Potential Improvement of Agricultural Output for Major Producers Based on DEA Efficiency Measurements

In this article we perform production efficiency analysis for the 40 countries with largest value added by agricultural sector in 2005. Under the assumption of a nonparametric frontier and production observations satisfying a statistical model including both random and inefficiency errors, we estimate an agricultural production function using DEA measures of efficiency with output orientation and variable returns to scale. We found evidence that the set of countries investigated could increase their total value added by agricultural sector for at least 53.9% without increasing input usage with the prevailing technology. This result has a direct impact on issues related to the recent food crisis.


INTRODUCTION
The world has been affected lately (2006 to 2008) by dramatic rises in food prices, generating a global crisis and causing political and economical instability and social unrest in both poor and developed nations.
Systemic causes for the worldwide increases in food prices continue to be the subject of debate. Initial causes of the late 2006 price spikes includes unseasonable droughts in grain producing nations and rising oil prices. Oil prices further heightened the costs of fertilizers, food transport, and industrial agriculture. Other causes may be the increasing use of biofuels in developed countries and an increasing demand for a more varied diet (especially meat) across the expanding middle-class populations of Asia. These factors, coupled with falling world food stockpiles, have all contributed to the dramatic worldwide rise in food prices. However, to explain the recent crisis, it is not possible to elect a specific guilty.
Long-term causes remain a topic of debate. These may include structural changes in trade and agricultural production, agricultural price supports and subsidies in developed nations, diversions of food commodities to high input foods and fuel, commodity market speculation, and climate change. In this context it is worth mentioning Nicholson & Esseks (1978), Dyson (1994), Food  Our main interest is not to investigate the causes of the food crisis, but the assessment of the actual world potential to increase the supply of agricultural goods. In this context we use a new Data Envelopment Analysis -DEA approach based on the work of Banker & Natarajan (2004,2008) in the presence of contextual variables. Using projections onto the frontier, with possible corrections for random effects, we show that the food crisis can be minored substantially if the economies become more efficient relative to the technology available. Hence, this article has two main contributions: a new approach for the assessment of contextual variables using two stage DEA models incorporating two error components, and a suggestion of a security food policy via reduction of production inefficiencies. This paper does not intend to propose solutions for the food crisis. Instead it provides a diagnostic that may be useful for policymakers to propose measures contributing to agricultural development via incentive policies to reduce the inefficiency of production of agricultural goods. To resolve the food crisis we understand that it is necessary a coordination of global policies to reduce the scarcity of food. In this context firstly it is necessary to define a rough diagnosis of the potential capacity of world producers.
Based on methods of efficiency analysis it is possible to rank countries via efficiency scores. The score of each country is the ratio of the frontier output to actual output. The frontier output is not necessarily achievable, since there are difficulties to compare countries with different technologies, land qualities, labor, capital etc. However, projections on the frontier are useful to pinpoint countries where, in a first approximation, it would be possible to increase production without demanding additional inputs. For example, we will see in this paper that many large producers of agricultural goods are classified as very inefficient, i.e., with a score of efficiency lower than the median. This result suggests that the agricultural production of these countries can be substantially improved, reducing substantially the world agricultural output gap.
The potential capacity is the output projection onto the frontier, and the output gap is the difference between the frontier output and current agricultural production. The efficiency frontier is a proxy for the world agricultural potential capacity, despite of all restrictions on estimation due to aggregation across countries.
Once potential inefficiencies have been identified, policy makers may provide a closer look on inefficient producers with the intent to create mechanism designs envisaging those producers to become more efficient.
In the literature there are several studies using efficiency analysis and output frontier across countries with the intent to provide support for prescriptions of public policies.
Arcellus & Arocena (2005) carry out a computational analysis of the tradeoffs between a good output and the CO 2 emissions or bad output of the production process across OCDE countries via a DEA formulation. The authors compute potential frontier CO 2 reduction and compare their results with targets defined by the Kyoto protocol emission limitations. Based on their findings they provide possible negotiation strategies for the various countries in their effort to reach a pollution control agreement. Sharma & Thomas (2008) examine the relative efficiency of the R&D process across a group of 22 developed and developing countries using DEA. The R&D technical efficiency is examined using a model with patents granted to residents as an output and gross domestic expenditures on R&D and the number of researchers as inputs. The emergence of some of the developing nations on the efficiency frontier indicates that these nations can also serve as benchmarks for their efficient use of R&D resources. The inefficiency in the R&D resources usage highlighted by this study indicates the underlying potential that can be tapped for the development and growth nations.
We follow here a similar line of investigation. We define the problem, use a method of efficiency analysis, compute the efficient frontier, point out the inefficient DMUs, and provide helpful information to policymakers to identify which countries can improve their agricultural production performance via inefficiencies reduction. The article proceeds as follows. Section 2 is on methodological aspects, where we specify the statistical model and the selection of participating countries. Section 3 analyzes efficiency and statistical results and proposes a world policy increase in agricultural supply. In Section 4 we present final comments and summarize the main findings of the article.

