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The Poor But Efficient Hypothesis Economics Essay

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In Chapter one we set in motion the purpose for this research and explain to the reader the essence of quantifying the amount the household is willing to pay for abating malaria both in the present and in the future. In this chapter we go a step further by reviewing literature in this area. This chapter is important because it provides the reader with a sort of 'history' into this area of research. It also gives the reader an opportunity to understand where our research stands vis-à-vis other researches in this area. Obtaining a value for the marginal effect of malaria on farmers' technical efficiency is one of the 'live wires' on which precise estimates for our Willingness-To-Pay depend. We therefore want to start by reviewing literature in the area of efficiency measurement; afterwards, we will research into literature in the area of Willingness - To - Pay.

Before we go ahead we highlight the purpose of measuring technical efficiency to the reader.

Technical efficiency primarily enables one to understand the relationship between input used and the output (total harvested crop). It also enables us to measure the performance of individual farms in an industry as well as provide an index for the average performance of the overall industry. This then leads us to propose policy recommendations that could help shift the production frontier- the maximum attainable harvest from each input- of the farm closer to the industry frontier at the prevailing technology. As we progress in this research the reader will further appreciate this concept and the reason why it is one of the most talked about concepts in development/resource economics.

At the moment, our aim is to examine some literature that relates to our area of research. We therefore start Section 2.1 by reviewing literature relating to the "poor but efficient" hypothesis of Schultz (1964). Section 2.2 reviews some agriculture-based literature on efficiency and health. In doing this we divide the study on inefficiency into two; the Frequentist (Section 2.2.1) and the Bayesian (Section 2.2.2) studies. Using another method of classification, we classify the study of efficiency into single output studies (Section 2.2.3) and multiple output studies (Section 2.2.4). This puts us in good standing to review literature on Willingness-To-Pay in Section 2.4.

Productivity/Efficiency Studies in Agriculture

The "Poor but Efficient" Hypothesis

The huge volume of research on efficiency in agriculture draws motivation from Schultz (1964) book "Transforming Traditional Agriculture". In the book he explains why rural farmers are efficient in the management and allocation of resources. He advances a hypothesis popularly called the "poor but efficient" hypothesis. Researchers try to verify this hypothesis quantitatively; in doing this, a lot of issues come to the fore, part of which is; the best way to measure productivity. Before the advent of the deterministic measure of productivity pioneered by Aigner and Chu (1968), and, Afriat (1972) researchers attempt to measure efficiency. Of great importance to us in this area are the works of Welsch (1965), Chennareddy (1967) and Lipton (1968) because they specifically test the validity of Schultz's 'poor but efficient' hypothesis.

Chennareddy (1967) utilizes the linear regression analysis on a data of one hundred and four rice and tobacco farmers in South India using a Cobb-Douglas production function. His findings were in accord with Schultz hypothesis. He recommends that South Indian farmers should adopt modern technology and extension education in order to move to a higher frontier. Lipton (1986) [1] disagrees with this recommendation. He argues that if Schultz's findings are correct then the rural farmers do not need any expert advice to improve their productivity in other words moving to a higher frontier should not be a problem for them. He further queries Schultz's assertion believing that it only works under a neo-classical theory of perfect competition; he affirms that if Schultz uses linear programming to analyse his data his findings would show that the rural farmer is inefficient.

Welsch (1965) in his study on Abakaliki rice in Eastern Nigeria makes use of the linear regression to affirm that peasant farmers respond to economic inducement by allocating efficiently among several resources at their disposal. Hence, he supports Schultz's hypothesis. One thing we want the reader to note in the above groups of literature is; the writers who concur with Schultz's assertion use parametric techniques to arrive at their conclusion while Lipton (1968) employs a non-parametric linear programming technique that assumes at least one factor is not fully employed.

Just as the argument is about to cease, Sauer and Mendoza-Escalante (2007) involve themselves in it. Their work serves to reconcile these diametrically opposing schools of thought. It puts to use a parametric normalized generalized Leontief (GL) profit function technique to analyse joint production of Cassava flour and maize by small-scale farmers in Brazil. The small-scale farmers are allocatively efficient, they assert, but they show considerable inefficiency in the scale of operation. At this juncture, we remind the reader that our digression is intentional. Our aim is to show how Schultz's assertion has brought an upsurge in the number of efficiency studies in agriculture with special focus on the developing economies of the world. We like to say that the work not only instigates research in development/resource economics but it also prompts research in anthropology and sociology (see Adams, 1986 and the review by Michelena, 1965 pp. 540-541).

Proper measure of productivity starts with Aigner and Chu (1968), Afriat (1972) and Richmond (1974) where they propose a deterministic method of frontier measurement. Though their studies are obsolete they however underscore the popularity of the Cobb-Douglas functional form in the early literature to show the relationship between input and output. Aigner, Lovell and Schmidt (1977), Meeusen and van den Broeck (1977), and, Battese and Corra (1977) [2] introduce the modern stochastic frontier analysis as we know it today simultaneously. Their model apart from incorporating the efficiency term into the deterministic model it also includes the effect of random shock, hence, the name 'stochastic'. Lau and Yotopoulos (1971) also introduce a dual profit function model to measure efficiency but their method is not as popular in production analysis because it only yields efficiency measures for a group of farms while the frontier method gives efficiency values for individual farms in the industry (Førsund et al 1980).

The reader should note that the linear regressions of Chennareddy (1967) and Welsch (1965) give the shape of the technology of an average farm in the industry while the stochastic frontier model gives the shape of the technology of the most productive farm in the industry against which the efficiency of every other farm is measured (Coelli 1995). In other words, Chennareddy (1967) and Welsch (1965) use an average response model for their analysis.

