Measuring Business Performance
3.3 Important Terms Used in Performance Studies
3.3.1 Economical, allocative and technical efficiency
Economists use the term productive efficiency to describe how well an organizational unit performs in utilizing resources to generate outputs or outcomes. In 1957,Farrell,a pioneer in this field,demonstrated that eco- nomical efficiency5can be decomposed into allocative efficiency and technical efficiency (Farrell, 1957).
A company is economically efficient when it produces a certain level of output at the lowest feasible cost. Costs may rise above the lowest possible level due to lack of either technical or allocative efficiency. Economic efficiency is a more inclusive requirement than technical or allocative efficiency,as both technical and allocative efficiency are required to achieve economic efficiency.
A company is technically efficient when it produces a certain level of out- put by using the minimum level of physical inputs. An example of technical inefficiency is when more people than necessary are used to carry out a certain task. A company is allocatively efficient when it uses inputs in the right propor- tion (for given input prices) to produce a certain level of output. An example of allocative inefficiency is when a high priced input is used when a cheaper one is all that is needed (i.e. wrong input mix),e.g. when company managers dedicate time to secretarial tasks such as typing (on a regular basis) instead of thinking how best to run the company (Cubbin and Tzanidakis, 1998).
The difference between technical and allocative efficiency is illustrated in Fig. 3.4,where it is assumed that output is produced by two factorsx1and x2,with the curveψbeing an output-isoquant. To bring allocative efficiency considerations into the picture,a budget (or cost) line associated with
5 Originally, Farrell (1957) introduced the term ‘overall efficiency’; today the term
‘economical efficiency’ is more commonly used.
Fig. 3.4. Efficiency measures by Farrell (1957).
c1x1+c2x2=k1,displayed by the broken line passing through P,is introduced. However,this cost can be reduced by moving this line in parallel fashion until it intersects withψ. The new solid lineφ represents the cost minimization plane with c1x1*+c2x2*=k0,where k0<k1 guarantees that total cost is reduced. The intersection betweenψandφis the overall optimal point for company P as further parallel movement in a downward direction would be associated with reduced output. To measure company P’s ineffi- ciency letOP,the line from O to P,crossφat A andψat B. Given this,the economical efficiency (sometimes also referred to as ‘overall efficiency’) of unit P is measured by:
E OA
=OP (3.4)
Technical efficiency (T),measured as the radial distance that P is from the isoquant,and allocative efficiency (A),measured as the radial distance from the cost minimization plane, are given by:
T OB
=OPandA OA
=OB (3.5)
Note that allocative efficiency provides a measure of the extent to which the technically efficient point,B,falls short of achieving minimal cost because of company P’s failure to make the reallocations necessary to move from B to the overall optimal point, which is located at the intersection betweenψandφ.
Economical efficiency (E) can also be computed from A and T as follows:
E OA OP
OA OB
OB OP A T
= = × = × (3.6)
In summary,firms can operate suboptimally for two fundamental reasons. The first is the failure to allocate resources in the most efficient manner (allocative inefficiency). The second way is related to a firm’s ability to utilize its resources given their allocation or technical inefficiency. In other words,two firms may have exactly the same resource allocation,yet one firm produces less output than the other. The difference between how a firm could potentially utilize its resources versus its actual utilization is termed ‘X-inefficiency’ (Leibenstein, 1966; Andersonet al., 1999).
The majority of X-efficiency losses,according to Leibenstein (1966),arise from inadequate motivation by firm management. He also suggests that moti- vation levels are linked to the structure and competitiveness of the market in which a firm operates. If managers and/or workers could be encouraged or persuaded to work more effectively,firms would improve performance without changing their resource allocation. If a firm is operating in a competitive mar- ket,managers and workers may feel pressure to work more efficiently and vice versa. In other words,there is another relationship that must be considered because obtaining a high-efficiency estimate is more likely to be observed in a competitive market and obtaining a low-efficiency measure is consistent with
a less competitive market. Thus,care should be taken in making definitive statements, as efficiency measures do not prove market or firm efficiency.