Output, Inputs and Contextual Variables
The countries considered in this article are listed in Table 1. They comprise a universe of the 40 countries with the largest value added by agricultural sector. Together they were responsible, in 2005, for roughly 80% of the world agricultural sector.
The production system in our analysis involves one output and four inputs. As a proxy for the agricultural output we use value added by the agricultural sector, in 2005, in 10 9 dollars at constant prices. Value added is the net output of a sector, after adding up all outputs and subtracting intermediate inputs. This information is available in World Bank (2008c).
Inputs are land, labor, fertilizers and capital. The source for the input data is Food and Agriculture Organization of the United Nations (2008b).
For land we use agricultural area, which refers to: (a) arable land (land under temporary crops, temporary meadows for mowing or pasture, land under market and kitchen gardens and land temporarily fallow, (b) permanent crops (land cultivated with crops that occupy the land for long periods and need not be replanted after each harvest, and (c) permanent pastures (land used permanently for herbaceous forage crops, either cultivated or growing wild (wild prairie or grazing land). Data are expressed in 1,000 hectares. We follow Coelli & Rao (2005).
The economic active population in agriculture defines labor. This variable is defined as the agricultural labor force, i.e., that part of the economically active population engaged in or seeking work in agriculture, hunting, fishing or forestry. Data are expressed in 1,000 people, in 2005. We follow Fulginiti & Perrin (1997) and Coelli & Rao (2005). As a proxy for capital we use the capital stock in agriculture that refers to a value that is attached to the total physical capital capacity available for repeated use in the production of other goods, in existence at specific point in time in the economy of agriculture sector. As stated in Production data is shown in Table 1, where HDI and R1, R2, R3, R4,  The raw data was screened for the presence of outliers using regression methods as follows. Let w = (1, y, x 1 , x 2 , x 3 , x 4 , R 1 , . . . , R 6 ) be the matrix formed with observations on output y and inputs x i plus a column of ones and regional dummies. It is a standard procedure in regression analysis (Kutner et al., 2004) to consider values greater than two times the average of the diagonal elements of the matrix w(w w) −1 w as outlying observations. Such observations were identified by a dummy contextual variable 'outlier'. These were Australia, China, Japan and United States. This variable did not show statistical significance in the second stage.

Statistical Production Model
The production analysis is carried out considering a nonparametric model. We assume that observations on production follow the statistical model (1), where g(•) is a continuous production function defined on the compact convex set K in the nonnegative orthant of R 4 , with nonempty interior, satisfying:

g(•)
shows variable returns to scale.
The random variables v j and u j represent random and inefficiency errors respectively. Following Banker & Natarajan (2004, 2008) we assume that the random errors have a two sided ( , ] continuous distribution concentrated on −V M , V M . The inefficiency error component is positive. It follows (2).
The component ε j is strictly positive. Following Banker (1993), Souza & Staub (2007), and Banker & Natarajan (2004, assuming, for example, a gamma family of distributions for the ε j , it is possible to use DEA, output oriented and under variable returns to scale, to consistently estimateg(x). Identical distributions are not required and one may let the mean μ of the inefficiency distribution be dependent on a linear function δ z of covariates or contextual variables. Following Simar & Wilson (2007), we considered a two stage statistical model to estimate δ using only the inefficient firms. For this purpose, we fit a gamma distribution ( p, λ j ) with mean μ j = p/λ j , where λ j = exp(−δ z j ), by maximum likelihood, to DEA residualŝ The empirical production function defined in (3), where the sup is restricted to vectors γ for which j γ j = 1, consistently estimatesg(x) for x ∈ K * . For input data points x j ,ĝ(x j ) = φ * j y j . The covariate of main concern here is HDI.
We obtain information on the constant V M assuming that the efficient units are producing on the technological frontier. In this context an optimum estimate would beV M = n l l=1μ l /n l , whereμ l is the maximum likelihood estimate of μ l and the sum is over the efficient units. The maximum likelihood estimate of μ l is computed from the inefficient units. This is a subtle modification on the methods proposed by Banker & Natarajan (2008). The use of the gamma distribution and the adaptation of the procedures of Simar & Wilson (2007) is also original. In this context another possibility to model the inefficiency distribution would be given by the truncation at zero of the normal with mean μ j and constant variance. This alternative did not fit well in our instance. Table 1 shows the estimates of efficiency computed under the assumption of variable returns to scale. The nonparametric one sided test of Wilcoxon rank sum (Conover, 1998) point to marginal significance for the difference between the assumptions of variable and constant returns. For this reason, our choice was the less restrictive variable returns to scale model.  Table 1 are inverted to bring their values to (0, 1].