The specification of a functional form and/or distributional assumption confers on a technique the nomenclature 'parametric' while the non-specification of a functional/distributional form confers on a technique the non-parametric nomenclature. The non-parametric nomenclature means, in the words of Koop (2003), you are "letting the data speak". This he says is very difficult to achieve as even in the non-parametric system, just like in the parametric, one need to impose certain structure on a particular problem in order to achieve ones objectives.

The use of the Data Envelopment Analysis (DEA) (another technique is the Free Disposal Hull, FDH) overshadows every other technique in the non-parametric class. Charnes, Cooper and Rhodes (1978) introduce this technique and gave it the name as we know it today. The data envelopment analysis technique uses the linear programming method to generate a piece-wise envelop over the data points. The technique is widely used in technical efficiency studies but it has the shortcoming of not incorporating randomness in measuring efficiency. Also, the envelop curve is not everywhere differentiable. Our focus in this research is the parametric technique.

The parametric technique has progressed so much in the literature that there are now two different econometric schools of thought for estimating efficiency. The first school of thought are the Frequentists who dominate this field since its inception and the second school of thought are the Bayesians into which our research belongs.

The Frequentist Studies

The first set of Frequentist study is deterministic in nature and use the technological structure of the mathematical programming approach (see Aigner and Chu, 1968; Timmer, 1971; and, Førsund and Hjalmarsson, 1979 for exposition on mathematical/goal programming). Richmond (1974) introduces the Modified Ordinary Least Square (MOLS) approach to analyse the efficiency of Norwegian manufacturing industries specifying a Cobb-Douglas production function. Richmond (1974) is a modification of the Corrected Ordinary Least Squares (COLS) approach. Winsten (1957) introduces this model by assuming a distribution (such as half normal or exponential) for the disturbance term. The Corrected Ordinary Least Square technique involves a two step process. The first step involves the use of the Ordinary Least Squares to obtain consistent and unbias estimates of the marginal effect parameters; on the contrary, the intercept parameters are consistent but bias. The second step involves the shifting of the intercept upwards so the frontier envelops the data from above.

Greene (1980) takes Richmond (1974) work a step further as he assumes a gamma distribution for the random error term using the maximum likelihood approach. He uses the data from Nerlove (1963) which is a sample of one hundred and fifty five firms producing electricity in the United States in 1955. Apart from replicating the results of Aigner and Chu (1963), Greene (1980) tries to explain the statistical relevance of his model. The reader should note that Greene (1980)'s model is deterministic.

One of the early applications of the deterministic frontier were Shapiro and Müller (1977), Shapiro (1983), Belbase and Grabowski (1985). Shapiro and Müller (1977) attempt to estimate the technical efficiency of forty farms in Geita district of Tanzania. They follow Timmer (1971) method of analysing technical efficiency by applying the linear programming to a Cobb - Douglas production frontier. Their result which is similar to that of Chennareddy (1967) shows that the traditional farmer can improve his technical efficiency by adopting modern farming practices through easy access to information. This, they say, will be at the expense of non-economic costs like the farmer being branded "unsociable" by his community. Shapiro (1983) working in the same district as Shapiro and Müller (1977) tries to confirm the 'poor but efficiency' hypothesis but discovers the hypothesis may not be applicable in terms of peasant agriculture in Tanzania because their output could still be increased if all farmers had the same efficiency as the most efficient farmer in the sample. These assertions echo the conclusion of Lipton (1968). He uses the same model and method of analyses as Shapiro and Müller (1977).

Belbase and Grabowski (1985) introduce a technique that is different from the other two stated above. They apply the Corrected Ordinary Least Square (COLS) approach of Winsten (1957) on cross-sectional sample of farms in Nuwakot district of Nepal. They record an average technical efficiency value of 80% for joint production of rice, maize, millet and wheat. The average technical efficiency value for individual frontier calculation for rice and maize is given as 84% and 67% in that order. They find correlation between technical efficiency and other variables which are nutritional level, income and education. Technical efficiency is however not correlated with farming experience.

Some studies investigate the impact of certain agricultural policies on productivity. A priori one expects these policies to actually increase productivity but this is not always the case. One of such study; Taylor, Drummond and Gomes (1986) use a deterministic production function and discover the World Bank sponsored credit programme - PRODEMATA - did not impact positively on the technical efficiency of farmers in Minas Gerais, Brazil. Their result shows that there is no difference between the technical efficiency of farmers who participate in the programme and those that did not participate. This paper is one of the few that compare both the results of the Corrected Ordinary Least Square and the maximum likelihood approaches. Unexpectedly, the participant farmers in the PRODEMATA programmes have slightly lesser allocative efficiency than non-participant farmers. The researchers also favour Schultz's hypothesis.

We want the reader to note that the deterministic frontier is still popular in the literature for example, Alvarez and Arias (2004) use Lau and Yotopoulos (1971) dual profit function model to measure the effect of technical efficiency on farm size using data from one hundred and ninety-six dairy farms in Northern Spain. They introduce technical efficiency as a parameter to estimate in a simple production function. They observe a positive relationship between technical efficiency and farm size after they control for output prices, input prices and quasi-fixed inputs. Also Amara et al (1999) use the deterministic frontier to discover the relationship between technical efficiency and the adoption of conservation technologies by potato farmers in Quebec. They found that farming experience and the adoption of conservation technologies have positive influence on technical efficiency.

