Efficiency impact of the agricultural sector on economic growth in Togo

The fundamental idea of this article is to study the efficiency of the Togolese agriculture and its relationship with economic growth on the basis of economies of scale. We tackled efficiency, in its input and output orientations, using parametric and non-parametric methods in which an annual product analysis is carried out. In this context, agriculture is modelled by the usual Translog and CobbDouglas functions and efficiency estimating techniques, such as the stochastic frontier analysis (SFA) and data envelopment analysis (DEA). Agricultural production was analyzed on a product basis depending on the cultivated area and the number of workers in the agricultural field. The study sample consists of 15 agricultural products for the period running from 1990 to 2009. The Togolese agriculture is generally inefficient according to the DEA and SFA methods.


INTRODUCTION
The agricultural sector in the developing countries is the focal point of the policy makers and international organizations that laid the foundation in the fight against poverty.Agriculture, beyond its economic dimension, remains a prerequisite for survival for the poor countries threatened by famine.The major global organizations that struggle for the welfare of the whole humanity put agriculture at the heart of their preoccupations.Financial assistance that developed economies grant to third world economies is based on the idea that agriculture is a key sector that should be promoted to back any idea of development.
The main question that we try to answer in this work is simple: Can we say that agriculture in the developing countries is efficient?This question leads to another more important one: What impact does the agriculture efficiency have on the economic growth of these countries?Or, more specifically, what role does an efficient or inefficient agriculture have on the GDP of a developing country?More clearly, our work raises the question of the agriculture impact on economic growth regarding efficiency.
An African country, particularly Togo, is going to be the subject of our investigation since this country has (Danklou, 2006;Thierry, 2010).In addition, more than 70% of the active workforce is engaged in agriculture; more than 60% of its arable land, while only 11% of these lands are being value according to official figures nevertheless, no signs of food self-sufficiency were observed in Togo.For this reason, we really wonder if the use of agricultural resources in Togo is optimal.
The issue here is to know whether economic growth is caused by agriculture or vice versa.In other words, is causality between agriculture and economic growth simple or double?Obviously, it is very logical and justified to say that it is agriculture that causes economic growth because its importance in economic growth has long been noticed by eminent economists, such as Lewis (1956).Economic growth, by the savings made, promotes the funding of research necessary for technical progress that sustains agriculture.Technical progress may reduce or complicate the appropriation of natural resources by humans over other species.However, some authors emphasize that economic growth measured by the GDP tends to destroy the natural capital.One of the criticisms of the market economy is that the environment is poorly reflected in the current economic models.When technical progress ignores the environmental constraints, growth and productivity can have negative effects on the environment.In short, agriculture contributes to economic growth which has both beneficial and devastating effects on it.

