Home | Business News | Browse by Publication | I | International Advances in Economic Research

Variable selection for dynamic measures of efficiency in the computer industry.

Article Excerpt
Abstract

Data Envelopment Analysis (DEA) measures of efficiency are very sensitive to the choice of variables for two reasons: the number of efficient firms is directly related to the number (n) of variables and the selection of the n variables greatly affects the measure of efficiency. A methodology is proposed which identifies the optimal number of variables, and which identifies the contribution of each variable to the measure of efficiency. The computer industry is used as an example to illustrate the method. (JEL L63)

Introduction

Two approaches are commonly used to measure efficiency: the parametric approach, which relies on statistical techniques to estimate the parameters of a production function, and the non-parametric approach, which compares the observed inputs and outputs of each firm with that of the most performing firms in the information set. The parametric approach has been subject to persistent criticism, centered on two points; the assumption that the production function has the same functional form for all the firms, and the fact that econometric estimation of efficiency can produce biased and inconsistent parameter estimates (since an econometric measure of efficiency reflects the average performance and not the best performance). Data Envelopment Analysis (DEA) is now the most popular method used to measure efficiency. (1) DEA is a non-parametric method, which does not assume any specific production function. Instead, it uses linear programming to identify points on a convex hull defined by the inputs and outputs of the most efficient firms (Any productive unit, like a firm, is called a Decision Making Unit (DMU) in the literature of DEA). Two critical elements account for the strength of the DEA approach: (1) no a-priori structure is placed on the production process of the firm, and (2) the models can yield a measure of efficiency even with a very small number of data points. The first point is particularly important because the measure of efficiency is based upon the best practice of the DMUs at any of the levels of output observed.

This paper is focused on measuring efficiency when the number of firms is few and or when the number of explanatory variables needed to compute the measure of efficiency is too large to allow for the statistical approach. Hence, a variable selection method is presented for the deterministic DEA approach. First, a definition of different measures of efficiency and the various DEA models used to measure efficiency is provided and then a variable selection method is proposed. Finally the method is applied to the computer industry.

Measures of Efficiency

Modeling efficiency with non-parametric tools was first introduced as an extension of activity analysis. The CCR model [Charnes, Cooper, and Rhodes, 1978] formally introduced the linear programming to measure technical efficiency with the assumption of constant returns to scale. In the CCR model, DMUs adjust either their use of inputs or their outputs to reach the production frontier. The BCC model [Banker, Charnes, and Cooper, 1984] removed the assumption of constant returns to scale, and Charnes et al. [1985] proposed the additive DEA model, where both inputs and outputs can be adjusted simultaneously. All models use the distance to one of the facets of the production or cost frontier to generate an efficiency index. Numerous stochastic extensions of the DEA approach allow for both a deterministic part and a stochastic element that captures random influences on optimization not under the producer's control [for example, Sengupta, 2000; Grosskopf, 1996].

Overall efficiency can be expressed as the product of two mutually exclusive components; (2) technical and allocative efficiency [Farrell, 1957]. Both allocative and technical efficiency can be obtained with DEA. Technical efficiency is a measure of a DMU's ability to produce at a point on the production frontier and is independent of input and output prices. A technically inefficient DMU can become more efficient by: (1) reducing its use of inputs while maintaining its outputs constant; (2) by increasing its outputs while maintaining its inputs constant; or (3) by changing both its inputs and outputs. Hence, measures of technical efficiency must specify the adjustment strategy chosen by the DMU. It is difficult to separate the effect of technological progress from technical inefficiency because both can contribute to an increase in output (or a decrease in inputs). Consequently, estimations of technical progress are biased and inconsistent when technical inefficiencies are present, and measures of productivity change may be incorrect.

Allocative efficiency is a measure of the DMU's ability to produce in an economically efficient manner while on the production frontier (that is, allocative inefficiency measures the degree by which a firm fails to allocate inputs optimally into the production process at prevailing input prices). Like technical efficiency, the measure of allocative efficiency can have an input orientation (minimize the cost of inputs), an output orientation (maximize revenue), or a mixed input and output orientation (maximize profits).

The DEA approach also has also earned its own set of criticisms, centered on two points: (1) measures of technical efficiency are very sensitive to the omission of variables from the production function and (2) efficiency scores are biased if the degree of freedom is not uniform for all DMUs. (3) Some critics also argue that the linear aggregation of inputs introduces a bias in the measurement, and that radial measures overestimate efficiency because they neglect the slack variables (for example, the BCC and CCR models). One should also consider the market structure for the interpretation of the measures of technical and allocative efficiency; a poor efficiency index it does not necessarily reflect a poor use of the inputs as it can also reflect the deliberate (profit maximizing) strategy of a DMUs who maintains excess capacity as a threat to entrants.

Variable Selection

The criteria for the choice of which explanatory variables (inputs or outputs) to include in a DEA model are rarely made explicit. The practice has been to select the variables by simply choosing the ones that make economic sense, and then validate the choice of a subset of the chosen variables using statistical analysis. Variable selection is crucial to the process as the omission of some of the inputs can have a large effect on the measure of technical efficiency. Variable selection is further complicated because it is difficult to measure some attributes of the inputs and outputs (quality of...