Croppenstedt and Demeke (1997) use a fixed-random coefficients regression to analyse data for small-scale farmers growing cereal in Ethiopia. They observe that land size is a major constraint to crop production and large farms are relatively less productive than small farms other things being equal. They note that most of the farms are inefficient. They also observe inefficiency in the use of inputs especially labour and fertiliser. Share cropping is positively correlated to technical efficiency.

Karagiannis et al (2002) propose an alternative for separating technical change form time varying technical inefficiency. Their proposition uses the general formulation index to model technical change (Karagiannis et al 2002 cites Baltagi and Griffin 1988). They also model technical change as quadratic function of time. Their proposition does not assume any distributional assumption for the one sided stochastic error term. They then apply their proposition to the United Kingdom dairy sector from 1982 to 1992 using a translog production frontier. They obtain a mean technical efficiency value of about seventy-eight per cent for the dairy industry with this period.

One major disadvantage of the deterministic frontier model is that it over-values our inefficiency estimates. For example, Taylor and Shonkwiler (1986) discover the deterministic frontier gives over seventy per cent inefficiency while the stochastic frontier gives twenty per cent value for inefficiency.

At present, a lot of papers utilize the stochastic frontier model in their analysis. Coelli et al (2003) makes use of the stochastic frontier to calculate the total factor productivity for a panel data of crop agriculture in Bangladesh. The data contains thirty-one observations collected between 1960/61 and 1991/92 from 16 regions and the result reveals technical change is convex in nature with increase starting about the time of the introduction of the green revolution varieties in the 1970s. Technical efficiency reduces at an annual rate of 0.47 per cent during the period they investigate. This has an effect on the total factor productivity which declines at the rate of 0.23 per cent per annum with the rate of reduction increasing in later years. This, they say, raises questions of food security and increase in agricultural productivity in Bangladesh. They point out the non-use of price data in their analysis which makes their work different from other authors (Coelli et al; 2003 cites Pray and Ahmed, 1991, and, Dey and Evenson, 1991). Wadud and White (2000) compare the stochastic frontier approach with the data envelopment analysis and discover both methods indicate efficiency is significantly affected by irrigation and environmental degradation.

There are a few papers that attempt to analyse technical, allocative and economic efficiencies at once in a single research. Bravo-Ureta and Pinheiro (1997) carry out a frontier analysis using the self-dual Cobb-Douglas production function to analyse farm data from Dominican Republic. They justify the use of the Cobb - Douglas production function because the method they adopt requires both the use of the production and cost frontiers. Their research is important because they use the maximum likelihood technique to emphasize the essence of not only estimating the technical efficiency but also, the allocative and economic efficiency. Another paper that follows in this light is that of Bravo-Ureta (1994) who attempts to measure the technical, allocative and economic efficiencies of cotton and cassava farmers in eastern Paraguay. He estimates economic efficiency for cotton and cassava farmers to be around forty per cent and fifty-two per cent respectively.

There could be spatial differences in the technical efficiencies of different farms based on ecological differences, farm size and interactions between these two variables. Tadesse and Krishnamoorthy (1997) set out to investigate this in their research on paddy rice farmers in the state of Tamil Nadu, India. They remark that the farmers still have opportunity of increasing their efficiency by seventeen per cent. They observe significant variation in the variation of mean technical efficiency in the four zones that make up Tamil Nadu. They use a two stage approach where the first task is to obtain farm-specific technical efficiency and then use a Tobit model to compare the differences in the technical efficiencies of each region and zone. Wang and Schmidt (2002) note a bias in the results obtained by this process and they went ahead to use the Markov chain Monte Carlo technique to prove that there is serious bias at every stage of the procedure.

Chen et al (2009) also examine the technical efficiency of farms in four regions of China. The four regions are North, North-East, East and South-West. They observe that different inputs need to be put to efficient use in the different regions. For example, inefficient use of industrial input is the main problem in the East while in the North it is capital. They assert that farms in the North and North-East are relatively more efficient than farms in the East and South-West. They recommend a change in the land tenure system to eliminate land fragmentation in China.

Other researchers have used the stochastic production frontiers to investigate the impact of government programmes on farmers' efficiency. For example, Seyoum et al (1998) use the Battese and Coelli (1995) stochastic production function to compare between farmers that participate in Sasakawa-Global 2000 project and those who do not in Ethiopia. They collect twenty samples from two different districts (Keresa and Kombolcha) of eastern Ethiopia and show the difference in the levels of production in these two districts by use of a dummy for one district. The data is panel in nature which justifies their use of the Battese and Coelli (1995) model. Battese and Coelli (1995) [3] is a panel data extension of the Kumbhakar et al (1991) research work. Seyoum et al (1998) recommend that policy makers should expand the Sasakawa-Global 2000 project as farmers who participated have better output, productivity and efficiency than farmers that did not.

Still on the impact of government programmes on efficiency, Abdulai and Huffman (2000) look at the impact of the Structural Adjustment Programme on the efficiency of rice farmers in Northern Ghana using a stochastic profit function. Their results show rice producers in the region are highly responsive to market prices for rice and inputs. They support the introduction of the structural adjustment programme because it makes the farmers more market oriented. Also, Ajibefun and Abdulkadri (1999) find the Cobb-Douglas production function as being adequate to represent the efficiency of Nigeria's National Directorate of Employment Farmers Scheme. They reject the half-normal distribution assumption for the inefficiency term. Ajibefun (2002) simulates the impact of policy variables on the technical efficiency of small-scale farmers in Nigeria. He discovers that increase in education level and the farming experience would significantly improve the small-scale farmers' technical efficiency. Amaza and Olayemi (2002) investigate the technical efficiency of food crop farmers in Gombe State, Nigeria and arrive at similar mean technical efficiency as Ajibefun and Abdulkadri (1999). However, the difference between the minimum and maximum technical efficiency score for Amaza and Olayemi (2002) is seventy-six per cent while for Ajibefun and Abdulkadri (1999) is about sixty-six per cent.

