**3.6. DEA model**

**3.4. Output variables**

200 New Developments in Renewable Energy

this research, are as follows:

changes.

each country.

**3.5. Research resource and sample**

Phase II Output Variables in: The results of recent studies have contributed to energy effi‐ ciency or environment efficiency evaluation problems that consider total production activity factors. Ramanathan [53] proposed an overall efficiency index that combined energy inputs, desirable outputs and undesirable outputs using DEA to study the relationships among global GDP, energy consumption, and carbon dioxide emissions. The final outputs used in

**1.** *TEPS/GDP ratio:* TPES per US. \$1000 of GDP. The ratios are calculated by dividing each country's annual TPES by their annual GDP expressed in constant prices and converted to US. dollars using purchasing power parities (PPPs) (www.OECD-iLibrary.org). TPES consists of primary energy production adjusted for net trade, bunkers and stock

**2.** *TPES/Population ratio:* TPES includes the sum of the unexplained statistical differences for individual fuels, as they appear in basic energy statistics [48]. TPES per population, ratios are calculated by dividing each country's TPES by unit people (www.OECD-iLi‐ brary.org). This ratio can be used to obtain the electricity consumption of residents for

**3.** *Grid:* The energy's transport length of line required to moor multiple devices is depend‐ ent on the spacing between devices and the array configuration. The length of cable re‐ quired depends on the array configuration, although groups of devices are typically

We used the intermediation approach to view the energy industry as intermediaries, and

This research is based on DEA of operating procedures. Though data collection and litera‐ ture review on performance measurement of renewable power, we can understand the dif‐ ferences in renewable energy efficiency among 34 OECD countries (Table 2) and provide suggestions for Taiwan. The data obtained for this analysis were gathered from many rele‐ vant data resources, including the IEA, Renewable Information, World Bank, and other en‐ ergy indices of a representative sample from 2007 to 2009. However, the data obtained from Renewable Energy Information [48] are used account for the full range of statistics collected from the Annual Renewables and Waste Questionnaire. This database of annual statistics for OECD countries covers hydroelectricity, solid biofuels, geothermal, renewable municipal waste, wind, gas from biomass, liquid biofuels, solar photovoltaic, solar thermal, tide/wave/ ocean, non-renewable municipal waste and industrial waste. It includes EOP and HOP from renewable sources and supply/demand balances of renewable and waste products. The pri‐

interconnected in series and each group is connected to a hub [38].

summarized the major input and output variables in Table 1.

mary data from this system are from IEA annual publications.

Data Envelopment Analysis (DEA) is a method for measuring the performance efficiency of decision units, characterizing by multiple input and output variables [8]. The DEA techni‐ que uses linear programming to estimate the maximum potential efficiency for various lev‐ els of inputs based on each firm's actual inputs and output. DEA includes two major models, the CCR model, and the BCC model. Charnes, Cooper and Rhodes [54] proposed a model under the assumption of constant return to scale (CRS), called the CCR model. This model is only appropriate when all DMUs are operating at an optimal scale. Banker, Charnes and Cooper [55] extended the CCR model to include the variable returns to scale named the BCC model, which can further decompose the TE into two components: pure technical efficiency (PTE) and scale efficiency (SE). The problem of calculating efficiency can be formulated as a fractional linear programming problem as below:

$$\begin{aligned} \text{Max } \mathbf{E}\_{j} &= \sum\_{n=1}^{N} \mathbf{U}\_{n} \mathbf{Y}\_{jn} - \boldsymbol{\mu}\_{0} / \sum\_{m=1}^{M} \mathbf{V}\_{m} \mathbf{X}\_{jm} \\ \text{s.t. } &\sum\_{n=1}^{N} \mathbf{U}\_{n} \mathbf{Y}\_{jn} - \boldsymbol{\mu}\_{0} / \sum\_{m=1}^{M} \mathbf{V}\_{m} \mathbf{X}\_{jm} \le \mathbf{1}; \text{ } \forall \mathbf{r} \\ \mathbf{U}\_{n'} \mathbf{V}\_{m} \ge 0 &\quad \mathbf{m} = \mathbf{1}, 2, \dots, \mathbf{M}; \text{ } \mathbf{n} = \mathbf{1}, 2, \dots, \mathbf{N}; \\ &r = 1, 2, \dots, j\_{\prime}, \dots \text{R} \end{aligned} \tag{1}$$

**4. Empirical analysis**

the inefficiency is result of inappropriate scale.

No. of Efficient DMUs Efficient DMUs

No. of Efficient DMUs Efficient DMUs

**Table 3.** BCC-efficiency Scores for operating efficiency for each year

*Note*. Source from this study

are all hold.

First, multi-collinearity analysis was employed to examine the correlation coefficient be‐ tween input and input variables, and then between output and output variables [56]. We used isotonicity diagnosis to examine positive correlation coefficients between input and output variables [57]. We then used sensitivity analysis to sequentially increase or reduce the input or output variables to examine variation of efficiency [8]. The obtained sensitivity analysis result does not consider the operating expenses because of their highly correlation. Additionally, we also test the rule of thumb issued by Golany and Roll [58]. The four tests

Comparative Analysis of Endowments Effect Renewable Energy Efficiency Among OECD Countries

http://dx.doi.org/10.5772/52020

203

Tables 3 and 4 report the BCC efficiency scores of OE and DE for the 34 OECD countries from 2007 to 2009. Table 3 shows the comparison of the main goal in phase I to evaluate how efficiently countries use their resources; in other words, to identify any inefficiency result from PTE or SE. The resource inefficiency 2007, 2008, and 2009 is primarily pure technical efficiency (0.729, 0.704, and 0.727, respectively). In other words, the inefficiency is a result of inappropriate input and output configuration, rather than inappropriate scale. Table 4 shows a comparison of the main goal in Phase II to evaluate how efficiency energy is used to identify inefficiency resulting from PTE or SE. The resource inefficiency during 2007, 2008, and 2009 is primarily scale efficiency (0.439, 0.431, and 0.45, respectively). In other words,

**Phase 1**

**Phase 2**

DMUs TE PTE SE TE PTE SE TE PTE SE Ave. 0.666 0.729 0.917 0.5 0.704 0.848 0.597 0.727 0.812 SD 0.26 0.247 0.148 0.266 0.255 0.176 0.274 0.247 0.183

DMUs TE PTE SE TE PTE SE TE PTE SE Ave. 0.387 0.735 0.439 0.373 0.726 0.431 0.367 0.718 0.45 SD 0.445 0.293 0.474 0.441 0.291 0.48 0.407 0.285 0.431

**2007 2008 2009**

9 11 11 6 10 7 7 13 7

**2007 2008 2009**

9 15 12 8 14 12 7 12 11

We utilized the BCC input-oriented model to measure phase I and II to find a maximum output with certain medial output.


**Table 2.** Country Names of each DMU
