Farm Household Production Efficiency Analysis in Ethiopia

Farm Household Production Efficiency Analysis

in Ethiopia: The Case of Dessie Zuria District

Ali, Beshir Melkaw Registration number: 851117011030

Supervisor: Prof. dr. ir. Alfons Oude Lansink

MSc Thesis Business Economics: BEC-80436 Number of credits: 36 ECTS Study program: Master Organic Agriculture (MOA)

April 2014 Wageningen

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.

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 off- farm 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.

Table of contents Acknowledgment ...... i Abstract ...... ii List of tables ...... v List of acronyms ...... vi 1. Introduction ...... 1 1.1 Background of the study ...... 1 1.2 Statement of the problem ...... 2 1.3 Objective of the study ...... 3 1.4 Organization of the thesis ...... 4 2. Theoretical Framework ...... 5 2.1 Agricultural household model ...... 5 2.2 Farm level versus household level analyses ...... 7 2.3 Measures of production efficiency ...... 8 3. Data and Methods ...... 10 3.1 Data ...... 10 3.1.1 Description of the study area ...... 10 3.1.2 Data source and collection ...... 10 3.1.3 Description of variables ...... 10 3.2 Methods of frontier estimation ...... 14 3.2.1 Output oriented DEA...... 14 3.2.2 Output oriented bootstrapping DEA ...... 16 3.2.3 Returns to Scale Tests ...... 19 3.3 Second stage regression analyses of determinants of efficiency ...... 19 4. Results ...... 23 4.1 Farm level efficiency measures ...... 23 4.2 Household level efficiency measures ...... 25 4.3 Efficiency differences between different groups ...... 26 4.4 Second stage regression analyses of determinants of efficiency ...... 29 4.4.1 Determinants of technical efficiency ...... 29 4.4.2 Determinants of economic efficiency ...... 30 4.4.3 Determinants of allocative efficiency ...... 30

iii

4.4.4 Determinants of scale efficiency ...... 31 5. Discussions, Conclusions and Policy Implications ...... 33 5.1 Discussions ...... 33 5.2 Conclusions ...... 35 5.3 Policy implications ...... 36 References ...... 38

List of tables TABLE 1: DESCRIPTIVE STATISTICS OF INPUTS, OUTPUTS AND PRICES (N=118) ...... 12 TABLE 2: DESCRIPTIVE STATISTICS OF THE EXPLANATORY VARIABLES (N=118) ...... 13 TABLE 3: MEAN FARM LEVEL EFFICIENCY SCORE ESTIMATES AND BOOTSTRAPPING RESULTS ...... 24 TABLE 4: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES AND BOOTSTRAPPING RESULTS ...... 25 TABLE 5: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES FOR MALE VS FEMALE HEADED HOUSEHOLDS ...... 26 TABLE 6: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES FOR LABOR INTENSIVE VS LESS INTENSIVE FARMS ...... 27 TABLE 7: MEAN HOUSEHOLD LEVEL EFFICIENCY SCORE ESTIMATES FOR SMALL VS LARGE FARMS...... 28 TABLE 8: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: BIAS-CORR. TE) ...... 29 TABLE 9: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: BIAS CORR. EE) ...... 30 TABLE 10: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL AE) ...... 31 TABLE 11: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL SE) ...... 31 TABLE 12: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL SE-IRS) ...... 32 TABLE 13: TRUNCATED BOOTSTRAPPED TWO-STAGE REGRESSION (DEPENDENT VARIABLE: ORIGINAL SE-DRS) ...... 32

List of acronyms

AE Allocative Efficiency

CI Confidence Interval

CRS Constant Returns to Scale

CSA Central Statistical Agency

DAP Diammonium Phosphate

DEA Data Envelopment Analysis

DGP Data Generating Process

DMU Decision Making Units

DRS Decreasing Returns to Scale

EE Economic Efficiency

ETB Ethiopian Birr

FEAR Frontier Efficiency Analysis with R

GDP Gross Domestic Product

IRS Increasing Returns to Scale

MoFED Ministry of Finance and Economic Development

PA Peasant Association

SD Standard Déviation

SE Scale Efficiency

SFA Stochastic Frontier Analysis

TE Technical Efficiency

UNDP United Nations Development Program

VRS Variable Returns to Scale

WFP World Food Program

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 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 1957. 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).

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 jointness1 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 well- functioning 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 non- parametric 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.

1Jointness refers to cases where off-farm activities are linked with (and contribute to) farm activities.

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.

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’ model2). 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:

( )

2The 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). 3Prices 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.

Suppose that the output market is a perfectively competitive market4, 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-satiated5 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’.

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.

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 output- oriented 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 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.

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.

3.1.1 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.

3.1.2 Data source and collection

To achieve the stated objectives, secondary data sources were used. Secondary data is obtained from a household survey by Hassen6 in 2009. 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).

3.1.3 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. E-mail: [email protected].

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%.

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 X1 0.815 0.5712 0.025 2.8 Farm labor X2 195.92 115.399 16 651.5 Off-farm labor X3 38.396 108.5072 0 1000 Ox days X4 32.998 17.3970 7 78 Other costs X5 2026.43 1559.559 151.89 6317.58 Crops (index) Y1 3691.15 2517.644 327.8 10344 Livestock products (index) Y2 1703.54 1821.694 0 7486 Off-farm income Y3 2385.17 3861.667 0 30800 Crop products’ price index P1 2.2497 0.7764 0.64 6.09 Livestock products’ price index P2 1.8111 0.8307 0 2.94

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.

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) 52.602 14.422 20 88 Education (Z3) 2.153 3.438 0 12 Number of plots (Z4) 4.373 2.029 1 9 Total household asset (Z5) 57485.8 64024.34 1620 587681 Total household expenditure (Z6) 10533.85 5343.269 2275 24305 Credit (Z7) 158.051 650.607 0 4000 Distance (Z8) 89.389 55.399 5 240 Extension service (Z9) 2.746 3.689 0 19 Formal training (Z10) Attended (37%) & Didn’t attend (63%)

3.2 Methods of frontier estimation

3.2.1 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 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).

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)

( ) ( ) (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.

3.2.2 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 data- generating 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).

