Measuring Technical Efficiency in the Stochastic Varying Coefficient Frontier Model

Measuring Technical Efficiency in the Stochastic Varying Coefficient Frontier Model

Due to the assumption that the best practice methods refer to each input separately instead of the whole set of inputs used by a firm, the benchmark technology as defined in the stochastic varying coefficient frontier model may be infeasible and theoretically improper whenever the maximum response coefficients are not coming from the same production unit. To overcome this problem we suggest an alternative procedure for measuring output-oriented and input-specific technical efficiency inspired from the maximum likelihood formulation of the non-neutral frontier model.

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Published in: Agricultural Economics

In an output oriented manner, technical efficiency is measured as a ratio of realized output to the potential output. The reliability of this measure of technical efficiency depends on how accurately the potential output is measured. It is in general assumed that the potential output is obtained by following the best practice methods, given the technology. This implies in turn that the potential output is determined by the underlying production frontier, given the level of inputs. Since by definition technical efficiency is the discrepancy of the actual (realized) output from the production frontier, its measurement cannot proceed without the estimation of the production frontier.

The estimated frontier depends on the assumptions about the nature and the determinants of best practice methods. The former is related to the question of whether the best practice is a realized method inherent in the data or it may not be realized yet. Consequently, the potential output used to measure technical efficiency may or may not be realized. Up to now in the efficiency measurement literature, all but Kalirajan and Obwona (1994a) have agreed that the frontier results from observed output levels, produced by the firms using the best practice methods.1 In contrast, Kalirajan and Obwona (1994a) suggested that the potential output need not necessarily be observed in the data at hand. They attempted to justify that by arguing that the best practice method varies from input to input and thus not every firm would be applying all input efficiency. However, it seems more reasonable whatsoever to think of best practice as referring to the whole set of inputs used by a firm instead of each input separately.

On the other hand concerning the determinants of best practice methods, two alternative models have been developed, which are referred to as neutral and non- neutral frontier models. The former assumes that technical efficiency is independent of the levels of input used but is dependent on the method of application of inputs. Thus, even for identical levels of the same inputs, output differs due to differences in the methods of application.2 In turn the effectiveness of the methods of application is determined by various organizational factors, which are influenced by socioeconomic, demographic etc characteristics that affect the managerial ability of firms. In such a case, the estimated frontier is modeled as a neutral shift of the traditional “average” production function. In contrast, the non-neutral frontier model assumes that both the methods of application of inputs as well as the level of inputs (i.e., scale of operation) determine the potential output and thus, the estimated frontier is modeled as a non- neutral shift of the traditional “average” production function. The non-neutral shift is related to that firms may acquire more information, knowledge and experience with respect to one input’s productivity than the other (Huang and Liu, 1994). Apparently, it seems intuitively more appealing to argue that technical efficiency stems from two sources: firm-specific intrinsic characteristics and input levels.

Two alternative approaches have been used to model non-neutral production frontiers. On the one hand, Kalirajan and Obwona (1994a) developed the stochastic varying coefficient frontier (SVCF) model that related the notion of the non-neutral frontier with cross-sectional and possibly temporal variation in production response coefficients, which include not only the intercept term as in the traditional frontier framework but also the slope coefficients. The idea of slope varying coefficients is consistent with the methods of application of inputs to depend on the level of inputs. On the other hand, Huang and Liu (1994) accommodated the notion of the non-neutral frontier by modeling the one-sided error term measuring technical efficiency as a function of not only the variables affecting the managerial and organizational ability of firms but also of input levels, including interaction terms between them.

Besides conceptual differences, these two non-neutral frontier models require quite different econometric estimation techniques. In particular, Huang and Liu’s (1994) model is estimated with maximum likelihood, which necessitate the imposition of particular distributional assumptions regarding the one-sided error term. In contrast, the SVCF model dispenses with this assumption as it can be estimated with generalized least squares by using Hildreth and Houck’s (1968) random coefficient regression procedure but the additive error term (appended to account for statistical noise) cannot be distinguished from the randomly varying intercept when only cross- section data are available (Kalirajan and Obwona, 1994b; Tsionas, 2002). Thus, in a cross-sectional setting, SVCF is deterministic frontier model. This is not true however with panel data as it is possible to have a (cross-sectional) random intercept and noise at the same time (Kalirajan, Obwona and Zhao, 1996; Tsionas, 2002)).

Despite its attractiveness as a non-neutral frontier model, SVCF’s assumptions about the nature of best practice methods raise doubts about the reliability of the resulting efficiency measures. In particular, it is shown that as long as the best response coefficients are coming from different firms in the sample, which as noted by Kalirajan and Obwona (1994a) is quite likely to happen in empirical applications, the resulting frontier is not well defined in theoretical grounds and infeasible for any sample participant. Consequently, by using it to compute the maximum attainable output yields misleading results regarding both the magnitude of technical efficiency and the ranking of firms according to their efficiency scores. Moreover, Kalirajan and Obwona’s (1994a) measure of single factor technical efficiency (defined as the ratio of the actual to the maximum response coefficient for each input) also raises concerns about its appropriateness as an efficiency measure.

In this paper, by relying on stochastic frontier methodology, output-oriented and single-factor technical efficiency measures for the SVCF model are developed that overcome the above shortcomings. The former is adapted from the error component literature and is adjusted accordingly to the stochastic nature of the SVCF model. In that sense, it is conceptually analogous to the measure used in Huang and Liu (1994) non-neutral stochastic frontier model. On the other hand, the proposed single factor measure of efficiency is based on Kopp’s (1981) notion of non-radial technical efficiency and it is shown that in the context of the SVCF model it could provide firm-specific estimates even with inflexible production frontiers, such as the Cobb-Douglas. After these adjustments, the SVCF model may be seen as a promising alternative to Huang and Liu (1994) non-neutral frontier model. 

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