Jara-Rojas et al (2012) look at the impact of the adoption of soil and water conservation practices on productivity and they discover a positive relation between soil and water conservation and technical efficiency. They discover that an enhancement of the technical efficiency also improves the net returns on investment.

The use of the stochastic frontier model to estimate the effect of health on farmers' efficiency is also very important in the literature. Croppenstedt and Müller (2000) take up this challenge when they research into the role of the Ethiopian farmers' health and nutritional status on their productivity and efficiency. They find that distance to the source of water as well as nutrition and morbidity affect agricultural productivity. Surprisingly, elasticities of labour productivity regarding their nutritional status are strong. They further affirm that this strong correlation continues with technology estimates and wage equations. However, they record considerable loss in production due to technical inefficiency even after accounting for health and nutrition of workers.

Ajani and Ugwu (2008) look at the impact of adverse health on the productivity of farmers living in the Kainji basin of North-Central Nigeria. Their study shows the health variable as being positive, large and statistically significant. They therefore conclude that health capital is an essential input in agriculture.

A paper that successfully combined the non-parametric technique of data envelopment analysis and an econometric model is Audibert et al (2003). They use a combination of the data envelopment analysis and the Tobit model to infer on the social and health determinants of the efficiency of cotton farmers in Northern Côte d'Ivoire. They use the high density of the malaria parasite in the blood of an individual as a proxy for the health of the household. They use a two step process; firstly, they use the data envelopment analysis to arrive at relative technical efficiency values and then they regress this efficiency scores against factors they think will affect efficiency. The 'high density of malaria parasite in the blood' variable enters the model at the second stage. Their results show that malaria greatly reduces farmers' technical efficiency. They further conclude that it is intensity of infection by the disease that is important rather than its presence. Our research collects data on the prevalence of the disease in an area rather than just hospital reported cases; this we believe will give further credence to our results.

Ajani and Ashagidigbi (2008) use numbers of days of incapacitation as a proxy for malaria incidence in Oyo State, Nigeria. Surprisingly, they ran a normal linear regression to investigate the effects of malaria on agricultural productivity. Their analysis shows that age and days of incapacitation are insignificant statistically. Olarinde et al (2008) explore the factors that affect bee keepers' technical efficiency in Oyo state, Nigeria. They observe that the bee keepers are efficient by about eighty-five per cent there is still room for to increase their efficiency by fifteen per cent. They point out that some of the farmers do not take bee-keeping as their main occupation. This, they say, is a major determinant of efficiency. Marital status is also another variable that affects technical efficiency, they note. They observe that a farmer who is single is likely to be more efficient than a married farmer.

Mochebelele and Winter-Nelson (2000) examine the effect of migratory labour (to mine fields in South Africa) on farm technical efficiency. They try to establish if migrant labour actually complement farm production or not. They establish that households with migrant farmers have higher production and are more efficient than households without migrant farmers.

In the use of the panel data for efficiency estimation, some researchers try to see if differences exist in efficiency values between the fixed effect model and the stochastic frontiers. Ahmad and Bravo-Ureta (1996) use panel data of ninety-six Vermont dairy farms between the periods 1971 to 1984. They carry out statistical tests to investigate the better model between the fixed effect model and the stochastic frontier model. The fixed effect model gave better results than the stochastic frontier model. Hence, they conclude that the fixed effect model needs to be considered in panel data analysis.

Reinhard et al (1999) estimate the technical and environmental efficiency of a panel of dairy farms. They assume the production of two outputs - dairy and excessive use of Nitrogen. They analyse their efficiencies separately. Their objective involves investigating whether farmers can both be technically and environmentally efficient. They also examine the compatibility of these two types of efficiencies. They obtain a mean output-technical efficiency of 0.894 while the input-oriented environment efficiency is 0.441. They remark that intensive dairy farming is both technically and environmentally more efficient than extensive dairy farming.

Reinhard et al (2000) examine comprehensive environmental efficiency in Dutch dairy farms. This paper is a continuation of Reinhard et al (1999) paper. In this paper, apart from surplus Nitrogen which they use in their earlier work, they also investigate excess use of phosphate and total energy use of these farms. They compare efficiency scores in the stochastic frontier analysis with the data envelopment analysis. The mean technical efficiency values for the two methods of analysis are different. The stochastic frontier has an output technical efficiency value of eighty-nine per cent while the data envelopment analysis has an efficiency value of seven-eight per cent. There is significant difference between their environmental efficiencies also. The stochastic frontier analysis records a value of eighty per cent while the data envelopment analysis records a value of fifty-two per cent. It is evident from the result of the two efficiencies that the stochastic frontier method over-values efficiency scores.

Before we close this section we refer the reader to a work by Strauss (1986). The work is important because it attempts to investigate the effect of nutrition on farm labour productivity in Sierra Leone. He uses an average response model to capture this effect. He estimates a Cobb-Douglas production function which accounts for simultaneity in input and calorie choice. His exercise shows calorie intake has significant impact on labour productivity. He, however, places a caveat on this result because individual-level nutrient and anthropometric data are not included in the analysis. His result supports the nutrition - productivity hypothesis to a great extent.

