Demand-Driven Technologies for Sustainable Maize ... - IITA

393Farm-specific efficiencyFor the investigation of the technical, allocative and economiceffi ciencies of improved maize producers, the following stochasticfrontier production function was estimated:lnY = β + β ln( land ) + β ln( labor )i 0 1 i 2i+ β ln( fertilizer) + β ln( materials ) + ( V −U)3 4i i i(9)where ln denotes the natural logarithm (base, e); Y idenotes the totalquantity of maize output in kg; land denotes the total land planted tomaize in hectares; labor denotes the total of family labor, exchangelabor, and hired labor used in man-days; materials denotes theimplicit quantity index of seeds and chemicals (pesticides, insecticides,herbicides, and fungicides) estimated as the value of all seeds andchemicals defl ated by a weighted price index of the inputs, theweights being the share of each input in total cost ; and βi, vi, uiareas defi ned earlier.The solution to the cost minimization problem in equation (10) isthe basis for deriving the dual cost frontier, given the input prices( Wk), parameter estimates of the stochastic frontier production functionβ ) and the adjusted output level Y .( ˆkKk = 1*iMin C = ∑ WkXkx(10)* ˆSubject to ˆ kYi= A∏X βkSubstitution of the cost k minimizing input quantities yields the followingdual cost function:* 1 2 α34 *CY ( , W) = ψW α AW α LWF W α MYμ(11)ˆwhere αk= μβk, μ = ( ∑ β ) ˆk−1K−μ1 ⎛ˆk , ˆ ˆ β ⎞kψ = A βkμ⎜ ∏ ⎟ ,⎝ k = 1 ⎠A ˆ = exp( βˆ0) , WAis the observed mean seasonal rent of a hectare ofland in Birr (1US$=8.50 Birr), WLis the observed mean daily wagesin Birr; WFis the price of fertilizer per kg in Birr; and WMis the priceindex of seeds and chemicals.Factors affecting efficiencySeveral factors could be hypothesized to explain technical, allocative,and economic effi ciency variations. Many authors (Kalirajan andShand 1989; Assefa 1995; Getachew 1995; Coelli and Battese 1996)suggested that the level of effi ciency of farmers is determined by a