Formation and efficient estimation of stochastic frontier production functions

Abstract

Technological change and efficiency improvement are important sources of productivity growth in any economy. The concept of technical efficiency (TE) is based on input and output relationships. Technical inefficiency arises when actual or observed output from a given input mix is less than a possible mix. The analysis of technical efficiency involves the assessment of the degree to which the production technologies are utilized. The present investigation on “Formation and efficient estimation of stochastic frontier production functions” was carried out in the Department of Agricultural Statistics, College of Horticulture, Vellanikkara during 2010-13, to assess the present economics of pepper cultivation, to formulate new stochastic frontier production functions and to compare them. The secondary data collected from the Department of Plantation Crops and Spices, College of Horticulture, Vellanikkara on area of holdings, number of vines, yield, expenses for machinary, labour, manure, and other expenses for the cultivation of pepper in the three blocks viz; Mananthavady, Kalpetta and Bathery were used for the analysis. The summary statistics revealed that irrespective of the blocks, the expenditure on labour was the highest followed by expenditure on manure and it was increasing according to the increase in age of plants. For the stochastic frontier production model to be realistic, exact measurement of the cost of the inputs as also the realized output is extremely necessary. Very few farmers keep records of the expenditure incurred on the various inputs and very rarely the output realized. Vegetable crops have a short duration. So the farmer will be in a position to give realistic figures regarding the various inputs as also the outputs. As regards plantation crops, there will be a lag right from establishment of the crop to the steady bearing stage. Therefore, it will be very difficult to trace back the exact cost, as no records would be available about the costs incurred. A rapid estimation survey is the only feasibility where in simultaneous estimation of the costs involved at from the nursery through the various stages of growth can be observed. Since a farmer who is already having a steady bearing crop, would have incurred lesser costs through the previous stages of growth of the crop, it is most feasible to use the concept of present worth to arrive at exact costs of previous stages of the crop. The stochastic frontier analysis was done using the present value (PV) as also with the present cost. The stochastic frontier analysis (SFA) was done for all the three blocks compounding all the costs starting from the nursery stage (First age group) up to the steady bearing stage (Fourth age group) using PV. The mean technical efficiency was observed to be 0.93, 0.91 and 0.94 for Mananthavady, Kalpetta and Bathery Blocks respectively. The stochastic frontier approach for each age group by pooling over the blocks, were also worked out using PV and it revealed a mean technical efficiency of 0.95 and 0.92 for the plantations in the third and fourth age groups respectively. To assess the factors influencing technical efficiency, the regression of TE on the factors like area of holdings, number of vines, cost for implements and machinary, labour, manure and other expenses was fitted for each block. About 91 per cent of the variation in technical efficiency could be explained using these variables. When the area of holdings increased, the technical efficiency seemed to decrease. With proper labour management, the technical efficiency can be significantly improved.