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 ( ), the output oriented Farrell measure of technical efficiency can be defined as:

{ ( )} (20)

refers to the possible proportional increase in all outputs if the existing inputs were efficiently utilized.

According to Simar and Wilson (1998), is unknown since , ( ) and ( ) are unknown for a given 7 unit ( ). Suppose that a DGP , , 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.

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 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.

3.2.3 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 and is a statistical noise. Since Equation 31 is usually estimated from sample data, it can be rewritten as:

̂ ( )

Where ̂ is the estimator of and is the sample error term.

Simar and Wilson (2007) argued that the efficiency scores computed in the first stage are correlated with the environmental variables used in the second stage, and thereby the second stage estimates will be inconsistent and biased. According to them, the problem in estimating equation (32) and making inference about arise from the serial correlation and bias of ̂ , and the correlation between and

. In addition to the correlation between and , they noted that, for , the serial correlations among the error terms ’s do not disappear quickly to make standard statistical inferences.

They demonstrated the problems related with the estimations of Equation 32 using either Tobit or OLS methods as follow mathematically. Statistically, ̂ can be writtens as:

̂ ( ̂ ) ( )

Where ( ) . Moreover, as defined in equation 24 above, the bias of ̂ can be given by:

( ̂ ) ( ̂ ) ( )

From equation 33, substitute for ( ̂ ) in equation 34 & by rearranging terms:

̂ ( ̂ ) ( )

Substituting for from equation 31 gives:

̂ ( ̂ ) ( )

Since ̂ is a consistent estimator of , is asymptotically negligible; yet, ( ̂ ) is not. However, the conventional methods of estimation of equation 32 (Tobit and OLS methods) assumed that ( ̂ ) is negligible. It means that statistical inferences based on Tobit or OLS models are valid if and only if Equations 32 and 36 are equal. However, as showed in section 3.3.3 above, the bias is different from zero.

To overcome these problems, Simar and Wilson (2007) proposed a bootstrapping DEA to compute the efficiency scores in the first stage and a truncated regression (instead of Tobit and OLS) with a bootstrap technique in the second stage regression. In the first stage, a bias corrected efficiency scores are obtained by using a bootstrap method as discussed in section 3.3.3 above. Then, these bias-corrected efficiency scores are used as a dependent variable in the second stage regression. In the second stage, a bootstrapped truncated regression8 (with lower limit of zero and upper limit of one) is used instead of the usual Tobit regression.

Specifically, the following semi-log linear model is estimated to analyze the determinants of TE of farm households:

̂ ( )

Where ̂ refers to a bias corrected Shephard’s output oriented TE score for household i. ln is the natural logarithm, Z1 is a dummy variable for the sex of the household head, Z2 is the age of the household head, Z3 is education level of the household head, Z4 is the number of plots that the household cultivated during the production year, Z5 is the total household asset, Z6 is total household expenditure, Z7 is the amount of credit the household borrowed, Z8 is the distance between the home of the household and the nearest market, Z9 is dummy variable for extension services, and Z10 is a dummy variable for formal training (refer section 3.1.3 for detailed description of variables).

However, since the bootstrapping DEA is not applicable to compute AE, EE and SE scores in the first stage, the second stage estimation is slightly different from the equation 37. A truncated bootstrapping technique (with lower limit of zero and upper limit of one) is used to estimate the second stage of regression. Therefore, the following semi-log linear model is estimated to analyze the determinants of EE, AE and SE of farm households:

̂ ( )

8 According to Simar and Wilson, the single bootstrap is enough to get consistent estimates. However, they advised double bootstrap to improve statistical properties of the coefficient estimates.

9 Where ̂ ̂ bias-corrected EE score for household i (in EE modeling), original AE score for household i (in AE modeling), original SE score for household i (in SE modeling), and the other variables as defined in equation 37 above.

The software package “STATA” is used for the truncated bootstrap regression. Refer Simar and Wilson (2007) for detailed discussion on second stage regression.

9 The term “bias-corrected” is loosely used in the analysis of EE. In this case, bias-corrected EE refers to the product between bias-corrected TE and original AE.

4. Results

This section presents the results of the data analyses. It presents the farm and household level efficiency score estimates, efficiency differences among different groups of farm households and the determinants of production efficiency of farm households. 4.1 Farm level efficiency measures

Returns to scale tests

The test result for returns to scale showed that the production technology is characterized by VRS. At

farm level, the test static is ∑ 0.8842, which is the mean farm level scale efficiency

(see Table 3 below). Based on the bootstrapping result, the critical value at 5% significance level is 0.962.

Since is less than the critical value, the null hypothesis of CRS is rejected. Therefore, the production technologies at farm level exhibit VRS.

TE and SE Estimates

Following Simar and Wilson (2007), two types of TE scores are reported: original TE scores and a bias corrected TE scores as described in section three of 3.2.2. The bias corrected TE scores are lower than the original scores. The minimum original and bias-corrected TE scores are 14.98% and 12.85%, respectively; while the maximum original and bias-corrected scores are 100% and 90.73%, respectively. The results showed that firms that were fully efficient in terms of the original TE become inefficient when the bias is corrected. There is no farm that is fully efficient after the bias is corrected. The average original TE score is 71.74% while it is only 55.96% for the bias corrected. On average, farmers could raise the productions of the two outputs (proportionally) by about 44% without employing extra inputs if they operated in a technical efficient way. The 95% confidence interval of the mean TE score is between 55% and 70.99%. The mean bootstrap bias and variance estimates are 0.1578 and 0.054, respectively (see Table 3 below). Therefore, all farmers are not fully efficient in the production of crops and livestock technically.

The minimum original and bias-corrected SE scores are 19.8% and 42.27%, respectively; while the maximum original and bias-corrected scores are 100% and 223.77%, respectively. For few observations, the results for the bias-corrected SE estimates are strange (i.e., greater than 100%). This implies that for some farms, the bias-corrected TE scores under CRS are greater than the respective estimates under VRS). This could be due to bootstrapping related problems. As Tung (2013) demonstrated, for two reasons DEA based statistics instead of bootstrap based statistics has to be used for scale efficiency analysis. Firstly, the experimental work of Banker et al. (2010a) showed that DEA based procedures yield comparable results with bootstrap based procedures, and DEA based procedures outperform in large samples. Secondly, Tung (2013) argued that a high performance computer is required to perform both

bootstrap based estimation of returns to scale and double-bootstrapping DEA. As a result, it would be a big challenge for an average computer to perform a large number of calculations in bootstrapping.

