**2. Literature Review**

The life of people without electricity was inconvenient, they worked by manual labour, and lived without light. Since electrical energy was invented in the18th century, the life of inhabitants has been changed with access to light, electronic equipment, and high-tech. The effectiveness of production operations is enhanced and upgraded sharply by the use of electrical machines. The process whereby people use electrical energy for lighting, heating, transportation, and so on is called "electricity consumption". The population is the major source that supports electricity development when utilizing electronic equipment. The electricity is consumed at a high or low level, the EC reflects an economic growth level. Chen denoted that the economic growth and population have a vital role on the electrical energy consumption when depending on the non-parametric model [16]. To explore the electricity demand in the future, Gajowniczek [17] displayed an approach to predict electricity load at the individual household level using CART, SVM and a MLP neutral network model; Gajowniczek continued studying electricity demand [18]; Singh [19] proposed Bayesian network prediction for energy usage forecasting.

On the other hand, the electricity causes greenhouse gas [20] that leads to climate change because of the emission of CO2, CH4, N2O [21] from electricity production processes [22]. Emissions from hydropower are estimated by using statistical global emission models through the reservoir water surface [23,24], that from natural gas and coal power plants is calculated by a simple model [25], and that from combustion power plants is counted by the values and data of emission factors exhausted from the circulating fluidized bed boiler [26], or that from wind power plants is formulated by a simple analysis method for the undesirable elements of electricity production processes [27]. In China emissions from EC are determined by a data analysis and measurement method [28], while in the United States a transparent method is used [29]. Hence, the previous researchers applied various methods to an examination of the emission of undesirable factors from EC.

Whereas DEA normally concerns calculating performance with the inputs and good outputs in various models such as dynamic-SBM, super-SBM, EBM, i.e., however, they cannot solve for undesirable outputs in social activities, air pollution, and the industrial manufacturing sector. For this reason, Tone proposed an undesirable outputs model in DEA to evaluate bad outputs [30], displaying a new scheme. A DMU acquires efficiency as the score approaches 1, and it is inefficient when the score is less than 1. Furthermore, the model can compute the performance by combining both undesirable and desirable outputs [31]. The efficiency valuations indicate not only the interplay between desirable and undesirable outputs, but also the ranking of each DMU in every year [32]. Many researchers have applied the undesirable model into their studies. For example, an analysis by the Organization for Economic Co-operation and Development (OECD) of countries with population and energy consumption as input factors, GDP as desirable output, and CO2 as undesirable output reveals the environmental efficiency [33]; the overall efficiency of the United States's electricity production is evaluated by escalating the desirable output and undesirable outputs [34]; counting the efficiency shows the relationship between labor force, energy consumption, governmen<sup>t</sup> expenditure as input, GDP as desirable output, and CO2 emissions as undesirable output [35]. Moreover, the undesirable model is used for examining performance in other aspects such as estimating the impact of production pollutants in the textile industry of China with inputs like labor, and energy, yam and fabric as desirable outputa, and wastewater as undesirable [36]. In addition, the researchers also utilized an undesirable model to analyze and evaluate efficiency in the energy sector. Measuring between inputs including gross fixed capital formation, labor and energy consumption and outputs including CO2 (undesirable output), and GDP (desirable output) indicated the energy performance in Brazil, Russia, India, China, and South Africa [37].

With the principle of the undesirable outputs model and its previous applications, the paper proposed undesirable outputs model of DEA to analyze the interplay between inputs such as population and EC and outputs such as GDP, CO2, CH4, N2O in the electricity production aspect of 42 countries during the 2008–2017 term.