In the last few pages we attempt to explain to the reader the preponderance of the Frequentist method of analysing the stochastic frontier especially in agriculture. We emphasize the diverse uses of the parametric method of efficiency measurement in agriculture. We believe that other literature in agriculture will fall into one of the categories we peruse above. Next, we take a look at the Bayesian econometrist view. The reader should note how few the literature is compared to the Frequentist method. Also, for a thorough perusal of the literature from the Frequentist perspective we refer the reader to Bravo-Ureta et al (2007) Delete.

The Bayesian Studies

The works of van den Broeck, Koop, Osiewalski and Steel (1994); Koop, Osielwalski and Steel (1994, 1997); Koop, Steel and Osielwalski (1992), and, Fernández, Osiewalski and Steel (1997) herald the Bayesian technique for estimating the compose-error model.

van den Broeck, Koop, Osiewalski and Steel (1994) is a primer for estimating a Bayesian cross-sectional composed-error data. They resolve the problem of choosing the best functional form experienced in classical econometrics by mixing over a number of distributions. They use the Bayesian model averaging to average over the results of the Jondrow et al. (1982) and Greene (1990). In other words van den Broeck, Koop, Osiewalski and Steel (1994) solve the problem of choosing the better distribution between the two. They also carry out predictive inference on their results using the Monte Carlo technique of importance sampling.

In continuation of van den Broeck, Koop, Osiewalski and Steel (1994) work; Koop, Osielwalski and Steel (1994) show how to use the Gibbs sampling Monte Carlo method to arrive at estimates for the stochastic cost frontier model. They fit an asymptotically ideal price aggregator, non-constant returns to scale composed error cost frontier. They use Barnett, Geweke, and Wolfe (1991) method for generating the asymptotically ideal price aggregator (Koop, Osielwalski and Steel, 1994 cite Barnett, Geweke, and Wolfe 1999). They caution that care should be taken in the choice of functional form for frontier analysis. We believe the use of the Bayesian model Averaging technique should circumvent this problem. Also, they discover that imposing regularity condition on the price aggregator is found to reduce the spread of the "Müntz- Szatz" expansion.

Koop, Steel and Osielwalski (1995) essentially show how to draw the different parameters in the composed-error model using the Gibbs sampler. They provide an algorithm to draw the different parameters of choice in the composed-error model. They show the ease with which this can be done using the Gibbs sampler. They also note the use of 0.875 as an informative prior for the inefficiency value. van den Broeck, Koop, Osielwalski and Steel (1994) propose this value.

Fernández, Osiewalski and Steel (1997) introduce the Bayesian method for estimating panel data using a class of non- or partly-informative prior. They assert that using this type of priors for a cross-sectional data will make its posterior inference unreliable and inaccurate. This is because the total number of parameters in the entire model is larger than the sample size. They circumvent this problem in the panel data where the researcher can impose a structure on the inefficiency terms. Koop, Osielwalski and Steel (1997) take Fernández et al (1997)'s work further as they introduce the Bayesian method for analysing the firm-specific inefficiencies in the presence of panel data using the fixed and random effect model. They propose the use of Monte Carlo integration or the Gibbs sampling in estimating this model. This work provides a Bayesian equivalent to the classical method of analysing fixed and random effect models. However, McCulloch and Rossi (1994) remark that "in the Bayesian point of view there is no distinction between the fixed and random effect, only hierarchical and non-hierarchical models. This is because the parameters themselves are random (Holloway, Tomberlin and Irz).

Most farmers in the developing world do not practice mono-cropping. They either practice mixed farming or mixed cropping. Hence, we have a situation of joint production of output. This is usually dealt with using the classical distance function stochastic frontier method. Another method is the use of data envelopment analysis. Fernández et al (2000) derive Bayesian tools for handling multi-output production frontiers. This method is only applicable where input and output data are available but price data are unavailable. They implement this using a Markov chain Monte Carlo algorithm. They test their proposition on both artificial and real data. Separability in input-mix and homoscedasticity is assumed in this paper.

Fernandez et al (2005) extends Fernandez et al (2000) work by developing different definitions for efficiency in a multiple-output production system. This time they assume non-separability in inputs and outputs. They also introduce a situation where some of the outputs are undesirable. They test their propositions using two practical data - banking and agricultural data. They added a caveat saying care should be taken when deciding on which efficiency definition to use. They advise that researchers should look into theory for help on which definition to use. In the absence of such guidance the researcher should present results for several choices.

O'Donnell and Coelli (2005) show how to impose the regularity conditions of monotonicity, quasi-convextiy and convexity using a panel data. They use the Bayesian technique to impose these conditions. Their work serves as a break -through in the efficiency literature because these conditions are difficult to impose. At present this condition is only imposed using the Bayesian methods. They adopt the Markov chain Monte Carlo techniques of Gibbs sampler with data augmentation, metropolis within Gibbs algorithm. They caution that their approach works when time-invariant effect is assumed. They assume a truncated distribution for the inefficiency variable. However they did not apply this approach on any agricultural data rather they use data from seventeen European railways. Their findings show that there are significant changes in the elasticities of the variables and shadow price ratios when the regularity conditions are imposed

In the next few paragraphs we review literature that has applied this technique in agriculture.

Kurkalova and Carriquiry (2003) introduce the Reinhard, Lovell, Thijssen (1999) approach to calculation of a single input-oriented technical efficiency to the Bayesian technique. They investigate a small sample of forty-one Ukrainian collective farms from 1989 to 1992. They posit that since the data size is small, the number of years precludes the estimation of the data by the classical approach. They further justify the use of the Bayesian approach by the fact that they are interested in changes in the efficiency values at the farm-level in the use of different inputs. Also, they point to the fact that the precision of the estimate may be heterogeneous across firms. This, they affirm, will be difficult to investigate using the maximum likelihood approach. The median of the posterior distribution of the average technical efficiency gives a value of 0.942.

