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 ) 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

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 () 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 ) 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.