditional on available inputs. Then, based on the results of Equations (11 and 13), the allocative efficiency (AE) scores can be computed as: ( ) [ ( ) ] ( ) [ ( ) ] ( ) (14) Where ( ) is a technically efficient output vector from equation 11 (refer Figure 1 for graphical illustration of AE computation). Like TE,. represents a revenue maximizing household that is allocatively efficient with respect to outputs. implies households are not efficient in allocating resources. Once TE and AE scores are calculated, economic efficiency (EE) and scale efficiency (SE) scores are computed, by using equations (15) and (16), respectively as given below. 15

23 ( ) ( ) ( ) ( ) (15) ( ) ( ) ( ) (16) However, as Simar and Wilson (1998; 2000; 2007) demonstrated, the TE scores computed from Equation (11) are biased estimates of the actual efficiency scores. They argued that statistical inferences based on the results of Equation (11) are invalid and misleading due to lack of use of a coherent data generating processes and complex (but unknown) serial correlations of the DEA estimates. As a result, they proposed bootstrapping DEA (as presented in the following section) to solve the above problems Output oriented bootstrapping DEA This section introduces how bootstrap method is used to compute a bias-corrected TE scores and how to construct confidence intervals for DEA estimates. Although non parametric estimators like DEA do not require specification of the functional relationship between inputs and outputs, statistical properties of the estimates depend on the model of datagenerating process (DGP) used to estimate the frontier and the sampling properties. In DEA, efficiency is measured relative to an estimate of the true unobserved production frontier. According to Simar and Wilson (1998), the measures of efficiency are sensitive to sampling variations since statistical estimators are obtained from finite samples. According to them, the bootstrapping technique introduced by Efron (1979) is an attractive method to obtain a statistical consistent estimates, and hence to make inference. Bootstrapping refers to a method where the DGP is repeatedly simulated through resampling, and applying the original estimator to each simulated sample so that the estimates mimic the sampling distribution of the original estimator (Simar and Wilson, 1998). In order to apply the bootstrap method, first, the model of the DGP has to be defined clearly. As Simar and Wilson (2007) argued all previous studies that followed the DEA approach to estimate efficiency scores failed to describe a coherent DGP, and hence their inferences are invalid. The following section presents how a bias-corrected efficiency scores are computed and a confidence interval is constructed using bootstrapping following the work of Simar and Wilson (1998). 16

24 Suppose that there are N farm households producing M outputs. Let ( ) be the inputs employed by the firms to produce outputs denoted by ( ). Then, the production set can be described in terms of ( ) as: *( ) + (17) The production set in expression (17) can be described by an output correspondence set as: ( ) * ( ) + (18) Given the assumptions of convexity of ( ) for all and disposability of all inputs and outputs, the Farrell efficiency boundaries which are subsets of ( ) can be given as: ( ) * ( ) ( ) + (19) Given equation (19), for a given point ( efficiency can be defined as: ), the output oriented Farrell measure of technical { ( )} (20) utilized. refers to the possible proportional increase in all outputs if the existing inputs were efficiently According to Simar and Wilson (1998), is unknown since, ( ) and ( ) are unknown for a given unit ( ). Suppose that a DGP 7,, generates a random sample *( ) +. By using some method, this sample can be used to define the estimators, ( ) and. ( ) Therefore, for a given unit ( ), its TE can be estimated as: { ( )} (21) Since is unknown in practice, suppose is an estimator of which is produced from the data. Let *( ) + is generated using the data. By the same method, this pseudo-sample defines the corresponding quantities as, ( ) and ( ). The corresponding measure of efficiency is given by: { ( )} (22) According to Simar and Wilson (1998), given, the sampling distributions of the estimators, ( ) and ( ) are completely known conditionally on. These sampling distributions can be easily approximated using Monte Carlo methods. Suppose samples, b= 1,, B are generated from. 7 Refer the assumptions A1-A8 of Simar and Wilson (2007) to define DGP in DEA models to obtain consistent estimates. 17

25 Given that is a good estimator of, the bootstrap method is based on the idea that the known bootstrap distributions will mimic the original unknown sampling distributions of target estimators. Specifically, for the TE measure of a given fixed unit ( ), the sampling distribution can be stated as: ( ) ( ) (23) Using expression (23), the bias of (which is the original estimator of ( ) ) can be estimated as: (24) Using the bootstrap estimate, expression (24) can be rewritten as: ( ) (25) The bias in expression (25) can be approximated using the Monte Carlo realizations as: (26) Then, a bias-corrected estimator of is given by: (27) The variance of can be estimated by: ( ) (28) After correcting the bias, the empirical distribution of, b= 1,, N provides the confidence interval for. Suppose one wants the empirical distribution to be centered on (which is the bias corrected estimator of ). Then, the bias-corrected bootstrapped estimator is given as: (29) Therefore, the percentile confidence interval for with level of significance can be given as: ( ) ( ( ) ( ) ) (30) Although the existing software packages do not include procedures for bootstrapping in frontier models (Wilson, 2008), the software package FEAR (Frontier Efficiency Analysis with R) 2.0 of Wilson (2008) which is an interface in R allows for computing DEA efficiency scores with bootstrapping. Using FEAR 2.0, farm level and household level technical efficiency scores are computed using the Shephard (1970) output distance function for each farm (which is the reciprocal of Farrell s (1957) DEA estimates). The 18

26 simplex method described by Hadley (1962) is used to solve the linear programming problems. The software package FEAR 2.0 of Wilson (2007) also allows computing allocative efficiency from revenue maximization perspective as described in Equations 13 and 14. However, as Simar and Wilson (2002) demonstrated the type of RTS has to be tested and determined before estimating efficiency scores; and the following section deals with this Returns to Scale Tests It is necessary to know first the type of returns to scale that the production technology exhibits before estimating DEA efficiency scores. As Simar and Wilson (2002) noted, the impositions of priori assumptions of CRS or VRS result in statistically inconsistent estimates of efficiency and a loss of statistical efficiency. According to them, the imposition of CRS while using DEA methods may seriously distort measures of efficiency if the true technology exhibits non-crs. This results in statistically inconsistent estimates of efficiency. On the other hand, a priori imposition of VRS will result in loss of statistical efficiency if the technologies actually exhibit CRS. As a result, Simar and Wilson (2002) developed returns to scale tests based on bootstrapping. In returns to scale statistical test, the null hypothesis is the production set is characterized by CRS and the alternative is that it exhibits VRS. To test this hypothesis different tests exist with their respective strengths and weaknesses. However, in this study, the mean of ratios that is developed by Simar and Wilson (2002) is used. According to this test. The null hypothesis is rejected when is statistically less than 1. The critical value for deciding whether is statistically less than 1 or not is derived from bootstrapping (Simar and Wilson, 2002). For detail information about the returns to scale tests refer to Simar and Wilson (2002). The argument in equations (11 and 13) above will be equated to one if VRS is assumed. 3.3 Second stage regression analyses of determinants of efficiency For the second stage regression, the method proposed by Simar and Wilson (2007) is adopted. Having computed TE scores, the second stage is to analyse the determinants of these efficiency measures as formulated in Equation (31) below. ( ) (31) Where is the estimated Shephard s (1970) output efficiency score for household i, is a smooth continuous function, is a matrix of the explanatory variables including a vector of ones 19