Balcombe et al (2006) apply the Bayesian, Classical stochastic frontiers and the data envelopment analysis to a sample of Australian dairy farms. They adopt van den Broeck, Koop, Osiewalski and Steel (1994) informative prior of 0.875 as their (in)efficiency value. They investigate the impact of imposing regularity conditions on their results at three different points in the data. Firstly, without regularity conditions imposed, secondly, with regularity conditions imposed at sample means and thirdly with regularity conditions imposed at all data points. They adopt the use of the random-walk Metropolis-Hastings step in imposing the regularity conditions at all points in the data. They emphasize that the imposition of the regularity conditions does not change the efficiency results significantly.

The Bayesian technique brings with it opportunities to resolve some econometrics problems. One of such problems is how to account for production risk. O'Donnell and Griffiths (2006) analyse risk using state-contingent frontier. Since state of nature like risk is unobserved, they treat it like a latent variable. They then apply a Bayesian finite mixture model to analyse the state-contingent frontier of Philippine rice data. The state-contingent framework gives different elasticities and technical efficiency estimates from the conventional frontier. The technical efficiency value is higher than the conventional frontier. This, they say, is because the error components in the conventional model measure noise, inefficiency and risk. In other words, the conventional frontier over-values noise and inefficiency.

Also, Fernández et al (2002) develop a method for dealing with undesirable outputs in the literature. They use exactly the same data as Reinhard, Lovell, and Thijssen (1999). In this paper, efficiency is divided into technical and environmental efficiency just like in the Reinhard, Lovell, and Thijssen (1999) paper. They obtain a median of sixty-seven per cent and thirty- nine per cent for technical and environmental efficiency respectively. This result is different from that obtained by Reinhard, Lovell, and Thijssen (1999). There is a moderate positive correlation between the two types of efficiencies. They bemoan the low value of environmental efficiency. They infer that dairy farmers can increase their environmental efficiency at no cost to forgone food output.

Benzemer et al (2005) examine the role of livelihood strategies in rural growth and poverty reduction in Georgia. The study incorporates livelihood diversity into the stochastic frontier. The results show that animals contribute more to output. They remark that involvement in non-agricultural activities have positive contribution to efficiency.

Balcombe et al (2007) examine the technical efficiency of rice producers in Bangladesh. They use the Bayesian technique to estimate the technical efficiency of the farmers. Their aim is to bridge the gap between potential farm yield and actual farm yield. They observe presence of technical inefficiency but this is to a lesser degree than other studies have pointed out.

Areal et al (2012) include milk quota system as one of the factors affecting efficiency. They affirm that the way the farmer behaves in the milk market has link with his technical efficiency. They note that farmers who purchase or lease their milk quota are more efficient. In the same vein farmers who tend to go above allocated quota are more efficient. They comment that other environmental production has link with technical inefficiency.

The Bayesian method is also applicable in fisheries. Flores-Lagunes et al (2007) use Horrace (2005) to estimate the technical efficiency of thirty-nine fishing vessels in the North Herring on the basis of each vessel's probability of being efficient. They develop a selection technique to identify groups of vessels at pre-stated probability levels. Holloway, Tomberlin and Irz (2005) present a pedagogic way to estimate the composed error model hierarchically. They explain how the marginal likelihood is calculated in a composed error model. They show how this procedure works by use of data from the Pacific Coast Groundfish Fishery. They also introduce the "good captain" hypothesis in their analysis. "Good captain" hypothesis focuses on the fact that skill and talent of the fisherman and not luck brings large harvest to the fisherman. Alvarez, Perez and Schmidt (2003) working on hake catches in Northern Spain disagree with this hypothesis. They demonstrate that luck rather skill is more important. We note that Alvarez et al (2003) use the classical method.

Holloway and Tomberlin (2007) take the work of Holloway et al (2005) a step further by calculating efficiency estimates as well as the probabilistic rankings of the relative technical efficiency of fishing boats. The sample is made up of ten thousand eight hundred and sixty-five fishing boat trips in the United State Pacific hake (or whiting) fishery during the period 1987 to 2003. They make use of the Gibbs sampler in arriving at their conclusion. They explore the likelihood of a particular boat being 'best' simultaneously with the technical efficiency scores. They ignore the problem of heterogeneity which results from different boats having different production frontier. In Tomberlin and Holloway (2008), they estimate two cross-sectional models for comparison with panel models. They divide their data into two layers of hierarchical models in each case. They discover that doing this yields the best results in the cross-sectional and panel data models considered. The results are similar in both models though their marginal likelihood differs a bit.

O'Donnell (2012) uses the Bayesian systems method to circumvent the problem of correlation between the explanatory variable and the error term in distance functions (He cites Fernández et al 2000). He applies this method to state-level data on United States' agricultural input and output quantities. He calculates the distance function and the Total Factor Productivity (TFP) change. O'Donnell (2012) decomposes the total factor productivity into technical and a measure of efficiency change. He concludes that the primary driver of long-term productivity change in the United States is technical progress.

In the last two sections we attempt to present to the reader classical and Bayesian perspectives to efficiency analysis in the literature. One advantage of the Bayesian method over the classical method is that the posterior pdf or properties of firm-specific efficiencies can be derived. In addition, the exact finite sample properties of parameters can also be calculated. Also, we believe that the knowledge of the Bayesian technique introduces variety and sophistication into the tool kit of an econometrician.

