*2.2. Double-Bootstrap DEA Model*

The double-bootstrap DEA model proposed by Simar and Wilson [15] is based on the simulation of sample distribution by mimicking of the data-generation process (DGP). Assuming that the original data sample was generated by the DGP, energy efficiency scores are re-computed with the simulated data [19]. In other words, the bootstrapping procedure generates *new* data that is used to re-estimate energy efficiency scores using Equation (1). Then, the distinction between the *true* and *estimated* frontiers allows for statistical inference in DEA, i.e., for the identification of determinants of energy efficiency [20].

*Energies* **2019**, *12*, 765

The double-bootstrap procedure employed in this study is Algorithm 2 of Simar and Wilson's model [20], summarized as follows:

	- 3.1 Generate the residual error, *<sup>ε</sup>j*, from the normal distribution *N*(0, ˆ *σ*2*ε* ).

3.2 Compute *θ*∗*j*= *bjβ* ˆ + *<sup>ε</sup>j*.


	- 6.1 Generate the residual error *εj* from the normal distribution *N*(0, ˆ *<sup>σ</sup>*<sup>∗</sup><sup>2</sup>).
	- 6.2 Calculate ˆ *<sup>θ</sup>*∗∗*j* = *bjβ* ˆ ∗ + *<sup>ε</sup>j*.
	- 6.3 Use the truncated maximum likelihood estimation to regress ˆ *<sup>θ</sup>*∗∗*j* on the explanatory variables, *bj*, and provide an estimate *β* ˆ ∗∗ for *β* and an estimate *σ*<sup>ˆ</sup>∗∗ for *σε*.