In this study, the DEA based results are used for scale efficiency analysis for the above reasons. The average scale efficiency is 88.4% with a standard deviation of 14.22%. This implies that farm households could have further increased the productions of the two outputs by about 11.6% (on average) if they had reached an optimal scale without employing additional inputs. About 16 % (N=19) of the farms have optimal scale of operations (TE=1). However, 28.8% (N=34) of the farms operate under increasing returns to scale (IRTS) (are too small) while 55. 2% (N=65) of the farms operate under decreasing returns to scale (DRTS) (are too large)10.

AE and EE Estimates

The minimum and maximum AE scores of the farms are 13.9% and 100%, respectively with a standard deviation of 26.93%. The average allocative efficiency score of the farms is 60.37% which implies that farms are not fully efficient in the production of the two outputs given the market prices. Therefore, given the current levels of employment of inputs and the market prices of the outputs, firms could raise their revenue by about 39.6% if they produced an optimal combinations of the two products (i.e., if they operated in an allocatively efficient way). The average original economic efficiency (the product between original TE and original AE) is 48.74% while it is 36.34% for the bias-corrected (the product between bias-corrected TE and original AE). From economic efficiency points of view, firms could increase their revenue by about 63.66% if they operated optimally. The minimum original and bias- corrected EE scores of the farms are 2.08% and 1.79%, respectively; while the maximum original and bias-corrected scores are 100% and 86.76%, respectively. Refer Table 3 below for the full results.

Table 3: Mean farm level efficiency score estimates and bootstrapping results

Bootstrapping results for TE-VRS-95% EE AE SE TE -VRS CI

Bias Bias L. U. Original Original Original Original Bias Var. corr. Corr. bound bound Mean 0.4874 0.3634 0.6037 0.8842 0.7174 0.5596 0.1578 0.0535 0.5452 0.7099 Min 0.0208 0.0179 0.1390 0.1980 0.1498 0.1285 0.0213 0.0001 0.1218 0.1480 Max 1.0000 0.8676 1.0000 1.0000 1.0000 0.9073 0.7013 0.6614 0.8518 0.9959 SD 0.3351 0.2409 0.2693 0.1422 0.2491 0.1983 0.1693 0.1497 0.1721 0.2467

10 The DEAP software package is used to determine the scale of operation.

4.2 Household level efficiency measures

Returns to scale tests

The test result for returns to scale showed that the production technology is characterized by VRS. At

household level, the test static is ∑ 0.8896, which is the mean household scale

efficiency (see Table 4 below). Based on the bootstrapping result, the critical value at 5% significance

level is 0.9682. Therefore, since is less than the critical value, the null hypothesis of CRS is rejected. This implies that the production technology at household level exhibits VRS.

TE and SE Estimates

At household level also the bias corrected TE scores are lower than the respective original scores. There is no fully efficient farm when the bias is corrected. The minimum original and bias-corrected TE scores are 25.41% and 22.81%, respectively; while the maximum original and bias-corrected scores are 100% and 92.96%, respectively. The average original and bias-corrected TE (VRS) scores are 74.77% and 60.4%, respectively. If households were fully efficient (technically), they could raise the productions of the three outputs (proportionally) by about 39.6% without extra employment of resources. The 95% confidence interval of the mean TE (VRS) score is between 57.22% and 74.24%. The mean bootstrap bias and variance (sigma) estimates are 0.1437 and 0.0513, respectively (see Table 4 below).

The minimum and maximum SE scores of the farms are 22.16% and 100%, respectively with a standard deviation of 13.62%. The average scale efficiency is 88.96% (refer Table 4 below). This implies that farm households could have further increased the productions of the three outputs by about 11% (on average) if they had reached an optimal scale without employing additional inputs. About 20.3 % (N=24) of the farms are technically efficient (TE=1). However, 31.4% (N=37) of the farms operate under increasing returns to scale (IRTS) while 48.3% (N=57) of the farms operate under decreasing returns to scale (DRTS).

Table 4: Mean household level efficiency score estimates and bootstrapping results

Bootstrapping results for TE-VRS-95 % EE AE SE TE -VRS CI

Bias Bias L. U. Original Original Original Original Bias Var. corr. Corr. bound bound Mean 0.4882 0.3762 0.5825 0.8896 0.7477 0.6040 0.1437 0.0513 0.5722 0.7424 Min 0.0509 0.0457 0.1448 0.2216 0.2541 0.2281 0.0229 0.0001 0.2118 0.2529 Max 1.0000 0.8629 1.0000 1.0000 1.0000 0.9296 0.5963 0.4706 0.8756 0.9972 SD 0.3328 0.2410 0.2750 0.1362 0.2458 0.2003 0.1570 0.1253 0.1710 0.2440

AE and EE Estimates

The minimum and maximum AE scores of the farms are 14.48% and 100%, respectively with a standard deviation of 27.5%. The average allocative efficiency score of the farms is 58.25% which implies that farms are not fully efficient in the production of the three outputs given the market prices. If households were fully allocatively efficient, they could raise their revenue by about 41.75% given the current levels of employment of resources and market prices of outputs. The average original economic efficiency (the product between original TE and original AE) is 48.82% while it is 37.62% for the bias-corrected (the product between bias-corrected TE and original AE). The minimum original and bias-corrected EE scores of the farms are 5.09% and 4.57%, respectively; while the maximum original and bias-corrected scores are 100% and 86.29%, respectively. Refer Table 4 above for the full results.

4.3 Efficiency differences between different groups

This section presents the efficiency differences among different groups/categories of respondents. The respondents are categorized into two groups on the bases of sex of household head, intensity of labor usage per hectare of land and size of farm.

Male versus female headed households

Out of 118 households used in this study, about 84% (N= 99) of the respondents are male headed households while the remaining 16% (N= 19) are female headed. The mean household level efficiency score estimates (relative to their own group frontier and the common frontier) of the two groups are presented below in Table 5.