In the literature the nature of the data that is; single or multiple output, determines the approach of the researcher to the analysis. This presents us with another method of classifying efficiency studies. As a result, we peruse the single and multiple output studies in the literature with particular focus on the technique and methods of analysis. Our objective in the next section is to emphasize the diverse nature of efficiency nature.

Single Output

Aly et al (1989) assume a ray-homothetic function to analyse a sample of eighty-eight Illinois grain farmers using the Corrected Least Square approach. They estimate a deterministic statistical frontier. They observe that the farms produce up to fifty-eight per cent of their potential capabilities. The farms have mean technical inefficiency value of sixty per cent and a scale inefficiency value of forty per cent. They also observe that the technical efficiency values are positively correlated with the size of the farm. In other words, large farms are more efficient than small farms.

Dawson et al (1991) measure farm-specific technical efficiency over time of rice farmers in the Philippines. The range of efficiency values across the twenty-four farms in the survey is between eighty-four per cent and ninety-five per cent. They affirm that it will be difficult to relate the narrow spread of farm-specific inefficiencies to farm socioeconomic factors. Instead they suggest that increase in rice production in the future will come from technological progress. They specify a Cobb-Douglas production function.

Kalaitzandinakes and Dunn (1995) investigate effect of education on technical efficiency in eighty-two corn family farms in Guatemala. These families participate in government's market-based land reform programmes. They analyse the data using the deterministic, stochastic and the data envelopment analysis. They compare the results of the deterministic frontier with that of the stochastic frontier. They find that the efficiency values in the deterministic frontier were higher than that of the stochastic frontier. On the contrary, most of the family farms are seen to be more efficient under the stochastic frontier than under the deterministic frontier. Comparison of the results of the data envelopment analysis with the other two frontiers suggests technical inefficiency is minimal. They support the assertion that empirical technical inefficiency measurements are not perfect measures of their latent theoretical analogue.

Heshmati et al (1995) investigate technical efficiency, technical progress and the bias in technical change using panel data from the Swedish pork industry. The panel covers period from 1976 to 1988. They use a generalized Cobb - Douglas model where input elasticities are linear functions of time. In other words they use a time varying model to estimate inefficiency. They use farm dummies to capture farm heterogeneity. Elasticities with respect to animal and material inputs increase over time. They record a mean technical efficiency value of about ninety-one per cent. About three per cent of farms are inefficient which shows most of the farms in the industry are efficient. They find technical change to be positive but regresses slowly between the periods 1981 to 1988.

They observe that maize production is done under increasing returns to scale. Many of the maize farmers are technically inefficient. The mean technical efficiency he records is fifty-three per cent. Farm-specific efficiency is as low as three per cent while the modal efficiency class being about sixty per cent. He observes that plot size, hired labour, use of hybrid seeds, education affect farmers technical efficiency. However adoption of new technology does not have effect on efficiency.

Ogundele and Okoruwa (2006) divide rice farmers in Nigeria into two: those that plant improved variety and those that plant local variety. Afterwards, they compare their technical efficiencies. Their result show there is no significant difference in the technical efficiency of these two groups. They assert that farming experience and number of visits by extension agents are the only socioeconomic characteristics where significant difference between the groups exists. They observe that farm size was the most important factor that influences technical efficiency in Nigeria. They query the success of the various rice development programmes in Nigeria as rice farmers' technical efficiency is still low.

Chirwa (2003) examines the sources of technical efficiency among maize farmers in Malawi. His results show the farms have an average efficiency score of about fifty-three per cent while fifty - eight per cent of the farms have efficiency scores below sixty per cent. We can then infer that inefficiency is still high in Malawi among maize farmers. They observe that inefficiency falls with plot size, use of hired labour, use of hybrid seeds and membership of farming association.

Also, Amos (2007) analyses the productivity and technical efficiency of smallholder cocoa farmers in Nigeria. He uses a Cobb-Douglas stochastic production function. He uses primary data of two hundred and fifty cocoa farmers in Ondo State, Nigeria. He shows that the farmers are experiencing increasing returns to scale in resource use. The average farmer needs to increase his efficiency by about twenty-eight per cent. However, the range between the least efficient farmer and the most efficient farmer is eighty percent. This is extremely high. He explains that age, education, and, family size influence technical efficiency. He advises the government to introduce sustainable education policy in Nigeria.

Some authors attempt to use a mix of both the parametric and non-parametric method in estimating efficiency. Rios and Shively (2005) use a two step approach to examine the technical and cost efficiency of coffee farmers in Vietnam. The first step involves the use of the data envelopment analysis to examine the technical and cost efficiency of the farmers. They estimate a Tobit model in the second step to explore the factors that affect these efficiencies. They observe lower technical and cost efficiency on small farms. They suggest that inefficiency may not necessarily be caused by farm size. They point to factors like irrigation pipe length, higher education, access to credit and land tenure system as the likely factors that affect inefficiency.

Alene and Hassan (2006) add to the few literature that attempts to examine the technical, allocative and economic efficiencies of farmers. They measure the efficiency of traditional and hybrid maize producers in eastern Ethiopia. Furthermore, their work input returns to scale variable in the traditional efficiency decomposition method. They then compare their results with the conventional efficiency decomposition approach. They observe that the conventional efficiency decomposition approach over-states the true efficiency measures under increasing returns to scale production of hybrid maize. Also, it under-states efficiency figures under decreasing returns to scale production of traditional maize. They further observe that the mean of technical and economic efficiencies are considerably lower in the conventional method than the scale-adjusted efficiency measure in traditional maize production and higher in hybrid maize production. They affirm that if one uses the conventional method one will draw the wrong inference. The reason, they say, is that one is likely to say traditional maize production exhibits significant inefficiencies while hybrid maize cultivation exhibits lower inefficiency.

