where α is the intercept, εj is the error term, and Xj represents a vector of observation-specific variables for firm j that is expected to be related to the firm's efficiency score, OEj. Instead of using Tobit estimation, Simar and Wilson [32] and [33] propose an approach based on a truncated regression with a bootstrapping procedure for estimating Eq. (6). The performance of their Monte Carlo experiments is satisfactory.
More specifically, the distribution of ε j is restricted by the condition ε j≥1−α −X jβ in Eq. (6). Following Simar and Wilson [32] and [33], this study modifies Eq. (6). The true but unobserved efficiency score, OEj, in Eq. (6) is replaced by its estimate , and the distribution is assumed to be truncated normal with zero mean (before truncation), unknown variance, and a truncation point, which are determined by different conditions. Accordingly, we estimate the following:
equation(7)