Table 5: Mean household level efficiency score estimates for male vs female headed households

Relative to own group frontier EE SE TE-VRS Bootstrapping results for TE-VRS-95 % AE CI Bias Original Bias L. U. Original Original Bias Var. Corr. Original Corr. bound bound Males 0.5109 0.4071 0.5987 0.9109 0.7741 0.6399 0.1342 0.0437 0.5979 0.7690 Females 0.7843 0.6704 0.8229 0.7612 0.9247 0.7933 0.1314 0.0183 0.7079 0.9198 Relative to the common frontier (male & female farmers together) Males 0.5010 0.3920 0.5943 0.9010 0.7591 0.6182 0.1409 0.0483 0.5818 0.7539 Females 0.4216 0.2940 0.5210 0.8306 0.6880 0.5300 0.1580 0.0665 0.5223 0.6825

Based on own group frontiers, on average, female headed households are by far more efficient than male headed households (except in SE). The bias-corrected EE, AE and TE (VRS) estimates are 67.04%, 82.3% and 79.33%, respectively, for female headed households; while for male headed respondents, the corresponding efficiency scores are 40.71%, 59.9% and 64%, respectively. If they were fully technically

efficient, male headed households could increase the production of the three outputs (proportionally) by about 36% while female headed households could increase only by about 21%.

However, based on the common frontier, male headed households are more efficient than the female headed households. The bias-corrected EE, AE and TE (VRS) estimates are 39.2%, 59.4% and 61.8%, respectively, for male headed households; while for female headed respondents, the corresponding efficiency scores are 29.4%, 52.1% and 53%, respectively (refer Table 5 above). If they were fully technically efficient, female headed households could increase the production of the three outputs (proportionally) by about 47% while male headed households could increase only by about 38%.

These imply that the frontier of male headed households lie above the female headed households, and the overall frontier lies above male’s frontier.

Labor intensive versus less intensive

In this section, the effect of labor intensity per hectare of land on efficiency estimates is presented. The respondents are categorized into two groups: labor intensive and less labor intensive. The labor intensive households are households who employed more than 400 labors per hectare of land in man days11. This group accounts 28.8% (N= 34) of the total respondents. On the other hand, households who employed less than 400 labor (in man days) per hectare of land are considered as less labor intensive, and accounts 71.2% (N= 84) of the respondents. The efficiency score estimates for the two groups are presented below in Table 6 based on their own group frontier and the common frontier.

Table 6: Mean household level efficiency score estimates for labor intensive vs less intensive farms

Based on own group frontier EE AE SE TE-VRS Bootstrapping results for TE-VRS-95 % CI Bias Original Original Bias Original Original Bias Var. L. bound U. bound Corr. Corr. Labor 0.7658 0.6968 0.7941 0.9171 0.9293 0.8480 0.0812 0.4519 0.7439 0.9278 Intensive Less 0.4992 0.3776 0.5881 0.9030 0.7708 0.6101 0.1608 0.0371 0.5843 0.7633 Intensive Based on the common frontier (all farms together) Labor Intensive 0.6236 0.4606 0.6792 0.9440 0.8608 0.6578 0.2030 0.0777 0.6273 0.8545 Less 0.4401 0.3429 0.5487 0.8672 0.7054 0.5803 0.1251 0.0453 0.5504 0.7006 Intensive

In both cases (based on their own group frontier and the common frontier), on average, labor intensive households are by far more efficient than the less intensive farm households. The difference in efficiency between the two groups is very large especially in economic and allocative efficiencies. For example, based on their own group frontier, the EE, AE and TE (VRS) estimates are 69.68%, 79.41% and 84.8%, respectively, for labor intensive households. However, for less intensive respondents, the

11 The benchmark (400 man days) for categorizing households into two groups is arbitrary.

corresponding efficiency scores are 37.76%, 58.81% and 61.01%, respectively (refer Table 6 above for the full results). If they were fully technically efficient, less intensive farms could increase the production of the three outputs (proportionally) by about 39% while labor intensive farms could increase only by about 15%. Based on own frontier, the frontier of less labor intensive farms lies above the corresponding labor intensive farms. However, based on the common frontier, the frontier of labor intensive farms lies above the less intensive farms’ frontier, and the common frontier lies above the labor intensive farms’ frontier.

Small versus large size farms

The households are categorized into two groups: small versus large farms, on the basis of the size of their land. The terms (small and large farms) are relative since all the farms are small in absolute terms. Accordingly, households with less than a hectare of land are considered as small farms, and households with more than or equal to a hectare of land are considered as large farms (provided that the average land size is 0.815 ha). Small farms account 66% (N= 78) while large farms account 34% (N=40) of the total households. The efficiency score estimates for the two groups are presented below in Table 7 (relative to their own group frontier and the common frontier).

Table 7: Mean household level efficiency score estimates for small vs large farms

Relative to own frontier EE SE TE-VRS Bootstrapping results for TE-VRS-95 % AE CI Bias L. U. Original Original Original Bias Corr. Bias Var. Corr. Original bound bound Small Farms 0.5609 0.4547 0.6221 0.9148 0.8311 0.6944 0.1367 0.0396 0.6364 0.8268 Large Farms 0.6964 0.5801 0.7588 0.8313 0.8549 0.7244 0.1304 0.0604 0.6566 0.8512 Relative to the common frontier (Small & large farms together) Small Farms 0.5166 0.3796 0.5920 0.9038 0.7874 0.6144 0.1730 0.0709 0.5906 0.7817 Large Farms 0.4328 0.3696 0.5640 0.8620 0.6703 0.5837 0.0865 0.0129 0.5364 0.6659

Based on own group frontier, large farms are more efficient than small farms (except in SE). However, based on the common frontier, small farms are slightly efficient than large farms (refer Table 7 above for the results). These imply that the frontier of small farms lies above the large farms’ frontier, and the overall frontier lies above small farms’ frontier. For example, given the current levels of employment of inputs and market prices of outputs and if farms were fully allocatively efficient, small farms could increase their revenue by about 38% while large farms could increase by only about 24% (based on own frontier). However, based on the common frontier, large farms could increase by about 44% and small farms by about 41%.

