Philip A. Viton

A Test of HTML Production in SWP4

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Econometric Approaches

Econometric approaches to cost efficiency estimate a parametric cost function and then identify cost efficiency via differences between observed cost and the minimum predicted cost. (A second approach is presented in section dea) Consider carrier in year . It has a -vector of system characteristics and produces the -vector of outputs from the -vector of inputs according to the transformation function It is assumed to face the factor prices Its (minimum) cost function is the indirect objective function of the problem: choose inputs to minimize cost subject to (the production function), ie:

If is the observed cost of carrier in year , we allow for a failure to attain the minimum cost by writing

where is a random variable, so that

Because the observed cost cannot exceed the theoretical minimum cost is necessarily non-negative. We obtain a parametric cost function by specifying a functional form for For the remainder of this section, we shall assume that the cost function is translog in inputs and outputs; but that system characteristics enter linearly. Note_1 Then we may write equation (linear) as:

The theory of cost minimization implies that is homogeneous of degree zero in input prices, which places restrictions on the parameters of the cost function (see, eg, [spady-friedlaender:78]); in addition the parameters and are symmetric, so that, for example

The DEA Approach

Data Envelopment Analysis, or DEA, see, eg [bcc:84], or [fgl:94], begins by constructing the set of feasible input-output combinations. (Another approach was presented in section econometric) It then finds, with reference to that set, the input bundle that minimizes the cost of producing the observed output. DEA is non-parametric in that it makes no assumption about the structure of the cost function --- indeed it does not explicitly obtain the cost function at all --- and, being non-statistical, it has no need for parametric distributional assumptions. Note_2 To construct the feasible set it begins by assuming that the observed input-output combinations (the data) are feasible and then adds unobserved combinations by considerations of additivity (scale) and disposal. Note_3

The upshot is that cost-minimizing carrier selects an input bundle to minimize total cost, subject to feasibility; and this is the solution to the non-linear program

and we define the cost-efficiency of carrier at period by

the ratio of observed to minimal cost.