LITERATURE REVIEW
Obviously, it is very logical and fair to say that it is agriculture that generates economic growth because its importance has long been noticed by eminent economists.Johnston and Mellor (1961) identified two important relationships that distinguish the agricultural sector in economic growth.Yorgason (1974) believes that in almost all countries, agriculture is actually an important sector.There is a temporal growth in the agricultural sector whenever we notice a process of growth or development.Besides, Johnston and Mellor (1961) indicated that the importance of the transformation and the size of the labor requirements and the capital needed to develop a modern industrial sector, represent a large burden for agriculture.These authors identified five categories of agricultural contributions to the economic development.These categories are the agricultural production for domestic consumption, the exports of agricultural products and substantial gains on external trade, the transfer of labor in the industrial sector, the flow of money for the capital development and the high incomes in agriculture as a market for industrial products.However, Kuznets (1968) identified only three categories of contributions: product contributions, market contributions and factor contributions.
Although Kuznets and Johnston-Mellor's classifications are artificially important, they did not reach the heart of the problem.Naturally, the contributions of agriculture to economic growth can take several forms.However, we may wonder under which conditions these transfers actually will take place.These classifications indicate what might have happened without giving any real idea of why the process starts or what must be done to maintain or strengthen it.There have been attempts by some economists to produce a theoretical basis for the development of the transfer process.In general, they used the model approach.Although they originally tackled the problem using the transfer of goods and factors, some market transfers were taken into consideration.
Given that the GDP is a perfect measure of economic growth, the debate will be formulated rather around the causality direction between agriculture and economic growth.It should be underlined that these two processes (agriculture and economic growth) are the essential part of our work.Nobody shall hold such a debate without resorting to the concept of efficiency since the concepts of efficiency and profitability cannot conclude this debate in a convincing way.Efficiency will be the centre of inertia of the triangle formed by the agriculture, economy of scale and growth.The concept of efficiency borrowed from the Life Sciences is a fundamental concept which is of a great importance today due to the extent of its field of application.In the managerial, social, and industrial sciences, the concept of efficiency is omnipresent.Today, even the health sector closely examined efficiency.Our study of agriculture is entirely based on the concept of efficiency.For this reason, agriculture will be modelled as a company which uses the capital and labor factors to achieve production.
The study of efficiency refers to the use of resources available in production.The theoretical framework of the efficiency measurement was originally developed by Farrell (1957) in measuring the efficiency of firms or production units within a production process.Efficiency is the best use of resources in production.The decision units, which manage to produce a maximum output from a given level of inputs, or equivalently, a given output from a minimum level of inputs can be considered efficient.The approach is particularly interesting because it uses a concept of relative efficiency, which helps avoids setting a standard characterizing of the efficient situations.A producer will then be considered to be relatively inefficient if another producer uses a lower or equal amount of inputs to produce as many or more outputs.The production function estimation, which is the relationship between the inputs and outputs of the production process in the considered sample, enables then to define the "best practices" located on the production frontier (Djokoto, 2012).This frontier represents the technological limits of what an organization can produce with a given level of inputs.The inefficiency of a decision unit is then measured according to the distance from the frontier.
In what follows, we will go back, in a second section, to a literature review that shows the causal relationship between economic growth and agriculture.The data and models will be presented in the third section.The parametric and non-parametric estimates of the efficiency scores will be the subject of the fourth section.
Finally, the main conclusions will be presented in the last section.

METHODOLOGY Data and variables
Efficiency seen from the angles of its input and output will be measured in a technical and allocative way through non-parametric and parametric methods.In fact, we focus on a third world economy, Togo, about which the data are obtained mainly from the Statistics Centre of Togo.Each variable is characterized by panel data with 15 agricultural products over a period of 20 years, which gives us 300 observations for each variable.The Translog and Cobb-Douglass functions will serve as working tools whereas the ordinary least squares methods help us estimate the coefficients of the models.The efficiency estimate will be ensured using the SFA and DEA methods.Finally, a special attention will be paid to the interpretation of the results.Agricultural data about Togo are very scarce today.The available ones stopped to exist in 1999 or 2001 at the General Directorate of Statistics and National Accounts of Togo (DGSCN).Although these data were of great help for us, we had to complete them in the field through surveys conducted over three months in some Togolese leading agricultural towns, such as, Tsévié, Kpalime Togoville Atakpamé, Sodoké, Dapaong and Sinkassé.In total, we could collect the information required to fill out the gaps left by the DGSCN to reach a 20-year period (1990 to 2009).
We selected a sample of 15 agricultural products to model the total agricultural production.These outputs include: Millet, maize, sorghum, fonio, rice, yam, sweet potato, taro, cassava, beans, cowpeas, bambara groundnuts, inshell peanuts, cotton seeds, cocoa beans and green coffee.The reader should have the right to wonder about the choice of these products.The answer is simple: They are the products selected by the DGSCN to collect national statistics which are more representative of the agricultural production in Togo since these products represent more than 80% of the Togolese agricultural production.The purpose of this choice is to make the Togolese authorities understand this work easily so that they will eventually use it for their future agricultural policies.The food products are at the forefront in terms of volume since they represent more than 75% of the production of this sample.The prevalence of food crops is due to the period chosen for the research.In total, worked work with three variables, namely production (Y), capital stock (K) and labor (L) over a period from 1990 to 2009.
Our major factor is the overall area of the cultivated area in Togo which is estimated at 1072100 ha per year (Table 1), that is to say, approximately 30% of the arable land in Togo.This area is increasing at a rate of 2.72% per year.The labor factor is the number of inhabitants in the agricultural sector in general.On average, 593900 inhabitants work in the agricultural sector each year whose number can vary more or less by 298400 inhabitants per year (Thierry, 2010).The overall production is measured in volume because we do not have the prices of the various products over the studied period.The average production in Togo is of 2082100 tons with an increase of 1.71% per year.