4.4 Second stage regression analyses of determinants of efficiency

The results of the second stage regression analyses of the determinants of farm households’ production efficiency (as formulated in Equations (37 and 38)) are presented in the following sections.

4.4.1 Determinants of technical efficiency

The truncated bootstrapped two stage regression (double bootstrapping) result for TE is presented as follow in Table 8 with the observed and bias corrected coefficients. The number of plots; total household asset; total household expenditure; distance between the home of the household and the nearest market; and extension services are statistically significant determinants of farm household TE (all positively). However, the explanatory variables like sex, age and education level of the household head, the amount of credit the household borrowed and formal training become statistically insignificant in affecting TE of farm households. Other things being equal, a one more unit of extension service leads to a 1.1% increase in TE of a household. TE also increases with the increase in the number of plots that the household cultivated, other things being constant. This could be due to the shortage of land to efficiently utilize other resources.

Table 8: Truncated bootstrapped two-stage regression (Dependent variable: Bias-corr. TE)

Bias-Corr. Bootstrap Bias-corr. TE= ̂ z p>|z| Bias-Corr. [95% CI] Coef. SE Sex 0.0711 0.0620 1.1300 0.2600 -0.0584 0.1946 ln(age) 0.0256 0.0658 0.4800 0.6290 -0.1065 0.1555 Education -0.0070 0.0061 -1.1400 0.2540 -0.0170 0.0060 ln(number of plots) 0.1101 0.0371 3.0100 0.0030 0.0485 0.2015 ln(total household asset) 0.0482 0.0240 2.0000 0.0460 0.0096 0.0920 ln(total household expenditure) 0.0800 0.0405 2.0400 0.0410 0.0092 0.1742 Credit 0.0000 0.0000 0.9000 0.3690 0.0000 0.0001 ln(distance) 0.0588 0.0227 2.6900 0.0070 0.0194 0.1026 Extension service 0.0111 0.0065 1.8000 0.0710 0.0016 0.0264 Formal training -0.0297 0.0444 -0.8300 0.4080 -0.1435 0.0479 Constant -1.2388 0.3804 -3.4100 0.0010 -1.9828 -0.5343 SD 0.1793 0.0107 16.0000 0.0000 0.1598 0.1814 Wald chi2(7)= 78.73, Prob>chi2=0.0000. Log likelihood= 49.217479

A 1% increase in total household asset and expenditure lead to a 0.048% and 0.08% increase in the TE, respectively, other things being constant. The increment in household expenditure could motivate households to utilize resource efficiently. A 1% increment in the distance between the home of the household and the nearest market leads to a 0.06% increase in TE, other things being equal (refer Table 8 above for the full results).

4.4.2 Determinants of economic efficiency

Out of the ten explanatory variables, only total household expenditure, and distance between home and market are statistically significant determinants of EE of farm households (refer Table 9 below). EE of farm households is positively related with total household expenditure, and distance between home and market. Other things being constant, a 1% increase in total household expenditure increases EE of households by about 0.339%. A 1% increment in the distance between the home of the household and the nearest market leads to a 0.066% increase in EE, other things being equal.

Table 9: Truncated bootstrapped two-stage regression (Dependent variable: Bias Corr. EE)

Bias-Corr. Bootstrap Bias-corr. EE= ̂ z p>|z| Bias-Corr. [95% CI] Coef. SE Sex 0.0890 0.0974 0.9900 0.3240 -0.0687 0.3040 ln(age) -0.0142 0.1271 0.0900 0.9310 -0.2831 0.2273 Education -0.0115 0.0110 -0.9900 0.3230 -0.0382 0.0071 ln(number of plots) 0.0827 0.0555 1.6100 0.1080 -0.0028 0.2076 ln(total household asset) 0.0595 0.0455 1.1000 0.2700 -0.0369 0.1450 ln(total household expenditure) 0.3392 0.0838 3.9300 0.0000 0.1505 0.5014 Credit 0.0000 0.0001 0.4400 0.6570 -0.0001 0.0001 ln(distance) 0.0662 0.0335 1.9900 0.0460 0.0156 0.1667 Extension service 0.0071 0.0094 0.9200 0.3590 -0.0026 0.0340 Formal training 0.0438 0.0733 0.2900 0.7700 -0.1323 0.1658 Constant -3.8759 0.7067 -5.3600 0.0000 -5.0619 -2.4904 SD 0.2642 0.0238 10.3400 0.0000 0.2154 0.3089 Wald chi2(10)= 57.89, Prob>chi2=0.0000. Log likelihood= 42.487223

4.4.3 Determinants of allocative efficiency

Total household asset and expenditure, and education level of the household head are the statistically significant determinants of allocative efficiency of households. Other things being constant, a 1% increase in total household asset and expenditure increases AE of households by about 0.0624% and 0.114%, respectively. Surprisingly, a 1 year increment in the education level of the household head results in a 1.3% decrement in the AE of the households, ceteris paribus (refer Table 10 below for the full results).

Table 10: Truncated bootstrapped two-stage regression (Dependent variable: Original AE)

Bias-Corr. Bootstrap Original AE= ̂ z p>|z| Bias-Corr. [95% CI] Coef. SE Sex 0.0462 0.0816 0.5600 0.5760 -0.0950 0.2252 ln(age) 0.0359 0.0687 0.4700 0.6370 -0.0957 0.1649 Education -0.0130 0.0073 -1.850 0.0650 -0.0309 -0.0014 ln(number of plots) 0.0409 0.0413 1.1900 0.2360 -0.0833 0.1062 ln(total household asset) 0.0624 0.0362 1.7800 0.0750 0.0032 0.1385 ln(total household expenditure) 0.1137 0.0475 2.3300 0.0200 0.0249 0.2098 Credit 0.0000 0.0000 0.9000 0.3670 -0.0001 0.0001 ln(distance) 0.0059 0.0213 0.2100 0.8310 -0.0377 0.0403 Extension service 0.0069 0.0070 1.2000 0.2300 -0.0072 0.0204 Formal training 0.0717 0.0483 1.4000 0.1630 -0.0224 0.1848 Constant -1.4715 0.3597 -4.050 0.0000 -2.2578 -0.7640 SD 0.1769 0.0189 9.0100 0.0000 0.1394 0.2406 Wald chi2(10)= 73.77, Prob>chi2=0.0000. Log likelihood= 39.665407

4.4.4 Determinants of scale efficiency

The result of the truncated bootstrap regression for SE is given below in Table 11. The Wald chi-square test shows that the explanatory variables (all together) are statistically significant in explaining the variation in SE of households at 10% significance level (overall significance). However, only the age of the household head and the number of plots are statistically significant determinants of the SE of households at 10% significance level. Other things being equal, a 1% increase in the age of the household head leads to a 0.412% increase in SE; whereas a 1% increase in the number of plots results in a 0.597% decrease in SE (in bias-corrected terms). The increase in SE of households following age increment of the household head could be due to experience (learning by doing) effect. However, the fragmented nature of land reduces the achievement of optimal scale of operation.

