*3.2. Forecasting*

In order to provide forecasts of eco-efficiency to the year 2040, forecasts of the DEA inputs and output need to be made. Since the data have a relatively short time span (annual data from 1996 to 2019), methods suited to forecasting short time series data sets are used. These methods include ETS, ARIMA, TBATS, and THETA [31]. ETS, which is based on exponential smoothing, is a state-space model with error (E), trend (T), and seasonal (S) components. The tradeoff between these components is controlled by smoothing parameters, and the optimal smoothing parameters can be determined using an automatic search algorithm. ARIMA is the acronym for autoregressive integrated moving average. While ETS models describe the trend and seasonality in the data, ARIMA models describe the autocorrelations in the data. The selection of the best-fitting ARIMA model can be easily achieved through a search algorithm. ETS and ARMA models are widely used in forecasting. The TBATS refers to an exponential smoothing state space model with Box-Cox transformations, ARMA error, trend and seasonal components. TBATS is estimated using a fully automatic modeling approach. The THETA model is equivalent to simple exponential smoothing with drift. The ETS, ARIMA, TBATS, and THETA models can be considered as examples of machine learning, since for each model, a fully automated search algorithm is used to find the best-fitting model. In order to reduce the dependence on forecasts from any one model, an average forecast is computed. Averaging forecasts often works well in practice [31]. The average forecast from these methods is referred to as the business as usual (BAU) scenario. Forecasting was done using the R package fpp2 [32].

The approach taken to forecasting in this paper is similar to the approach taken by international agencies such as the International Energy Agency (IEA) in their World Energy Outlook [33] and the US Energy Information Agency (EIA) in their Annual Energy Outlook [34] where they make long-term projections (20–30 years or so) for energy demand. A reference case, base case, or business as usual (BAU) scenario is taken as the benchmark

where past data trends are assumed to continue into the future, and policy assumptions are assumed to be fixed. The forecasting methods used in this paper are useful for creating forecasts under a BAU scenario. *Sustainability* **2021**, *12*, x FOR PEER REVIEW 7 of 16

#### *3.3. Data* FRA 6103.18 7316.91 10038.14 12078.57 14397.68 2.57 5 1.78 3

Country-level data on CO<sup>2</sup> emissions, GDP, labor, capital, energy consumption, and non-fossil fuel energy consumption are required for the analysis. Data on GDP (real GDP in millions of 2011 US dollars: gdpna), capital (capital stock in millions of 2011 US dollars: rnna), and labor force (number of persons employed in millions: emp) come from the Penn World Tables (PWT 9.1) [35]. Data on CO<sup>2</sup> emissions (millions of tonnes) from the consumption of energy, energy (fossil fuel and non-fossil fuel) consumption (Exajoules), and non-fossil fuel energy consumption (Exajoules) come from the BP Statistical Review [36]. CO<sup>2</sup> emissions from the consumption of energy include emissions that result from the consumption of petroleum, natural gas, and coal and from natural gas flaring. Total energy consumption includes coal, natural gas, petroleum and other liquids, nuclear, renewables, and other. The 18 countries included in this study include Argentina (ARG), Australia (AUS), Brazil (BRA), Canada (CAN), China (CHN), France (FRA), Germany (DEU), India (IND), Indonesia (IDN), Italy (ITA), Japan (JPN), South Korea (KOR), Mexico (MEX), Russia (RUS), South Africa (ZAF), Turkey (TUR), Great Britain (GBR), and the United States of America (USA). These 18 countries along with the European Union and Saudi Arabia form the group of countries known as the G20. The dataset covers the years 1996 to 2019. Saudi Arabia is not included in the analysis because the share of non-fossil fuel energy is very low (close to zero). The dataset starts in 1996 to accommodate the breakup of the Former Soviet Union in 1991 and the turmoil that followed for those countries involved. GBR 3875.79 4852.46 8055.22 10591.27 13127.32 3.80 1 2.48 1 IDN 4348.61 4555.83 4885.15 4893.71 4904.26 −0.78 18 −0.02 15 IND 2836.82 3143.15 3727.49 4087.08 4446.67 1.39 10 0.88 11 ITA 5508.29 6174.88 7656.65 8379.11 9152.01 1.48 9 0.89 10 JPN 3554.71 3893.36 4568.16 4932.84 5297.52 1.09 13 0.73 12 KOR 2432.16 2863.68 3495.61 4018.35 4541.09 2.11 6 1.33 5 MEX 4755.46 4394.05 5281.04 5232.37 5222.25 0.67 15 −0.06 18 RUS 1510.82 2357.20 2686.68 3091.27 3470.76 3.26 2 1.30 6 TUR 4523.68 4998.02 5826.36 5889.67 5952.98 1.02 14 0.08 14 USA 2463.67 3062.75 4225.92 5257.28 6444.34 2.76 3 2.10 2 ZAF 1223.90 1341.53 1561.66 1714.58 1867.85 1.22 12 0.95 9 GR1 and GR2 are the average annual growth rates from 1996 to 2019 and 2019 to 2040, respectively. Great Britain, Russia, the United States, Germany, and France have recorded the highest growth rates in GDP per unit of CO2 over the period 1996 to 2019 (Table 1). The lowest growth rates were recorded for Indonesia, Brazil, Argentina, Mexico, and Turkey. Over the period 2019 to 2040, the countries with the highest growth rates are Great Britain, United States, France, Germany, and South Korea. The countries with the lowest growth rates are Mexico, Argentina, Indonesia, Brazil, and Turkey. Four of these countries (Mex-

