Abstract
Parametric production frontier functions are frequently used in stochastic frontier models, but there do not seem to be any empirical test statistics for the plausibility of this application. In this paper, we develop procedures to test whether or not the parametric production frontier functions are suitable. Toward this aim, we developed two test statistics based on local smoothing and an empirical process, respectively. Residual-based wild bootstrap versions of these two test statistics are also suggested. The distributions of technical inefficiency and the noise term are not specified, which allows specification testing of the production frontier function even under heteroscedasticity. Simulation studies and a real data example are presented to examine the finite sample sizes and powers of the test statistics. The theory developed in this paper is useful for production managers in their decisions on production.
Highlights
Since the seminal works of [1,2], stochastic frontier analysis (SFA) has been a very appealing and popular approach for studying productivity and efficiency analysis
Sustainability 2018, 10, 3082 where Y is the log of output, X is the log of inputs of dimension p, m(·) is an unknown smooth production frontier function, U is the inefficiency term, and V represents random noise
Parametric SFA models specify the functional form of the production frontier function, m(·), as well as the distributions of the inefficiency term, U, and the independent noise, V
Summary
Since the seminal works of [1,2], stochastic frontier analysis (SFA) has been a very appealing and popular approach for studying productivity and efficiency analysis. Parametric SFA models specify the functional form of the production frontier function, m(·), as well as the distributions of the inefficiency term, U, and the independent noise, V. Fan et al [14] introduced the quasi-likelihood method, where the production frontier is not specified, but distributional assumptions are imposed on the stochastic components. The studies discussed above call for the specification testing of the production frontier function. Due to well-established theories, easy computation, and interpretation, parametric SFA models have been dominant in the area of productivity and efficiency analysis. We aim to develop procedures to test whether the production frontier function can be described by some known parametric functions.
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