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Brief Literature Review
This introduction presents a critical appraisal of the existing literature,
to indicate the position of our program in it, and to identify and motivate the prime areas for further study.
The traditional revealed preference approach (Samuelson, 1948) has been most directly applied and adapted to the production analysis by
Afriat (1972), Hanoch and Rothschild (1972), Diewert and Parkan (1983), and Varian (1984, 1985, 1990). This literature has a strong
neoclassical flavor: the firms are seen as rational price-taking profit maximizers in the competitive setting. The approach is concerned of testing
the optimization hypothesis, but the main objectives lie in the analysis that follows it after acceptance of the hypothesis. The key benefit of the
nonparametric approach is the ability to test for rationality within the general domain of ALL production technologies, not merely for a particular
family of production functions (like e.g. Cobb-Douglas or Translog) as in the parametric approach. For drawing conclusions, the nonparametric
approach offers upper- and lower-bounds, which may (or may not) provide sufficient information for policy- or decision-making purposes.
Another prominent line of nonparametric production analysis has focused on the measurement and analysis of productive efficiency following
the influential work of Farrell (1957) and Koopmans (1951). Besides Economics, this stream of literature has seen remarkable development in
the field of Operations Research, where the methodology is known as Data Envelopment Analysis (DEA), terminology coined by Charnes,
Cooper, and Rhodes (1978). In sharp contrast to the revealed preference driven literature, the DEA literature concentrates on "irrational",
inefficient behavior. It is generally accepted within this domain that inefficiencies are real, and the methodology focuses on the identification and
the measurement of the degree and impact of these inefficiencies. One major advantage of the DEA approach, besides avoidance of the
explicit specification of the function form of the production function, is the immediate compatibility with multiple inputs and multiple outputs.
This is an important feature especially in environmental applications.
A more dynamic view is offered by the Total Factor Productivity (TFP) measurement literature, which is intimately related to the efficiency
paradigm. The prime challenge in TFP measurement lies in the aggregation of various inputs and outputs into a single input and a single output
index. A paramount difficulty with the classic Fisher and Törnqvist index formulas is the need for complete and accurate information of prices or
cost/revenue shares, consider e.g. intertemporal valuation of capital goods, goods emerging/exiting the market, free goods, externalities, etc.
The so-called Malmquist TFP index suggested by Caves, Christensen, and Diewert (1982) offers a purely quantity-based aggregation method,
using the Shephard (1953) input or output quantity distance functions. The distance functions can be estimated in a nonparametric fashion
following the DEA approach, as shown by Färe, Grosskopf, Norris, and Zhang (1994). Besides the possibility of accounting for non-market
goods (like clean air) in the productivity index, another attractive feature of the nonparametric approach is the possibility to decompose the TFP
index into components of technological change and the change in operational efficiency, which might provide a feeling of the underlying causes
of productivity development.
All these variants of the nonparametric approach are subject to some
common problems. One is the availability of sufficient empirical data. Since the nonparametric approach requires minimal input in terms of
maintained assumptions, it must compensate it with informative data. The ability to 'let the data speak for itself' is a great opportunity, but it
should not be abused. In general, the nonparametric method necessitates a relatively large set in terms of the number of observations.
Although the approach is well compatible with multiple input and output dimensions, it is also subject to the so-called "curse of dimensionality":
as the number of inputs+outputs increases, the number of observations needed for meaningful analysis increases exponentially. In addition to
the quantity of the data, also the quality of the data is an issue of importance. Most nonparametric methods are quite sensitive to missing
variables, sampling errors, and data errors. In some cases, the nonparametric methods also are computationally demanding, although this is
by no means a general characteristic of the approach.
In spite of these problems, we see that in many application areas the advantages of the nonparametric approach outweigh the opportunity costs.
On the other hand, we find that these shortcomings and limitations can often be alleviated, as some of our earlier studies have convincingly
demonstrated. We expect the application of the nonparametric techniques to increase in the future.
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References
Afriat, S. (1972): Efficiency Estimation of Production Functions, International Economic Review 13, 568-598.
Caves, D.W., L.R. Christensen, and W.E. Diewert (1982): The Economic Theory of Index Numbers and the Measurement of Input, Output and Productivity, Econometrica 50, 1393-1414
Charnes, A., W. Cooper, and E. Rhodes (1978): Measuring the Efficiency of Decision Making Units, European Journal of Operational Research 2, 429-444.
Diewert, W.E. and C. Parkan (1983): Linear Programming Tests of Regularity Conditions for Production Frontiers, in Quantitative Studies on Production and Prices (W. Eichhorn, R. Henn, K. Neumann and R.W. Shephard, Eds.), Physica-Verlag, W?rzburg.
Färe, R., S. Grosskopf, M. Norris, and Z. Zhang (1994): Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries, American Economic Review 84(1), 66-83.
Farrell, M.J. (1957): The Measurement of Productive Efficiency, Journal of the Royal Statistical Society Series A 120, 253-281.
Hanoch, G. and M. Rothschild (1972), Testing Assumptions of Production Theory: A Nonparametric Approach, Journal of Political Economy 80, 256-275.
Koopmans, T.C. (1951): Analysis of Production as an Efficient Combination of Activities, in: Activity Analysis of Production and Allocation: Proceedings of a Conference (T.C. Koopmans, Ed.), Yale University Press, New Haven.
Samuelson, P.A. (1948): Consumption Theory in Terms of Revealed Preference, Economica 15, 243-253.
Shephard. R.W. (1953): Cost and Production Functions, Princeton University Press, Princeton.
Varian, H.R. (1984): The Non-Parametric Approach to Production Analysis, Econometrica 52, 279-297.
Varian, H.R. (1985): Non-Parametric Tests of Optimizing Behavior with Measurement Error, Journal of Econometrics 30, 445-458.
Varian, H.R. (1990), Goodness-of-Fit in Optimizing Models, Journal of Econometrics 46, 125-140.
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