Application of Stochastic Frontier Production Function to Separate the Effect of Random Variation in Output from Inefficiency in the Agricultural Production of African Countries

Abstract

The paper applied the stochastic frontier production function to separate the effect of random variation in output from inefficiency in the agricultural production of African countries. The general Cobb-Douglas and translog functional forms were tested for adequate functional form. A Quasi-translog production frontier function was specified using a balanced panel data of 26 African countries, drawn from Food and Agriculture Organization covering the period 1961-2009. The parameters in the Quasi translog stochastic frontier production function were estimated by the maximum-likelihood method using FRONTIER 4.1. The stochastic frontier incorporates stochastic output variability by means of a two-part error term. In order to separate deviations away from the frontier production function into random variation and inefficiency, a distribution assumption for both parts of the error term was imposed and the error term of the stochastic frontier calculated. The test result suggests that the random term has a truncated normal distribution. Out of the five input variables used, land, labour and livestock significantly influence the agricultural production of the panel of African countries. Furthermore, the agricultural production function operated at a technical regress in a panel of African countries, implying that there is a possibility to increase production by improving the use of input resource. It was observed that 92.4% of the variation in output was due to technical inefficiency. While 7.6% of the variation in output is explained by the stochastic random variation, implying that the agricultural industry stochastic random error is important in explaining the total variability of agricultural output produced. This was not unexpected in the African agricultural production where random shocks or measurement error are assumed to be vital sources of variation in output.