EMPIRICAL RESULTS
The distribution of efficiency scores depicted in Figure 1 has no outliers, but seems to have two models. The median efficiency is 0.466. The first quartile is 0.298 and 30% of the countries are fully efficient. Some interesting considerations may be drawn from the efficiency scores in Table 1 (Annex). Among G-7 countries, France, Japan, USA and Canada are efficient, while UK, Italy and Germany show greater efficiency levels than the median. Other countries of high income, Netherlands, and middle income, Greece, Korea Republic, Venezuela and Saudi Arabia are efficient as well. At least, three countries of low income are also efficient: Algeria, China and Sudan.
Nine of the twenty countries with the largest output have efficiency scores lower than the median. These countries are Brazil, Indonesia, Turkey, Mexico, Pakistan, Russian Federation, Egypt, Iran and Argentina. This result suggests that the value added by the agricultural sector of these countries can be substantially improved reducing substantially the world agricultural output gap.
The gamma distribution fitted to non-efficient units produced Table 2. Regional dummies R5 and R7 were removed, since they are not represented in the regression. The base for the dummies R1-R4 represented in the analysis is R6. We see that the coefficient -b1 is negative and statistically significant, indicating that an increase in HDI causes an increase in efficiency. The regional dummies coefficients indicate that R6 and R4 are equivalent and efficiently superior to the other three regions.  In added values terms the agricultural sector could grow 53.9% using the available technology. Table 3 shows individual outputs and projections of potential outputs resulting from efficiency adjustments. It also shows the output gap. In absolute terms the median gap is 14, 879 × 10 9 and the third quartile is 38, 192 × 10 9 . Pakistan and Malaysia are the leading relative contributors to potential increase in agricultural GDP since they are highly inefficient. Likewise other important countries are Mexico, Turkey and Indonesia. Table 3 shows the output gap in 10 9 dollar values. The upper quartile includes Pakistan, Malaysia, Mexico, Turkey, Indonesia, Iran, Brazil, Ukraine, Russian Federation and Thailand. This is an indication that these countries may increase substantially agricultural production with proper incentive policies.

CONCLUSIONS
This article assesses the efficiency of production for the major agricultural producers in the year of 2005. We estimated the output gap due to inefficiency for each economy and concluded that if these countries were working on the efficient frontier, the supply of agricultural GDP would increase by 53.9%.
From the efficiency scores we depicted that among G-7 countries, only France, Japan, USA and Canada were efficient. Nine of the twenty countries with the largest output had efficiency scores lower than the median, including Brazil. This suggests that the value added by the agricultural sector can be improved by reducing the world agricultural output gap.
The regression analysis showed that an increase in HDI can cause an increase in agricultural efficiency. Regions R6 and R4 were equivalent and more efficient than the others in this model. A possible implication for economic policy resulting from this article is that a way to minimize food scarcity in the world is reducing the inefficiency of the producing units of agricultural goods. Moreover, the statistical results also indicate that HDI is an important variable to increase agricultural efficiency. However, if on one hand an increase of HDI in producing units induces a decrease in inefficiency in agricultural production, and thus an increase in supply, on the other hand, the same increase of HDI, as a proxy for welfare of population, will increase the demand for food.
The net social benefits of the interaction between demand and supply in this context were not studied here. Further research is needed in this direction. However a startling conclusion is that there is space and technology to increase agricultural production in 53.9% without requiring additional resources.