An endogenous spatial stochastic frontier model for tourism

A for an overview of the two hypotheses. 2 SFA methods for studying efficiency determinants fall into two main approaches: the "two-step method" and the "one-step method."The "twostep method" involves first estimating the frontier equation to obtain the inefficiency, and then regressing the inefficiency or its variations on multiple influencing factors.However, this strategy assumes inefficiency terms are identically distributed in the first step, while explaining inefficiency variations using influencing factors in the second step, which leads to model misspecification.To overcome this technical problem, Battese and Coelli (1995) proposed a "one-step method" estimation strategy that estimates both the frontier and efficiency influencing factors, avoiding assumption contradictions and ensuring theoretical consistency and efficiency of the estimators.3 Empirical models that introduce an inefficiency equation related to the mean of the inefficiency error term or adopt a scaling function allow the same covariates to appear in both the frontier and inefficiency equations without raising identification concerns (see Battese &Coelli, 1995 and Kutlu et al., 2020 for technical details).For other SFA specifications, researchers should exercise caution when including identical variables in both the frontier and the inefficiency function, as identification could theoretically rely on efficiency functional form assumptions.