Models
Using two production factors, namely, capital and labor, as well as a trend component to measure evolution over time (t), we limit our work to the use of the Cobb-Douglas and Translog functions (Eric et al., 2004).
The Cobb-Douglas production function is then defined by: Similarly, the Translog production function takes the form:  (Levin et al., 2002).

Variables
To know if the Cobb-Douglas production function advantageously substitutes the Translog specification, we used the likelihood ratio test (LR) to see whether the general Translog functional form, as specified, dominates the Cobb-Douglas functional form.Therefore, we marked by M1 the Cobb-Douglas model and M2 the Translog specification.

Integration analysis
As previously specified, the efficiency estimation is made through two types of methods: the parametric (SFA) and the non-parametric (DEA).However, before we get there, it would be interesting to study the correlations between the study variables.
The used transformed variables are spread over a 20-year period.We therefore need to justify the long-run relationship between them.The tests proposed by Levin et al. (2002) show that none of the variables is stationary in level (Table 2).
Since the variables are not stationary (I[1]), it is necessary to check the existence of a co-integration relationship between the long-term variables of the model (Table 3).Actually, the tests of Pedroni (1999) and McCoskey and Kao (1998) show that the variables are co-integrated and, therefore, the long-term equilibrium relationship is justified.

Estimation models
Concerning the parametric analysis, the efficiency of the agricultural sector in Togo was estimated using four models: A Cobb-Douglas model with and without technical progress (M1) and ( M3) and a Translog model (M2) and (M4) with and without technical progress (Table 4).
In most models (M1, M3 and M4), the results show that the capital and labor, the factors production as well as the trend and the constant are all significant.Moreover, for M2, which represents the Translog function with a nonneutral technical progress model, the results show that the capital output factor is significant whereas the labor and trend are insignificant.This means that agricultural production in Togo depends on the area of the cultivated land and the number of workers in the plantations.
Actually, this production induces an upward trend for M1 of 2.4% per year.Hence, if the cultivated area increases by 1%, production rises by 0.94%, and if the number of workers goes up by 1%, production rises by 0.18%.
The minimum log production in Togo is 1.673, which gives a real production of 5328 tons per year.However, at the level of the M4 model, production induces an upward trend of 3.3% per year.Thus, if the cultivated area increases by 1%, production rises by 0.9%, and if the number of workers increases by 1%, production goes up by 0.27%, that is a minimum production of 5640 tons per year.
The LR tests of maximum likelihood help choose the model that best describes the Togolese agricultural production.Indeed, comparing M1 and M3 models gives a value of the likelihood ratio equal to 13.84 above the critical value of the chi-square table at 5% (7.11), which makes us reject the null hypothesis.In other words, M1 model is preferred to M3, and the Cobb-Douglas model for non-neutral technical progress is preferable in this case.Furthermore, the comparison of M2 and M4 models gives a value of the likelihood ratio equal to 2.32 but inferior to the critical value of the chi-square table at 5% (7.11), which makes us accept the null hypothesis.Consequently, the M4 model is preferred to M2.For the Translog specification, we accept the model with a neutral technical progress.
Finally, the comparison of the M1 and M4 models gives a value of the likelihood ratio equal to 4.2 but inferior to the critical value of the chi-square table at 5% (7.11).Therefore, the null hypothesis where the M4 model is preferred to M1 is accepted.In the end, the Translog specification with a neutral technical progress is better than the Cobb-Douglas one.