Table 11: Truncated bootstrapped two-stage regression (Dependent variable: Original SE)

Bias-Corr. Bootstrap Original SE= ̂ z p>|z| Bias-Corr. [95% CI] Coef. SE Sex 0.2044 0.1773 0.9500 0.3440 -0.0253 0.5400 ln(age) 0.4117 0.1800 1.9000 0.0570 0.0795 0.8334 Education 0.0064 0.0248 0.2200 0.8290 -0.0353 0.0599 ln(number of plots) -0.5973 0.2561 -1.840 0.0650 -1.2872 -0.2143 ln(total household asset) 0.2672 0.1700 1.0800 0.2800 -0.1140 0.6401 ln(total household expenditure) 0.0000 0.0000 -0.400 0.6870 -0.0001 0.0000 Credit 0.0000 0.0002 0.0300 0.9770 -0.0004 0.0006 ln(distance) 0.1503 0.1062 1.1100 0.2650 -0.0102 0.5809 Extension service 0.0250 0.0239 0.7400 0.4590 -0.0244 0.0618 Formal training 0.3120 0.2486 1.0400 0.3000 -0.0216 1.4121 Constant -2.7916 1.5325 -1.210 0.2250 -6.7192 0.0325 SD 0.3659 0.0639 4.6100 0.0000 0.2283 0.5029 Wald chi2(10)= 17.77, Prob>chi2=0.0590. Log likelihood= 102.18791.

Based on the type of returns to scale that farms exhibit, the determinants of SE can also be analysed for “too small farms (farms exhibiting increasing returns to scale (IRS))” and “too large farms (farms exhibiting decreasing returns to scale (DRS))”. The results of the bootstrapped two stage regression are given below in Tables 12 and 13. As shown in table 12, total household asset and expenditure, and the distance between home and the nearest market are statistically significant determinants of the SE of “too small farms”. Other beings being constant, for “too small farms” a 1 % increase in the total household asset and expenditure, and the distance between home and the nearest market leads to a 0.33%, 0.275 % and 0.276 % increase in SE of households, respectively.

Table 12: Truncated bootstrapped two-stage regression (Dependent variable: Original SE-IRS)

Bias-Corr. Bootstrap Original SE-IRS z p>|z| Bias-Corr. [95% CI] Coef. SE Sex 0.2135 0.1353 1.1800 0.2400 0.0446 0.8809 ln(age) -0.1473 0.1356 -0.6200 0.5350 -0.4228 0.1023 Education 0.0079 0.0692 0.0900 0.9320 -0.1155 0.1483 ln(number of plots) 0.1158 0.1421 1.1400 0.2560 -0.0809 0.4550 ln(total household asset) 0.3311 0.1042 2.6200 0.0090 0.0271 0.3460 ln(total household expenditure) 0.2750 0.1246 2.1300 0.0330 0.1134 0.6922 ln(distance) 0.2764 0.0728 3.0700 0.0020 0.1494 0.5368 Extension service 0.0572 0.0597 1.0000 0.3200 -0.0532 0.1879 Formal training -0.0711 0.5424 -0.3200 0.7480 -1.0499 1.3006 Constant -5.7036 1.9770 -2.5800 0.0100 -10.9064 -1.8531 SD 0.1246 0.0212 4.6300 0.0000 0.0890 0.1572 Wald chi2(9)= 23.87, Prob>chi2=0.0045. Log likelihood= 66.72.

For “too large farms”, only the age of the household head is statistically significant determinant of SE of households. A 1% increase in the age of the household head results in a 0.493 % increase in SE, ceteris paribus (see Table 13 below).

Table 13: Truncated bootstrapped two-stage regression (Dependent variable: Original SE-DRS)

Bias-Corr. Bootstrap Original SE-DRS z p>|z| Bias-Corr. [95% CI] Coef. SE Sex 0.0922 0.1855 0.1400 0.8860 -0.1258 0.3020 ln(age) 0.4929 0.1725 2.3700 0.0180 0.2118 1.0441 Education 0.0069 0.0156 0.3600 0.7210 -0.0193 0.0393 ln(number of plots) -0.1947 0.1490 -1.230 0.2180 -0.6109 0.0224 ln(total household asset) -0.1752 0.1035 -1.140 0.2540 -0.3684 0.0069 ln(total household expenditure) 0.1134 0.0919 0.9600 0.3380 -0.0700 0.2413 Credit 0.0000 0.0001 0.1600 0.8700 -0.0002 0.0002 ln(distance) 0.0489 0.0808 0.3800 0.7020 -0.0976 0.2377 Extension service 0.0205 0.0195 0.6800 0.4960 -0.0085 0.0681 Formal training 0.0592 0.1385 0.4700 0.6410 -0.2103 0.3513 SD 0.2521 0.0507 4.0000 0.0000 0.1366 0.3132 Wald chi2(9)= 145.89, Prob>chi2=0.0000. Log likelihood= 61.95.

5. Discussions, Conclusions and Policy Implications

5.1 Discussions

The number of studies that analyzed production efficiency at household level and/or that used the bootstrapping DEA method of Simar and Wilson (2007) are very limited. Although there are no directly comparable studies, this section discusses the results of this study in line with other related studies.

