Input Use and Efficiency across Stages of Crop Production: A Micro Level Decision Making Process of Farmers

According to Wharton (1963), agricultural development consists of essentially three stages  traditional (or static), transitional (Labour intensive) and dynamic (capital intensive). Mellor (1966) further places two boundaries between these three stages. The first stage is a technological boundary between the traditional and labour intensive transitional stage; and the second boundary between transition and dynamic stage is identified by change in the cost of labour relative to capital (Hatchett, 1984).
       
The traditional agriculture is characterized by large dependency on agriculture, rise in the demand for agricultural produce, scarce capital, small farm size and less mechanization due to non viability. In the transitional stage, increase in agricultural output and productivity are seen as dependent on technological and institutional changes, which gradually gather momentum (Hayami and Rutton, 1971). In this stage, the emphasis is on increasing the yield per unit of land due to relative shortage of land. The dynamic stage points to a fundamental economic change. Non-farm sectors become larger and draw increasing quantities of labour out of agriculture, and hence, agricultural labour becomes more costly relative to capital. More labour saving machinery is profitably used in agriculture. This agricultural stage model assumes that all less developed nations pass in sequence from the traditional stage into a labour intensive transitional stage before the cost of labour rises appreciably relative to capital.
       
The yield per unit of land and other variable inputs differs in different stages of development (Antle, 1983). As most of the agricultural technologies are location specific, the highly productive technologies which were progressively more advanced in the developed countries exhibit poor results in developing nations where the climatic condition and resource endowments are totally different or scarce. This makes the diffusion model inapplicable in developing countries. After observing the poor performance of the diffusion model, Schultz (1964) developed a high pay off input model.
 
Theoretical underpinnings- High pay off input model
 
Schultz (1964) emphasizes that peasants in traditional agriculture are rational resource allocators and nevertheless, they remain poor because in most poor countries, there are very limited technical and economic opportunities to which they can respond. Schultz (1964) stated that agricultural experiment stations and businesses, which provide higher  productivity capital equipment and other inputs to farmers, are the source of the new high pay off, or high  return, inputs for agriculture. He further proposes that increase in the quality of farm people increases the agricultural productivity. He hypothesized that the right sort of education to farmers can provide high returns to farmers and the rest of society (Ibid).
       
These two hypotheses provide the fundamental elements for a micro economic theory to explain both the stability of agricultural production in traditional agricultural areas and how more rapid agricultural growth may be achieved (Roumasset, 1976). Nevertheless, Schultz’s high pay off input model is largely limited to micro level. As the high  pay  off input model envisages, in conformity with the change in the stages of technological development, the yield from the same quantum of input changes from one category of farmers to other. In addition to this, the timing of input application also plays a significant role in getting a good result. The dynamic production function of different stages explains clearly the result of the timing of inputs and engineering relationship of inputs.

This study intends to analyze the input efficiency across different stages of crop cultivation for different crops in two diverse agro climatic regions like assured irrigated wet region and drought prone rainfed dry region. Data for the study was enumerated from assured irrigated modern agriculture region namely Cholavandhan and from highly drought prone traditionally rainfed agriculture region viz., Usilampatti in Madurai district in Tamil Nadu. A stratified random sampling technique was used to identify the respondents. At the first stage of sample design, the whole population was stratified into three strata, viz, large farmers, owner cultivators and tenant cultivators. This classification was done with the help of ownership of land and extent of land owned (less than five acres as owner cultivators and above five acres as large farmers). On the basis of these criteria, three categories were identified from the sample frame. Since tenant cultivation was not practiced much in the dry land region, this category was not taken in the dry region.  From each of this category, randomly 35 farmers were taken as respondents for the study. Initially a census survey to identify the population for the study was done. After identifying the population and sample respondents, survey was conducted with a pretested questionnaire. A total of 175 samples were taken from irrigated modern agriculture region (35 * 3 = 105) and drought prone traditional agriculture region (35 * 2 = 70).
               
This production process is modeled by breaking it into a series of stages, for each stage inputs have different efficiency on the output. It has been thus broken into three stages, viz.,
 
(a) Initial crop stage – land preparation, basal manuring and planting
(b) Intermediate crop state or vegetation stage- from planting to blooming stage
(c) Maturation stage – blooming to harvest
 
       
The decisions on each subsequent stage depend on the decisions made at the preceding stage. The input decisions in each stage are thus complementary in nature.
       