The inputs to the DEA analysis are the capital to labor ratio (klratio), output to labor ratio (ylratio), capital to energy ratio (keratio), and non-fossil fuel share of energy (nffshare). The output variable in the DEA analysis is labeled eco and is measured by GDP/CO<sup>2</sup> emissions. ico, Argentina, Indonesia, Brazil) recorded negative growth rates, indicating that production-based CO2 productivity is expected to decline over the period 2019 to 2040. Each country in the G7 has experienced an increase in production-based CO2 productivity, but the rate of increase varies considerably (Figure 1). Great Britain has the highest

The time-series pattern of production-based CO<sup>2</sup> productivity varies considerably between countries (Figures 1–3). Actual data are recorded up to and including 2019, after which time forecasts are shown (Figures 1–3; Table 1). In order for production-based CO<sup>2</sup> productivity to be increasing over time, GDP must grow faster than CO<sup>2</sup> emissions. growth in production-based CO2 productivity over both periods (1996 to 2009 and 2009 to 2040). France has the highest production-based CO2 productivity and one of the highest growth rates of the countries studied. Japan has the lowest growth rate of productionbased CO2 productivity in the G7 over the period 2019 to 2040.

**Figure 1. Figure 1.**  GDP per unit of CO GDP per unit of CO2 emissions for the G7 countries. <sup>2</sup> emissions for the G7 countries.

Among the BRICS, Brazil has the highest production-based CO2 productivity (Figure 2). Over the period 2019 to 2040, Russia and South Africa experience the fastest growth.

Brazil recorded the slowest growth in production-based CO2 productivity.

**Figure 2.** GDP per unit of CO2 emissions for the BRICS countries. **Figure 2.** GDP per unit of CO<sup>2</sup> emissions for the BRICS countries.

**Figure 3.** GDP per unit of CO2 emissions for the other countries. **Figure 3.** GDP per unit of CO<sup>2</sup> emissions for the other countries.

Summary statistics for the inputs and output to the DEA analysis are shown in Table 2. Each variable is increasing over time. Between 2000 and 2020, production-based CO2 productivity grew the greatest followed by the capital to energy ratio. The slowest growth was observed for the share of non-fossil fuels. In the BAU scenario, each variable grows less over the period 2020 to 2040 than it did over the 2000 to 2020 period. For each of the years shown, the coefficient of variation (CV) shows that the non-fossil fuel share has the greatest amount of variability. For most of the years shown, eco has the least variability.

**2000 klratio ylratio keratio nffshare eco**  mean 277,076.531 56,563.527 964,298.382 0.148 3645.413 min 21,421.861 6647.760 371,245.827 0.034 1223.902 max 685,330.501 103,538.244 2,096,226.960 0.440 6648.001 sd 181,172.821 32,356.395 444,240.280 0.126 1633.171 CV 0.654 0.572 0.461 0.853 0.448 **2010 klratio ylratio keratio nffshare eco**  mean 312,698.881 63,813.004 1,083,100.190 0.155 4104.001 min 42,319.065 11,167.207 405,927.151 0.027 1341.533 max 743,960.972 119,401.134 2,532,021.912 0.456 7316.906 sd 195,609.458 32,417.909 529,437.749 0.128 1751.996 CV 0.626 0.508 0.489 0.824 0.427 **2020 klratio ylratio keratio nffshare eco**  mean 338,651.529 69,381.077 1,276,345.426 0.181 4963.391 min 73,993.932 19,033.970 537,705.879 0.045 1561.656 max 739,140.772 131,053.041 2,992,167.107 0.486 10,038.137 sd 190,770.768 33,649.249 647,702.338 0.126 2227.819 CV 0.563 0.485 0.507 0.697 0.449 **2030 klratio ylratio keratio nffshare eco** 