There are two empirical approaches to the measurement of efficiency based on the above concepts of technical and allocative efficiency. The first, favoured by most economists,is parametric (either stochastic or deterministic).
Here,the form of the production function (the isoquantψin Fig. 3.4) is either assumed to be known or is estimated statistically. The advantages of this approach are that any hypotheses can be tested with statistical rigour and that relationships between inputs and outputs follow known functional forms.
However,in many cases there is no known functional form for the produc- tion function and,in some cases it may even be inappropriate to talk in terms of such a concept. This becomes clear when someone considers the case in public sector organizational units that are not,for example,concerned with taking unfinished goods (or raw materials),processing them and producing finished goods for sale or transfer.
In the parametric approach the functional form usually chosen is Cobb–Douglas. In this context the Cobb–Douglas functions are estimated by ‘averaging’ statistical techniques,such as regression. Each unit is then compared with an average,but it is not immediately clear what this average represents. It clearly does not refer to a firm of ‘average size’ nor indeed to a firm having ‘average means at its disposal’ (or ‘average technology’).
In the non-parametric approach no assumptions are made about the form of the production function. Instead,a best-practice function is built empirically from observed inputs and outputs. This will necessarily be piecewise linear and,as such,is an approximation of the ‘true’ function,if one exists. In this case,the observed points are assumed to provide empirical evidence that pro- duction is possible at the rates specified by the coordinates of any point in this region (Cooperet al.,2000: 7). For example,Fig. 3.5 shows observations for a number of similar companies,P1–P10,where the axes are input per unit output produced. From the efficiency point of view,it is natural to judge companies that use smaller inputs to get one unit output as more efficient. Therefore, companies P8, P2, P7 and P10 are identified as efficient,as there is no other company that produces the same amount of output with less input. The line joining P8to P2, P2to P7,and P7to P10,designates the efficiency ‘frontier’, which is assumed to extend parallel to the axes beyond P8and P10. Technical, allocative and economical (‘overall’) efficiencies are calculated in an analo- gous manner to the approach shown in Fig. 3.4.
The inefficiency of companies not on the frontier line can be measured by referring to the companies that build the frontier. For example,company P4
is inefficient. The technical inefficiency of this company is represented by the line from zero to P4divided by the line from zero to B. Hence,the inefficiency of P4is to be evaluated by a combination of P2and P7because the point B is on the line connecting these two points. Companies like P2 and P7 are commonly referred to as the ‘reference set’ or ‘peer members’ for company P4. The refer- ence set for another inefficient company,P3,consists of companies P2and P8,
which clearly shows that the reference set may differ among inefficient companies.
Similar to the example illustrated in Fig. 3.4,economical efficiency can be calculated. Given input prices,the isocost line is reflected by the broken line passing through P4. Reducing the total costs by moving this line in parallel fashion until it intersects with the frontier at P7 gives A,the point that determines the economical (or overall) inefficiency of P4. The relative distance between zero and A and zero and B measures the amount of allocative inefficiency of company P4. In Fig. 3.5 only company P7is both technically efficient and allocatively efficient,whereas companies P8, P2 and P10 are technically but not allocatively efficient.
From the simplistic case shown in Fig. 3.6,it can be deduced that company P1is the most efficient and,if no other management units are included in the
Fig. 3.5. A piecewise-linear efficiency frontier.
Fig. 3.6. Comparative efficiencies.
analysis,P1can receive a reference efficiency score and scores for P2, P3and P4
relative to P1can be computed. Thus,if P1is assigned an efficiency score of 1,it is possible to say that P1‘is efficient relative to P2, P3and P4’. Therefore:
1 1
1 1 2
1 3
1 4
=OP > > >
OP OP OP
OP OP
OP
OP (3.7)
and the ratios for P2, P3and P4determine their own relative efficiency scores.
This is analogous to a Leontief single process input–output system. Farrell extended it to cover many processes and many inputs.