The choice of functional form in empirical models involves weighing theoretical and practical considerations. According to Hatchett (1984) the two important considerations include viz. (1) Is the model valid? (2) Is it tractable? Tractability becomes particularly important when the equations are to be derived from the dynamic stochastic model. The great majority of functional forms used in economic production analysis are categorized as first order expansions. Widely used first order functions are:
 
Linear: (Additive Separable)  ...........1
Y =  a + b1X1... bnXn+e      
Y =  a + bIni + e
Y =  a + bVeg + e
Y =  a + bMat + e
Y =  a + b(Ini + Veg) + e
Y =  a + b(Ini + Veg + Mat) + e
 
Cobb Douglas: (Additive Separable)  ............2
InY = a + b1InX1... bnIXn +e
InY = a + bInIni + e
InY = a + bInVeg + e
InY = a + bInMat +e
InY = a + bIn(Ini + Veg) + e
InY = a + bIn(Ini + Veg +Mat) + e
 
       
These two are scrimpy in the parameters and additively separable. The restrictions imposed by the linear model are: constant marginal product and unbounded output. The Cobb Douglas imposes constant input elasticity and unitary elasticity of substitution. These two functional forms are used to find out the efficiency of inputs in different stages to output and to derive the elasticity of substitution at different stages to output.
 
Analytical framework
 
These first order functional forms have been used to assess the efficiency and elasticity of inputs in different stages on output. Correlation matrices were computed for all crops and for all categories of farmers. It exhibited that there is a high correlation between inputs and output. This high correlation also explicates the presence of the multi-collinearity problem. But it is understood that the cost of cultivation data always will have this problem as all the inputs have to be increased in some proportion to raise the production in a given engineering relationship of inputs. Accordingly each stage is regressed separately on output with zero intercept (through origin) for all crops and for all categories of farmers in the two situations separately.

The results of the linear regression are presented separately for the two different situations. Table 1 presents the linear regression co efficients for different stages of inputs and additive inputs in wet area. This manifests that inputs at the vegetation stage are more efficient on output than inputs of other stages. Across the categories of farmers, vegetation stage is more efficient for large farmers except in the case of banana, for which owner cultivator category exhibits higher efficiency. In all the stages except initial stage, large farmers demonstrate a higher efficiency for all crops except banana. In the initial stage, owner cultivators are more efficient to all crops, for initial stage inputs like ploughing, manure and seed are owned by the owner cultivators and they use it liberally and efficiently. The owner cultivators are not able to follow the same tempo in the subsequent stages because the inputs used in the subsequent stages are purchased inputs like fertilizers, pesticides, weedicides, etc., and the use of which inflicts heavy financial burden on them. But in the case of banana, owner cultivators register a high efficiency because banana crop requires daily care and personal touch.
 

 
In the case of paddy, while the maturation stage inputs exhibit more efficiency for owner cultivators, the vegetative stage inputs demonstrate a higher co efficient in the other two categories of farmers. In the case of additive variable of all the three stages, large farmers disclose a higher co efficient. The tenant cultivators exhibit a very low efficiency in all stages because they pay exorbitant rent. In the case of banana, owner cultivators show a high efficiency in all stages and in the additive variable too. As mentioned earlier, banana requires personal care at every stage of input decision. In the case of sugarcane, owner cultivators display a low efficiency in all the stages because it requires more monetized inputs.
       
The above discussion leads to infer that owner cultivators are more efficient in the initial stage input decisions while large farmers reported a higher efficiency in all other stages and all stages together for all crops except banana. Tenant cultivators show a better efficiency only in the case of sugarcane. This also indicates that the inverse relationship between land and productivity works for only banana crop or in other words to highly labour intensive crops. 
       
Contrary to this, in the dry area, Table 2 explicates that owner cultivators are more efficient input decision makers than the large farmers in the case of paddy and groundnut. It is because large farms are exposed to many exogenous factors like rodents, birds and other cattle attacks. In all the stages, owner cultivators exhibit a higher efficiency including for additive inputs for both paddy and groundnut. In both cases, they show higher efficiency in the maturation stage input, for they are able to manage the exogenous elements efficiently. In the case of paddy, rats and birds take away the yield while for groundnut wild animals and cattle remove the nuts and spoil the plants. In the case of cotton, large farmers are more efficient because the yield increase depends on the use of pesticides to combat white flies menace at the blooming stage. Pesticide use is limited in the case of the owner cultivators due to financial constraints. In the case of jowar, large farmers are more efficient decision makers. The results also transpire that the small farms are exceedingly efficient in the cultivation of food crops like paddy whereas the large farmers are remarkably efficient in the cultivation of commercial crops.
 

       
This discussion brings out that maturation stage inputs are more efficient contributors to output. It also exhibits that while owner cultivators are more efficient in the case of paddy and groundnut, large farmers are efficient in the case of other two cultivars, viz. jowar and cotton.
       
