Nonlinear Effects in the Asymmetric Copula-Based Stochastic Frontier Model

Several stochastic frontier production analysis problems are not linear regression problems; two error components (inefficiency and noise) may not have symmetric dependence. In nonlinear problems, the data are divided into two or more regimes according to turning points or change points; the relationships between the output and all the inputs are allowed to differ between regimes. In the problem of two-error dependence, the inefficiency component generally plays a more dominant role than the noise component, thereby the output of each firm is mainly influenced by the inefficiency; in such cases, the symmetric dependence is not suitable. It is, therefore, desirable to come up with a new nonlinear asymmetric copula-based stochastic frontier model (SFM). Two nonlinear structures, namely kink and threshold and skew-normal copula, are suggested to SFM to deal with these problems. The Monte Carlo simulations and analysis of a real data set are employed to evaluate the accuracy and performance of proposed models. The results show that the proposed models show a higher performance when compared with the conventional linear SFM with symmetric two-error dependence.