ICT and e-Business Impact in the Retail Industry - empirica

e-Business in the Retail SectorK = capital, L = labourSource: DIWThe stochastic production possibility approach is not a method for directly estimatingimpact factors on labour productivity. However, through modifying the variables, i.e.through dividing them by Total Working Hours, a constellation can be created that allowsto draw conclusions about the contribution of single variables on labour productivity.If, given the factor input set, the produced output level stays below the potential maximumlevel, then the respective inefficient use of resources indicates indirectly that the wholeproduction system or, at the micro level the single producer, faces an inability to matchthe best available practice. Farrell (1957) was the first to distinguish between technicaland allocative efficiency. Technical efficiency reflects the ability of a firm to obtainmaximal output from a given set of inputs. Allocative efficiency is used for the ability of afirm to use the inputs in optimal proportions, given their respective prices. Thecombination of both gives a measure of the total economic efficiency.Assuming log-linear production function where i countries produce their output given thetechnological parameter β , the stochastic production possibility frontier is nowdetermined by two types of random errors. The always positive inefficiency randomvariable u , and the new random error term v , which has the usual properties ofiidentical independent normally distributed errors with a mean value of zero and aconstant variance, σ .2vm∑ln( y ) = β + x ⋅ β + v − u for i = 1,..., Ni 0ij j i ij=1iThe production frontier is therefore determined by the deterministic part plus a stochasticpart consisting of a mixture of two probability distributions: a non-negative one, forinstance a positive truncated normal distribution, and the usual normal distribution of theerror term. Estimating a stochastic production possibility frontier therefore involvesestimating the parameters of the two probability distributions simultaneously.The stochastic frontier function is accordingly bounded from above by205