The linear regression results by and large, leads us to draw the inference that while vegetation stage input use remain more efficient contributors on output in wet area, the maturation stage inputs tend to be  significant factors in the dry area. However, in the wet area, owner cultivators are more efficient in the initial stage input decision for all crops but in the dry area, they are significantly efficient in all stage input decisions for paddy and groundnut. This manifests that large farms remain unviable in the dry regions. This also indicates that inverse relationship hypothesis works well in the case of labour intensive food crops while it is otherwise in the case of commercial crops.
 
Controlled Cobb Douglas Production Function
 
Optimal input stage is derived from the controlled model with the three stage Cobb Douglas production function. An important feature of this model is that it is not necessary to have knowledge of the structural co efficients of the single stage production functions. The results of this function are presented in Table 3 and 4.
 

 

       
Table 3 presents the results of the double log function for different crops in the wet area. It indicates that all the variables have more than unity elasticity of output. Banana shows higher elasticity for all input stages and in additive inputs for all categories of farmers. Similar to linear regression results, banana has the highest elasticity of output for inputs in all stages. This insinuates that vegetation stage inputs have higher elasticity on output than other stage inputs. By category of farmers, elasticity coefficients are relatively higher for banana and paddy crops for owner cultivators, while among large farmers, it is higher for sugarcane. The tenant cultivators, in all crops, displayed a lower elasticity. This reiterates that owner cultivators remain highly efficient in their input use in the case of food crops where as large farmers tend to be effective in the cultivation of commercial crops.
       
In contrast to this, in the dry area, Table 4 discloses that owner cultivators’ input decisions have more than unity elasticity of output for paddy and groundnut. Initial stage input decisions have higher elasticity for all crops. This substantiates that owner cultivators are more efficient in initial stage input decisions. In the maturation stage too, owner cultivators exhibit a very high elasticity for all crops. Even in the vegetation stage, they show a higher elasticity for all crops except jowar. This draws the inference that owner cultivators’ input decisions are highly efficient.
       
Similarly, across stages, the maturation stage displays a high elasticity to both categories of farmers for all crops. This reveals that maturation stage input decisions contribute more than other stage decisions in dry area. In the additive variables, it shows higher elasticity in the first two stage additive than the elasticity of all the three stages together. Among the crops, groundnut shows the highest response to inputs while jowar shows the lowest.
       
This double log function analysis draws the inference that while vegetation stage inputs have a higher elasticity of output in wet area, the maturation stage inputs have a higher elasticity of output in dry area. It also manifests that while large farmers are more efficient in commercial crops, owner cultivators appear to be more efficient in the food crops. This also reiterates that the inverse relationship hypothesis between land size and productivity still holds water in the case of food crops.
 
Concluding observations and Policy implications
 
The dynamic input decision analysis produces information quite different from experimentally based production function studies (Puhazhendi, 1987). The dynamic process examined here brings out input use at different stages of the crop cultivation and its impact on the stochastic output.
       
The linear regression results indicate that while vegetation stage inputs contribute more on output in wet area, maturation stage inputs are more efficient in dry area. The Cobb Douglas production function result manifests that while input decisions of large farmers have a higher elasticity of output in wet area, the decisions of owner cultivators have a higher elasticity of output in the dry area. The Total Factor Productivity calculated through additive inputs of all stages also and presented in the last column of the Findings indicate an increasing return to scale in the input efficiency. Similar observation was made by Sanap et al., (2016). Structure of input decision making process differs from wet area to dry area and the consequent output as well as efficiency also differs between categories of farmers. Once the farmers begin their cultivation, they only focus their efforts on maximization of output not on farm gate prices This was reiterated in an earlier study by Rajasekaran (2010).
      
Thus findings vividly manifest that there remains a multitude of input efficiency differentials across crops, across stages of production and across regions. Hence a deeper understanding of input use becomes an essential component in the policy making. It reiterates the relevance of bringing more structural equality in the climatic regions to improve the efficiency of the input and its use. This was substantiated in the study of Kumar and Upadhyay (2019). The findings also emphatically suggest the relevance of time in input use, for input use in vegetation stage tends to be remarkably productive for certain crops where as input use in maturation stage remains phenomenally efficient for some crops in the dry region. Similar results were found in the study of Singh and Vaishali (2016). The poor efficiency of tenant cultivators due to high rent suggests that tenancy in all forms should be reformed to improve its efficiency. Hence it advocates the policy makers to provide emphasis on these components and make the necessary inputs available during the appropriate stage of crops. 

I gratefully acknowledge Dr. R.S. Deshpande and Dr. V.S. Satyapriya, ISEC, Bangalore for helping me unassumingly in formulating the idea and completing the analysis. I thank profoundly the referees of the journal and editorial personnel for their intriguing comments and suggestions to enhance the quality of the paper. Nevertheless I remain responsible for the errors and omissions if any.