Hassen et al. (2012) conducted a farm level production efficiency analysis in the same region (in Dessie Zuria and Kutaber districts) using a stochastic frontier analysis. The mean EE, AE and TE scores they found were 28.9%, 50.94% and 61.61%, respectively. However, the corresponding scores of this study are 36.34%, 60.4% and 55.96%, respectively. Although the results are not directly comparable since the data and the methods employed by the two studies are different, the results of economic and allocative efficiencies of households are relatively higher in this study. However, in terms of technical efficiency, the results of Hassen et al. (2012) are higher. Although the results are different to some extent, both studies imply that households are inefficient in terms of all measures of efficiency.

Another farm level study by Mussa et al. (2012) analyzed households’ crops production efficiency in the Central Highlands of Ethiopia. Using a DEA method, their estimated original EE, AE and TE scores were 50%, 68% and 74%, respectively. In this study, the original EE, AE and TE scores are 48.7%, 60.4% and 71.7%, respectively Although the study by Mussa et al. (2012) did not account livestock productions, which are equally important in a crop-livestock mixed agricultural system of the region, the results are comparable with this study (without accounting biasedness). The results of Mussa et al. (2012) are also misleading since they are not corrected for biasedness.

A study by Chavas et al. (2005) conducted a household level production efficiency analysis in Gambia. The original AE and TE scores they found were 56.7% and 95.2%, respectively. They concluded that the farm level and household level measures resulted in comparable results for TE, while farm level AE is by far higher than household level AE. Unlike their result, in this study, the household level TE scores are higher than farm level TE scores. The average bias corrected TE score at household level is higher by about 4.5%. In this study, the farm level average allocative efficiency score is higher by about 2% compared to the household level score. According to Chavas et al. (2005), this implies that farmers are allocatively inefficient in the allocation of labor between farm and off-farm activities due to labor market imperfections and other household related factors. However, the economic efficiency scores at household level are comparable with the corresponding scores at farm level. Still, the efficiency estimates of Chavas et al. (2005) were not corrected for biasedness.

The efficiency differentials between male headed and female headed households were analysed. The results showed that female headed households are more efficient than the corresponding male headed households based on their own group frontier. However, male headed households are more efficient than female headed households based on the common frontier. This gender differential in efficiency is also tested statistically in the second stage regression analysis of determinants of efficiency scores

(based on the common frontier approach). Like most studies as indicated by Quisumbing (1996), the result showed that the gender of the household head is not statistically significant determinant of production efficiency; hence, females are equally efficient with males. Quisumbing (1996) summarized most of the studies that analysed differences in technical efficiency between male and female farmers found that the dummies for sex of farm manager or household head were not statistically different from zero. In other words, female headed households are equally efficient with male headed households, provided that individual characteristics and input levels are constant. However, the study by Mussa et al. (2012) found that females are more economically efficient than males in the productions of crops in the Central Highlands of Ethiopia. On the other hand, the study by Udry (1996) found a weakly significant negative dummy for female which implies that females are less efficient. According to him, this implies that gender differences may lead to allocative efficiencies within the household. However, the studies are criticised from methodological points of view (refer Quisumbing (1996) for detail). The result that females are more efficient than males based on own group frontier imply the need for empirical works to check the differences in production technologies of males and females.

The impact of the intensity of labor per hectare of land on production efficiency is analyzed. The result showed that labor intensive households are more efficient than less intensive households. This could be due to the seasonal shortage of labor in farm production to efficiently utilize other resources and lack of employment of modern technologies that substitute farm labor. Like in the other parts of Ethiopia, the labor demand is very high compared to its supply during the cultivation, weeding and harvesting seasons in Dessie Zuria districts. However, farm labors are unemployed throughout the rest of the seasons.

Based on the size of land, large farms are more efficient than small farms relative to own group frontier; whereas small farms are slightly efficient than large farms based on the common frontier. There are different studies that analyzed the impact of farm size on production efficiency of farms (based on the common frontier approach). Most of the studies support the argument that larger farms are more technically efficient than smaller ones due to being able to use specialized management resources. Padilla-Fernandez and Nuthall (2012) analyzed the effect of farm size on the productive efficiency of sugar cane farms in Central Negros in The Philippines. By using a non-parametric DEA technique, they concluded that small farms are not as economically efficient as the larger ones while medium and large farm groups appear to be equally economically efficient. A comparative study of productive efficiency among Kansas small and large crop farms by Lall et al. (2001) indicated that, on average, small farms are 25% less efficient than large farms.

Although most studies indicated that large farms are more efficient than small farms, there are also studies supporting the other way round. For example, a study by Lerman and Sutton (2006) on the comparative analysis of the productivity of small and large farms in Moldova based on a cross-section data by using Stochastic Frontier and Data Envelopment Analyses algorithms showed that small individual farms are more productive and more efficient than large corporate farms. On the other hand, some others argue that it is not totally fair to compare small and large farms since their production technology may completely be different. Therefore, an empirical work is needed to check as the production sets of the two groups are different. The difference in the results of the two approaches (based on own frontier and common frontier) imply the need for empirical works.

The truncated bootstrapped second stage regression showed that farm households’ production efficiency are significantly affected by number of plots, total household asset, total household expenditure, distance between the home of the household and the nearest market, and extension services. However, age (except in AE), sex and education level of the household head, formal training and credit are not statistically significant determinants of efficiency. Previous studies used the Tobit model in the second stage analysis of determinants of efficiency. As Simar and Wilson (2007) demonstrated inferences based on such studies are invalid and misleading. However, for the purpose of comparisons, the results of some of these studies are presented. Like the result of this study, Hassen et al. (2012) found that age and education level of the household head are not statistically significant in explaining farm households’ production efficiency in North Eastern Highlands of Ethiopia. Mussa et al. (2012) showed that livestock ownerships and off-farm income are among the important determinants of efficiency in the Central Highlands of Ethiopia. Moreover, a study by Makombe et al. (2011) found that age, sex and education level of the household head are not statistically significant determinants of efficiency of rain-fed agriculture in Ethiopia. Generally, most of the previous studies (Hassen et al. 2012; Mussa et al., 2012; Makombe et al. 2011) concluded that livestock ownerships, land size and off-farm income are important determinants of households’ production efficiency in Ethiopia. Unlike such studies, this study included livestock ownerships, land size and off-farm income in the input-output variables of estimating the efficiency scores. Since these variables are not external factors, the inclusion of them in the second stage regression is misleading. 5.2 Conclusions

Farm level and household level efficiency scores were estimated using an empirical data from 118 farm households from Dessie Zuria district, Ethiopia. For the farm level analyses, four inputs (land, farm labor, oxen days and other input costs) and two outputs (crop and livestock- in indices) were used for estimating the efficiency scores using an output oriented bootstrapping DEA method. For household level analyses, off-farm labor were added to farm labor and off-farm income was included as a third output while the others are the same with farm level inputs and outputs.

