Dynamic efficiency measurement: theory and application.

Comparison of technical and allocative efficiency results suggests substantial differences between the technical and allocative performance of Pennsylvania dairy operators in the long-run. (18) Specifically, Pennsylvania dairy operators reveal higher technical efficiency levels than allocative efficiency levels indicating that Pennsylvania dairy operators perform better in exploring their production potential than combining variable and dynamic factors in optimal proportions in the light of the prevailing prices.

Conjectures on Efficiency Differences

Upper bounds on technical efficiency levels are generated using only quantity data (i.e., the inner bound on the production technology). In contrast, lower bounds are estimated using the outer bound on the production technology. Specifically, the lower bound on the technical efficiency of variable inputs is generated using the dual variable cost representation of the production technology whereas the lower bound on the technical efficiency of all inputs is estimated using the dynamic dual shadow cost representation of the technology. The dual variable (shadow) cost representation of the production technology requires consistency of, at least, some data points with the variable (dynamic) cost minimization hypothesis.

Considering the percentage of technically efficient farm operators in the use of variable inputs indicated by the upper and lower bounds, a significant number of observations determine the inner and outer bounds on the production frontier although a smaller subset of observations determine the outer bound. The subset of observations that determines the outer bound on the production technology is, by definition, composed by dairy operators that are variable cost efficient.

In contrast, the percentage of technically efficient firms in the use of all factors of production indicated by the upper and lower bounds is low implying only a few observations determine the bounds on the production technology in each year. Specifically, the number of observations determining the outer bound is very low in each year. This result is consistent with the empirical findings in Silva and Stefanou (2003). The gap between the inner and outer bounds on the production technology is much wider when a dynamic shadow cost perspective is adopted rather than a restricted (or variable) cost is employed. This may explain why the technical efficiency bounds convey the same information on the efficiency performance of dairy operators in the short-run whereas there are substantial differences between the efficiency bounds in the long-run. Although the upper and lower bounds on allocative efficiency are generated using both the inner and outer bounds on the production technology, a substantial gap (approximation) between the latter bounds probably explains also the disparity (similarity) between the efficiency bounds in the long-run (short-run).

Despite those contrasting results, comparison of the empirical results for the short- and long-run indicates ostensible efficiency differences in the allocation of variable inputs and all factors of production: (i) short-run efficiency is significantly higher than long-run efficiency and (ii) allocative efficiency is substantially lower than technical efficiency, namely in the long-run. The substantial differences in the efficiency performance in the short- and long-run are, to a certain extent, expected a priori. The challenges of the efficient management of Pennsylvania dairy production operations lie essentially in managing the assets of the operation. The allocation decisions involving dynamic factors are a substantial source of inefficiency reflecting that capital (both human and physical) is of a different nature than variable inputs. Variable inputs can be adjusted in a complete fashion to the optimal level while capital is managed as an asset following a lagged adjustment due to adjustment costs. The result in (ii) indicates that dairy operators reveal a higher managerial ability to avoid waste than to combine inputs in optimal proportions in the light of the prevailing prices. Low allocative efficiency levels can be attributed to several sources, including a divergence between expected and actual prices or a systematic under- or overvaluation of prices.

However, there are several issues relevant to the dynamic production analysis, in general, and dynamic efficiency measurement, in particular that are not explicitly addressed in this framework. Uncertainty over the future market and production environment and risk preferences that are not considered in this study are likely to affect the variable input and investment decision-making process, and, consequently, affect the efficiency level achieved by farm operators. If producers are uncertain about production and prices, they are confined to make decisions that likely appear to be inefficient.

Learning and technical change are not considered in this framework. Learning can play a significant role both in the decision-making process and as a source of intertemporal shifts in the production technology and the production structure can change with technical change. However, it is difficult to distinguish between human capital improvement and technological change since learning may be the source of intertemporal shifts in the production technology (Luh and Stefanou 1993). Neglecting these two aspects can translate into an upward-biased effect on the inefficiency levels.

The quality of the quasi-fixed factor data influences the long-run results. Difficulties can arise in the use of quasi-fixed factor data that depend on self-reported (book) valuation than market valuation. Input levels used in the short-run (such as energy, hired labor, materials) are probably recorded and reported in a reliable fashion. However, reporting of quasi-fixed factor levels can be subject to considerable error. Measurement errors as well as other sources of statistical noise can contaminate the efficiency levels although in an unknown way and a deterministic approach is very sensitive to these errors.

Concluding Comments

Nonparametric dynamic measures of technical, allocative and economic efficiency are developed in the context of an adjustment-cost technology and intertemporal cost minimization. Lower and upper bounds on each efficiency measure are proposed using a nonparametric revealed preference approach. Long-run efficiency measures indicate the relative efficiency of both variable and dynamic factors. Short-run measures indicate whether variable inputs are employed efficiently in the production process.

The empirical implementation of these efficiency measures is illustrated for a panel data set of Pennsylvania dairy operators during the time period 1987-92. Briefly, the empirical results indicate farm operators are more efficient in the allocation of variable inputs than in the use of all factors of production. Also, the technical performance of Pennsylvania dairy operators is superior to their allocative performance.

There are many directions in which future research may proceed. An obvious one is the development of a nonparametric stochastic approach to dynamic efficiency measurement that can address some of the issues discussed at the end of the last section (e.g., uncertainty). Specifically, a stochastic dynamic approach would allow the replacement of static output and price expectations with non-static expectations. Consistency with the essence of the theoretical framework proposed requires non-static expectations to be incorporated in a nonparametric fashion.

Additionally, there is a growing body of studies offering empirical evidence on lumpy and infrequent adjustments revealed by microeconomic data (e.g., Ramey 1991; Bresnahan and Ramey 1994; Caballero, Engel, and Haltiwanger 1995; Caballero 1997; Nilsen and Schiantarelli 2003). The convex adjustment cost model cannot explain these types of adjustments. Lumpy and infrequent adjustments should be allowed by considering nonconvexities in the cost function. Nonconvexities can be incorporated in the theoretical framework proposed by introducing indivisibilities and other forms of increasing returns in the adjustment technology.

[Received August 2004; accepted March 2006.]

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