BUKU: Distance Function Approach to Measure Efficiency: Data Envelopment Analysis

In order to measure the technical efficiency of any observed input-output bundle one needs to know the maximum quantity of output that can be produced from the relevant input bundle. One possibility is to explicitly specify a production function. 

The value of this function at the input level under consideration denotes the maximum producible output quantity. It is common to estimate the parameters of the specified function empirically from a sample of input-output data. Because the least squares procedure permits observed points to lie above the fitted line, in a stochastic frontier model one includes a composite error. 

The composite error is a sum of a one-sided disturbance term representing shortfalls of the actually produced output from the frontier due to inefficiency and two sided disturbance term representing upward or downward shifts in the frontier itself due to the random factors. The econometric procedure requires relation of a particular functional form.The distance function representation of a production technology, proposed by Shephard (1953, 1970), provides a multi output primal alternative, which requires no aggregation, no prices and no behavioural assumption.