Estimation of technical efficiencies in the agricultural sector of Togo
From the above estimates, we will discuss the estimation of the efficiency scores of the Togolese agriculture.Actually, the SFA method shows the following efficiency scores related to the various specifications selected above: 75.3, 75.6, 75.8 and 76.3% (Figure 1).These scores show that the rate of the input use is generally acceptable (Somayeh et al., 2012).More precisely, the Togolese farmers can use at least 25% of the agricultural resources to achieve the same level of production.
Rice, maize, bambara groundnut, peanut, coffee bean, cocoa are products that have efficiency scores above the found average scores (Figure 2).These five products are all grown in highlands where agriculture is flourishing.This area receives annually a large amount of rainfall and farmers there are very laborious.Cocoa takes the top spot with 97.6% while the yam is around 7%. Products that have high efficiency scores are either for exportation or food products mainly for consumption.
Using the SFA approach, we could see that the Togolese agriculture has a minimum efficiency of 75%, which means that is very efficient in using these resources.Besides, we can observe a uniformity of efficiencies along the 20-year study period.The consistency of this efficiency shows that farmers are steady in the management of the agricultural resources.We noticed that the labor force shrinks through time whereas efficiency remains stable.Furthermore,  production remains constant or tends to decline slightly.We can see from this that agriculture is being specialized and modernized because the minimum number of farmers who keep domestic production constant owe it to an efficient work organization.
On the basis of the non-parametric DEA approach, overall efficiency is estimated at 61.2% for constant returns to scale and 45.8% for variable returns to scale (Figure 3).The highest efficiency is that of the cocoa, with 83.6%.Beside cocoa, the other products that have efficiency above 80% are coffee and beans (Figure 4).We can wonder why coffee and cocoa are export products; is it because they are the most favorable cultivated products?We do not think so because cotton, the Togolese main export product, is efficient only at 49% whereas the bean, which is a food product for local consumption, reached an efficiency score of more than 80%.The most frightening case is that of the yam which has an efficiency of 0%, in fact, it is the most inefficient product maybe due to the archaic way it is grown.Yam is predominantly grown in highland areas where the other products have very high efficiency scores.Would farmers have preferred some kinds of products to others?
The DEA method gives efficiency scores that do not exceed 65%.Taking into account the constant returns to scale, we can see that efficiency scores are around 60%, whereas those of the variable returns to scale do not exceed 50%.This second consideration shows a totally inefficient agriculture throughout the reporting period of this research.This vision of the Togolese agriculture can be explained by the youth's widespread lack of interest in agriculture, which means that the resources (labor and land) are available but poorly used.However, the opposite view, which considers constant returns to scale, goes with the SFA vision of the Togolese agriculture.

COMPARISON AND DISCUSSION OF RESULTS
The efficiency estimate of the Togolese agriculture using the SFA and DEA methods identified different and sometimes contradictory results.However, the SFA method showed that the Togolese agriculture, with or without technical progress, is efficient regarding the Cobb-Douglas and Translog functions (Table 5).However, the DEA method revealed conflicting results depending on whether we put ourselves in a context of constant or variable returns to scale.With the constant returns to scale, the efficiency score is 0.612 because there is no huge wastage.This means that the Togolese  agricultural resource management is acceptable.With non-constant returns to scale, the efficiency score is 0.458.This clearly means that the management of the Togolese agricultural wealth has failed.The differences between the SFA and DEA are based on the concept that these approaches have some distance from the efficiency frontier.
The DEA method ignores the measurement errors.Therefore, the whole distance from the frontier is considered inefficiency.On the other, the SFA method, which considers measurement errors, seems to be more realistic.It is noteworthy that the SFA method is more efficient for theoretical studies, whereas the DEA is very useful for practical or empirical studies.Therefore, the conclusion drawn is that, in general, the Togolese agriculture is inefficient like the finding of Agossou (2009).
The general findings show that the agricultural labor in Togo is shrinking the cultivated is increasing nonchalantly and production tends to stagnate.Instead of announcing the death of the Togolese agriculture, these indices are rather encouraging because it is easily seen that the increase of agricultural labor in Togo will necessarily propel agricultural production.We should not either declare victory because the results via the DEA analysis are inconsistent with the idea of a promising Togolese agriculture.All we can keep from this analysis is that agriculture in Togo is promising and all the efforts made to increase awareness, investment and innovation in this area will pay off.

Conclusion
The empirical study of the Togolese agriculture efficiency gave results that defy the prejudices about agriculture.Beyond the pessimistic views that discourage investors, this study revealed a reality quite opposite to the widespread ideas about the Togolese agriculture and Africa in general.The stochastic frontier analysis method shows that the Togolese agriculture is weakly efficient.This observation was affirmed by the results of the DEA method.However, we prefer the SFA which shows that the Togolese agriculture is generally better efficient.By referring to the DEA, which is more empirical than the SFA, we will find ourselves forced to consider that the Togolese agriculture is globally inefficient.

Figure 2 .Figure 3 .
Figure 2. By product average efficiency with SFA

Figure 4 .
Figure 4.By product average efficiency with DEA.

Table 1 .
Descriptive analysis of the variables.
S-D, Standard deviation.

Table 2 .
Unit root test of

Table 3 .
Co-integration tests of the various variables.

Table 4 .
Estimates of the models through the SFA.

Table 5 .
Comparison of the average efficiency scores SFA and DEA.