**Table 2.** Summary statistics.


**Table 1.** Summary statistics for GDP/CO<sup>2</sup> (US dollars per tonne of CO<sup>2</sup> emissions).

GR1 and GR2 are the average annual growth rates from 1996 to 2019 and 2019 to 2040, respectively.

In 2020, the countries with the highest values of GDP per unit of CO<sup>2</sup> were France, Great Britain, Italy, Brazil, and Germany. The countries with the lowest values were South Africa, China, Russia, Australia, and Canada. Notice that the economics of four of these countries (South Africa, Russia, Australia, and Canada) are heavily reliant on natural resource extraction. These rankings are mostly unchanged in 2040. In 2040, the countries with the highest values of GDP per unit of CO<sup>2</sup> are France, Great Britain, Italy, Germany, and Brazil. As in the case of 2020, the countries with the lowest values of GDP per unit of CO<sup>2</sup> in 2040 are South Africa, China, Russia, Australia, and Canada. In general, productionbased CO<sup>2</sup> productivity tends to be low in countries that have a large amount of mineral or fossil fuel resource extraction (Australia, Canada, South Africa, Russia). Canada, Australia, Russia, and South Africa are sometimes referred to as the CARS group of countries.

Great Britain, Russia, the United States, Germany, and France have recorded the highest growth rates in GDP per unit of CO<sup>2</sup> over the period 1996 to 2019 (Table 1). The lowest growth rates were recorded for Indonesia, Brazil, Argentina, Mexico, and Turkey. Over the period 2019 to 2040, the countries with the highest growth rates are Great Britain, United States, France, Germany, and South Korea. The countries with the lowest growth rates are Mexico, Argentina, Indonesia, Brazil, and Turkey. Four of these countries (Mexico, Argentina, Indonesia, Brazil) recorded negative growth rates, indicating that productionbased CO<sup>2</sup> productivity is expected to decline over the period 2019 to 2040.

Each country in the G7 has experienced an increase in production-based CO<sup>2</sup> productivity, but the rate of increase varies considerably (Figure 1). Great Britain has the highest growth in production-based CO<sup>2</sup> productivity over both periods (1996 to 2009 and 2009 to 2040). France has the highest production-based CO<sup>2</sup> productivity and one of the highest growth rates of the countries studied. Japan has the lowest growth rate of production-based CO<sup>2</sup> productivity in the G7 over the period 2019 to 2040.

Among the BRICS, Brazil has the highest production-based CO<sup>2</sup> productivity (Figure 2). Over the period 2019 to 2040, Russia and South Africa experience the fastest growth. Brazil recorded the slowest growth in production-based CO<sup>2</sup> productivity.

For the remaining group of countries, Australia and South Korea have low values of production-based CO<sup>2</sup> productivity (Figure 3). Notice that over the period 2019 to 2040, Australia and South Korea also have the highest growth rates of production-based CO<sup>2</sup> productivity in this group of countries.

Summary statistics for the inputs and output to the DEA analysis are shown in Table 2. Each variable is increasing over time. Between 2000 and 2020, production-based CO<sup>2</sup> productivity grew the greatest followed by the capital to energy ratio. The slowest growth was observed for the share of non-fossil fuels. In the BAU scenario, each variable grows less over the period 2020 to 2040 than it did over the 2000 to 2020 period. For each of the years shown, the coefficient of variation (CV) shows that the non-fossil fuel share has the greatest amount of variability. For most of the years shown, eco has the least variability.


**Table 2.** Summary statistics.

Klratio (US dollars per worker), ylratio (US dollars per worker), keratio (millions of US dollars per Exajoules), nffshare (a ratio between 0 and 1), and eco (US dollars per tonne of CO<sup>2</sup> emissions). BAU is the business-as-usual scenario. GR1 and GR2 are the average annual growth rates from 2000 to 2020 and 2020 to 2040. CV is the coefficient of variation.
