However, by 1994-95 industry profitability rebounds and is positive for both city and regional banks before falling during 1995-96 to about zero with gains by regional banks just a little more than offset by losses by city banks. The second columns are reserved for the average annual growth rate of each index. As it turns out, there is a common thread—namely the directional distance function, which also gave us our title. If we assume t h a t one price is known, for example one of the prices of the desirable outputs, then we may compute t h e absolute price for t h e undesirable output. Similarly, we may construct a quantity index of bad outputs based on distance functions which satisfies conditions similar t o those itemized above.
Thus the two axioms A. The approach gauges performance relative to the best practice frontier constructed from enveloping observed data points. We end the essay with an empirical application of profit efficiency and aggregation by Fukuyama and Weber. Lovell 1985 The Measurement of Efficiency of Production. The denominator serves to normalize the indicator so that it is independent of unit of measurement. Shadow Pricing Undesirable Outputs As we have mentioned earlier, in general there are no markets for undesirable outputs, thus their prices must be estimated. Nonnormalized shadow prices can then be estimated using 2.
Then xi,X2 belongs to L 2 , i. This is done by the two following proposi- Essay 1: Efficiency Indicators and Indexes 19 tions: Proposition 4 : Let Qy b e strictly positive, i. If the Pii are assumed to be fixed parameters, then the model is known as Essay 2. Values of any of t h e efficiency indicators greater t h a n zero denote inefficiency. Recall t h a t values of the indicators equal to zero signify efficiency and values of the indicators greater t h a n zero signify inefficiency. Under fairly general conditions these provide complete characterizations of technology, as well as having useful dual representations in the cost and revenue functions.
Our comparative analysis will be based on the average performance indicators evaluated with respect to the base year. Again allocative efficiencies play a key role for unbiased aggregation. Monitoring uses scarce resources and results in lower profits. We also show how both types of data may be incorporated into our efficiency models. From its definition, the input distance function immediately inherits its H o m o g e n e i t y P r o p e r t y in inputs which has nothing to do with returns to scale : Di.
Series Title: Responsibility: Rolf Färe and Shawna Grosskopf ; in collaboration with H. Clearly, larger values are 'better' as long as u is undesirable. There has long been debate about whether finance plays an active or passive role in the process of development. Lee T h e absence of property rights has long been recognized as a source of market failure. Property rights serve t h e same purpose in preventing the tragedy of the commons. Subtracting actual profits from both sides of 3. The technology T consists of the area between and including the xaxis and the ray emanating from the origin.
As for our other indicators, we can add an allocative efficiency component to 1. This proposition shows that there exist directional vectors such that the distance function can identify inefficiency as defined earlier. In both cases we have assumed some form of allocative efficiency to simplify the expression, however, in the index case, we still require a price related term—namely the share—to accomplish aggregation. Printed in the United States of America. Industry profitability grows from 1992 to 1993 and is positive for both city and regular banks. By inspecting the component quantity indexes, one may determine if the environmental index is improving due to relatively fast growth in desirable outputs, declines in undesirable outputs or some combination of the two.
With these two observations at hand we may construct industry efficiency as a share weighted aggregate of firm efficiencies. Therefore we need input prices w G 3? Proofs of these properties are to be found in Fare and Primont 1995. Appendix: Proofs Proof of 2. Some bank owners may prefer a 'quiet life' and seek to protect equity capital through greater monitoring of the bank loan and security portfolio by bank employees. To translate the shadow price formula 2.
This is consistent with the definition of the cost function which seeks to minimize cost by choosing inputs given the allocation of outputs and input prices, i. From the definition, we obtain the following Translation Property D T. The Nerlovian Profit Indicator Perhaps the most natural measure of performance that is based on differences is profit; so it follows that the natural form for a measure of profit efficiency is as a difference rather than as a ratio. We include an example of a network model applied to the case of an environmental externality, which we use to show the effect of various property rights arrangements on profitability. The E-mail message field is required. In contrast, the translog function can readily be restricted to satisfy homogeneity, but not translation.
Activity Analysis of Production and Allocation, New York: Wiley. Equivalently if some positive amount of the good output is produced then some bad output must also be produced. Like inputs, outputs can be weakly or strongly disposable, which we model with the following two axioms. Recall that the Shephard distance function seeks to radially expand all outputs proportionally, with the imphcation that more of all outputs is desirable. The second set of inequalities states that each firm produces at least one bad output. Next we turn to an application. We begin with a numerical example as motivation, and then turn to a more formal presentation of the problem for both Essay 3: Aggregation Issues 121 Farrell technical efficiency indexes as well as our technical efficiency indicators.