Wouterse (2010) uses the variable returns to scale data envelopment analysis to explore the impact of migration on cereal farmers' technical efficiency in Burkina Faso. She observes that intercontinental migration improves remittances to and productive capital of cereal farmers. On the other hand it prevents them from moving to a higher frontier because they cannot expand land for farming. She remarks that remittances will not be enough to improve agriculture. She recommends that policy makers need to look at imperfections in the labour market of the migrant-sending economies.

Apart from Croppenstedt and Müller (2000), another researcher who attempts to explore the impact of farmers' health on agricultural productivity is Loureiro (2009). She uses secondary data from Staistics Norway and Tax Revenue Service of Norway to investigate this. She uses the heteroscedastic stochastic frontier model. She inputs the farmers' health as one of the variables that affect agricultural efficiency. She looks at health as anything that could cause physical injury and hazards to the farmer. Her result shows the farmers' health plays statistical significance in affecting his efficiency. She recommends that government should endeavour to enlighten the farmers on health and safety attitudes on the farm.

In the same vein, Ulimwengu (2008) studies the effect of health on the farmers' technical efficiency. He estimates a Cobb-Douglas stochastic frontier to explore this relationship. He uses data from the fifth round of the 1999 Ethiopian Rural Household Survey (ERHS). He observes that illness increases the probability of child labour. He motivates his conceptual framework from the household model, modifies and carries out comparative statics analysis on it. He further asserts that reducing the remoteness of villages will lessen the likelihood of the farmer being constrained by illness. He infers that sickness reduces agricultural efficiency.

Multiple Crop Studies

Shah et al (1994) examine crop specific technical efficiency in Pakistan. The crops they investigate are wheat, maize, sugarcane and vegetable. They use the corrected ordinary least square approach and the maximum likelihood techniques to analyse their data. Both techniques show the farmers as being inefficient. Maize and sugarcane give the highest inefficiency values among the crops. There are differences in the cause of inefficiencies among the crops. Their analysis show inefficiency in maize and sugarcane is due to technical inefficiency. On the other hand in wheat and vegetable inefficiency is due to random shocks.

Some researches investigate the impact of a particular economic reform on efficiency. Abdulai and Eberlin (2001) look at the effect of the economic reform in Nicaragua on maize and beans farmers' technical efficiency. They collect their data from two regions in Nicaragua during the 1994 - 1995 planting season. They employ the translog stochastic frontier model in analysing their model. Their analysis gives an average efficiency value of about seventy per cent and about seventy-four per cent for maize and beans respectively. Schooling, formal credit and farming experience have positive effect on efficiency while farmers' participation in non-farm activities reduces efficiency.

Binam et al (2004) use a Cobb-Douglas production function to examine factors affecting technical efficiency among smallholder farmers in Cameroon. He surveys four hundred and fifty farmers over fifteen villages in the 2001/2002 planting season. They calculate the technical efficiency for each crop (groundnut and maize) and then for joint production of groundnut and maize. They obtain seventy-seven per cent, seventy-three per cent and seventy-five per cent respectively as efficiency values for groundnut monocrop, maize monocrop and joint production of groundnut and maize. They conclude that the differences in efficiency are as a result of credit, soil fertility, social capital; distance of the plot from access road and extension services.

Haji (2007) investigates technical, allocative and economic efficiencies in the vegetable dominated mixed farming system in eastern Ethiopia. He uses a two-stage method. The first stage is the use of the data envelopment analysis method to estimate this. He observes mean technical, allocative and economic efficiencies to be ninety-one, sixty and about fifty- five per cent respectively. He states that inefficiency is rife in the study area. He uses the Tobit model in the second stage to examine the determinants of these efficiencies in the study area. He reveals that asset, off/non-farm income, farm size, extension visits and family size have significant impact on technical efficiency. He further states that asset, off/non-farm income, farm size, extension and family size are the significant factors that affect allocative and economic efficiencies. His study goes ahead to estimate the excess cost caused by allocative inefficiency. He puts this value to the excess of forty-four per cent of allocative efficiency. He attributes this to low asset ownership, farm size, high consumer spending, crop diversification and obstacles to the flow of labour between farm and off-farm activities.

Arlene et al (2006b) study the efficiency of the intercropping systems of production in Ethiopia. They examine annual and perennial crops in southern Ethiopia. They analyse their data using the stochastic frontier analysis, data envelopment analysis and the parametric distance function. They compare the results of the stochastic frontier analysis, data envelopment analysis and the parametric distance function. They affirm that the efficiency rankings using the three different methods are similar. However, the single output stochastic frontier analysis records the lowest efficiency scores among the three methods. Results from the multiple output methods - the data envelopment analysis and the parametric distance function - are similar. The data envelopment analysis and the parametric distance function also show significant correlation with each other. Their efficiency estimates are bigger than those of the stochastic frontier analysis. The average technical efficiency is about ninety per cent. This means that intercropping improves technical efficiency. They further remark that increase in productivity occurs from diversification from the subsistence method of food production to the cash crop method of food production. They comment that their findings are in line with Schultz (1964) work.

After reading the above selected works on efficiency we hope that the reader will appreciate the essence of efficiency as a concept. We also hope that the reader will appreciate why research in efficiency using the Bayesian framework needs to emphasized. As the reader will note, the body of literature using the Bayesian framework is little when compared with the classical methods. The reader will therefore agree that our work is pertinent in this regard.

Our research concerns estimating the Willingness-To-Pay hence we will proceed with reviewing literature in this area. The essence as said is to explore research in this area…….


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