At farm level, the mean original and bias-corrected TE scores are 71.7% and 55.9%, respectively. At household level the corresponding efficiency scores are 74.8% and 60.4 %, respectively. Unlike in the original TE measures where some farms are fully efficient (TE=1), in the bias-corrected TE measures, no one is fully efficient. This implies that there exist opportunities to raise all farmers’ outputs by about 44% without the employment of additional inputs. The household level TE scores are higher than the respective farm level scores, for example, by about 4.5 % in the bias corrected case. Therefore, parts of technical inefficiencies that farm focused previous studies reported are attributed to methodological issues.

The mean farm level and household level bias-corrected EE (the product between bias-corrected TE and original AE) scores are 36.3% and 37.6%, respectively. The corresponding mean original AE scores are 60.4% and 58.3%, respectively. Given the current levels of employment of resources and market prices of outputs, farmers could raise their revenue by about 41.7% if they produced the optimal combinations

35 of the three products; i.e., if they operated in an allocatively efficient way. Although not significant, the farm level average AE is higher than the household level score by about 2%.

The SE scores were also estimated at farm and household levels. The mean household level SE efficiency score 88.9% imply that farm households could have further increased their output by about 11% if they had reached an optimal scale without employing additional inputs. Although the mean SE scores are almost the same in both cases (88.4% at farm level and 88.9% at household level), there is a difference in the types of returns to scale that firms operate. At farm level, about 16 % (N=19) of the farms operate optimally (TE=1) while 20.3 % (N=24) of the farms are technically efficient (TE=1) at household level. At farm level, 28.8% (N=34) of the farms operate under increasing returns to scale (IRTS) (are too small) while 55. 2% (N=65) of the farms operate under decreasing returns to scale (DRTS) (are too large). However, at household level, 31.4% (N=37) of the farms operate under increasing returns to scale (IRTS) while 48.3% (N=57) of the farms operate under decreasing returns to scale (DRTS).

The difference in production efficiency between different groups of farm households (male vs female headed households, labor intensive vs less intensive farms, and small vs large farms) is analyzed. The results showed that female headed households are more efficient than the corresponding male headed households based on their own group frontier. However, male headed households are more efficient than female headed households based on the common frontier. Labor intensive households are also more efficient than less intensive households (based on both the own frontier and the common frontier). Based on the size of land, large farms are more efficient than small farms relative to own group frontier; whereas small farms are slightly efficient than large farms based on the common frontier.

The truncated bootstrapped second stage regression showed that the EE of farm households is significantly affected by total household expenditure, and distance between home and the nearest market. The number of plots; total household asset; total household expenditure; distance between the home of the household and the nearest market; and extension services are statistically significant determinants of farm households’ TE (all positively). The allocative efficiency of farm households in the region is affected by total household asset and expenditure (positively), and education level of the household head (negatively). The age of the household head (positively) and numbers of plots (negatively) are statistically significant determinants of the SE of households. However, when scale efficiency is decomposed into IRS and DRS, total household asset, total household expenditure, and the distance between home and the nearest market are statistically significant determinants of the SE of households whose production technology is characterized by IRS. For “too large farms”, only the age of the household head is statistically significant determinant of SE of households (positively). 5.3 Policy implications

The following policy implications can be made based on the results of the analyses.

Since household level production efficiency scores are greater than the corresponding farm level measures (with the exception of AE), creation of off-farm employment opportunities could improve

36 households’ efficiency in the region. The result showed that credit is not a statistically significant determinant of production efficiency. This could be due to the fact that off-farm income plays an important role in solving financial constraints of households.

The EE of households is very low (with a mean of about 37%). The EE of households could be increased by 63% without extra employment of inputs at the current level of prices of outputs. However, the achievement of this requires improvement in TE and AE of households. Total household asset and expenditure are important determinants of TE and AE. In other words, farm households’ efficiency is directly related with households’ resources. Rich farmers have better access to capital to purchase fertilizer and veterinary medicines, and adopt modern breeds compared to poor farmers. Moreover, rich farmers have better access to manure from their livestock ownerships. These factors imply that wealth is one of the determinants of smallholders’ production efficiency. This suggests that programs that enhance availability of farm resources could improve production efficiency.

The group wise efficiency analyses showed that labor intensive farmers are more efficient than the corresponding less intensive farmers. These results could be due to the fact that off-farm activities withdraw labor out of farm activities and therefore dampen land productivity (Wang et al., 2011) of the less-labor intensive farms. If the negative effect of labor withdraw from farm activity outweigh the farm improvement effect brought by off-farm income, the overall household production efficiency will become low. However, further empirical (experimental) work is needed to investigate whether the effect of off-farm activity outweighs its negative impact on farm productivity for households with less labor force availability.

Although the sex of the household head is not a statistically significant determinant of farm households’ production efficiency (based on the common frontier), female headed households are by far more efficient than the corresponding male headed households relative to their own frontier. Given the fact that female headed households are poorer than male headed households, females might become more efficient relative to the common frontier than males if they owned the same resources as males. However, further empirical work is needed to check whether the production technologies of the two groups are statistically different or not.

TE of households is positively affected by extension services. It implies that consultancy (extension) services of development agents contribute to the improvement in TE of farmers. Therefore, there is a need to strengthen extension services.

The results showed that households’ EE and TE are positively affected by the distance between the home of the household and the nearest market. This could be due to the fact that the households are subsistence producers (produce only for home consumption), or the market is functioning perfectly in areas far from the market center. Therefore, an empirical work is needed to investigate the linkage between farm production and market access in the region.

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