A Copula-Based Approach to Stochastic Frontier Models with Application to Healthcare Efficiency

This paper develops a copula-based extension of stochastic frontier analysis (SFA) to account for dependence between inefficiency and random error components, an assumption commonly ignored in classical models. By integrating copula functions into the SFA framework, the proposed approach allows flexible modeling of joint distributions while preserving marginal specifications. A log-linear Cobb-Douglas production frontier is employed, and the likelihood function is derived under dependent error components, with parameters estimated via maximum likelihood.The empirical application focuses on regional healthcare efficiency across twelve NUTS-۱ regions in Turkey. Efficiency scores obtained from Data Envelopment Analysis (DEA), classical SFA, and copula-based SFA models are compared. The results indicate that DEA tends to overestimate efficiency, whereas stochastic frontier models provide more conservative estimates. Importantly, the copula-based specifications reveal a strong dependence structure between inefficiency and noise components, suggesting that the standard independence assumption may lead to biased inference.The findings demonstrate that incorporating copulas improves both the flexibility and theoretical consistency of stochastic frontier models. Moreover, efficiency rankings remain robust across different copula families, highlighting the stability of the proposed framework. From an applied perspective, the results emphasize that regional performance differences are largely driven by inefficiency rather than random variation.Overall, the proposed copula-based SFA framework offers a more general and realistic approach for efficiency analysis and provides a foundation for further methodological developments.

کلیدواژه ها:

Data Envelopment Analysis (DEA) ، Copulas ، Healthcare Efficiency ، Stochastic Frontier Analysis (SFA) ، Regional analysis