Production Functions for Wheat Farmers in Selected Districts of Pakistan: An Application of a Stochastic Frontier Production Function with Time-varying Inefficiency Effects

Abstract

Two models of technical inefficiency with a stochastic production frontier are considered in this paper. In the frrst model, it is assumed that the frontier itself does not vary with time, while in the second, the frontier is allowed to move. These models are applied to four years of panel data on wheat farmers in four districts of Pakistan: Faisalabad and Attock in the Punjab, Badin in Sindh, and Dir in the NWFP. Using essentially the same stochastic frontier production function in each of the four districts involved, different stochastic specifications for the inefficiency effects are obtained for the different districts. Technical efficiencies of production of the individual farmers are predicted in each year in which they are observed. Varying patterns of technical inefficiency are observed. The null hypothesis (of no technical inefficiency) cannot be rejected in only one district. In the other districts, while inefficiencies appear to be present in all of them, they are declining at a fairly rapid pace in one. The results highlight the importance of analysis at a disaggregated level because it is clear that both the rate of technical change and relative efficiencies vary across regions and explicit cognisance must be taken of this both in research and policy formulation.