Estimate of the Societal Energy Return on Investment (EROI)

Abstract

Access to abundant and affordable primary energy resources has been recognised as an essential factor for the prosperity of human societies. To measure their quality, understood as the ease with which the energy system can extract and transform them into a form useful to society, the concept of energy return on investment (EROI) is widely used. Yet, so far, very few estimates of this indicator exist at a society level. This paper first aims at providing an estimate of the societal EROI using a simple macroeconomic model with two sectors, an energy sector and a final sector aggregating the rest of the economy. For the year 2018 and at a worldwide level, we obtain a gross EROI of 9.4, and a net EROI of 8.5. The estimation of the net energy ratio (NER), a second indicator more comprehensive than the EROI, allows assessing the energy embodied in the intermediate and capital consumptions of the entire economy. The NER calculation reveals that only 39% of the final energy produced contributes to total consumption (private and public) and economic growth, the remaining 61% being consumed within the economy. These intermediate energy consumptions (direct and indirect) are unevenly distributed between the two sectors: 11% of the production goes to the energy sector, while no less than 50% is consumed within the final sector. These figures proved to be very insensitive to variations in the value of estimated model parameters.

Appendix 1

Development of (17)

Unlike in Fagnart and Germain (2016), there are in the present model deliveries of the ES to private and public consumption ($C_{\text{e}}\ne 0$). In the following, we develop a relationship between the useful ouput of the economy and the energy production $Y_{\text{e}}$. The first approach is based on the definition of final consumption and establishes its relationship with $Y_{\text{e}}$, while the second approach consists in directly calculating the fraction of $Y_{\text{e}}$ contained in the ICCs of both sectors.

Link between final consumption and $Y_{\text{e}}$

(1), (4), (5), (6), (7) lead to the following equations linking sectoral outputs $Y_i$ and final consumptions $C_i$ ($i=e,f$):

$$\begin{aligned} Y_{\text{e}}=\, & {} q_{\text{e}}Y_{\text{e}}+q_{\text{f}}Y_{\text{f}}+C_{\text{e}} \\ Y_{\text{f}}= & {} (x_{\text{e}}+\delta _{\text{e}} v_{\text{e}})Y_{\text{e}}+(x_{\text{f}}+\delta _{\text{f}} v_{\text{f}})Y_{\text{f}}+C_{\text{f}}+\Delta K\\= & {} w_{\text{e}} Y_{\text{e}} + w_{\text{f}} Y_{\text{f}} + C_{\text{f}}+\Delta K \end{aligned}$$

We define $D_{\text{f}}$ as the final demand (sum of consumption of final goods and net investment), and isolate both $C_{\text{e}}$ and $D_{\text{f}}$ to find:

$$\begin{aligned} C_{\text{e}}= \,& {} (1-q_{\text{e}}) Y_{\text{e}} - q_{\text{f}} Y_{\text{f}} \end{aligned}$$

(28)

$$\begin{aligned} D_{\text{f}} \triangleq C_{\text{f}} + \Delta K= \,& {} (1-w_{\text{f}}) Y_{\text{f}} - w_{\text{e}} Y_{\text{e}} \end{aligned}$$

(29)

The first equation gives an expression for $Y_{\text{f}}$ that we incorporate in the second equation to write the following relationship between $Y_{\text{e}}$, $C_{\text{e}}$ and $D_{\text{f}}$:

$$\begin{aligned} D_{\text{f}} = (1-w_{\text{f}}) \frac{(1-q_{\text{e}})Y_{\text{e}}-C_{\text{e}}}{q_{\text{f}}}-w_{\text{e}} Y_{\text{e}} \end{aligned}$$

Let $\zeta =C_{\text{e}}/Y_{\text{e}}$ be the fraction of energy production sold for final consumption. Then the previous equation becomes:

$$\begin{aligned} D_{\text{f}}= \,& {} \bigg ( \left( 1-w_{\text{f}} \right) (1-q_{\text{e}}-\zeta )- q_{\text{f}} w_{\text{e}} \bigg ) \frac{Y_{\text{e}}}{q_{\text{f}}} \nonumber \\= \, & {} \bigg ( (1-q_{\text{e}}-\zeta ) - \bigg ( q_{\text{f}} w_{\text{e}} + (1-q_{\text{e}}-\zeta ) w_{\text{f}} \bigg )\bigg ) \frac{Y_{\text{e}}}{q_{\text{f}}} \end{aligned}$$

(30)

This equation gives the quantity of goods that can be delivered to final demand (sum of consumption and net investment) from a certain amount of final energy. The theoretical maximal output is given by the ratio $\frac{Y_{\text{e}}}{q_{\text{f}}}$. The fraction that actually reaches the FS is given by $(1-q_{\text{e}}-\zeta )$, it corresponds to the energy flow $E_{\text{f}}$. Then the first loss is the fraction of $Y_{\text{e}}$ consumed by the NEIC and capital consumption (CC) of the ES, measured by $q_{\text{f}} w_{\text{e}}$, and the second loss is the fraction of $Y_{\text{e}}$ consumed by the NEIC and CC of the FS, measured by $(1-q_{\text{e}}-\zeta ) w_{\text{f}}$. These losses can be further distributed between $C_{\text{e}}$ and the rest of the ouput $Y_{\text{e}}$ (see Sect. 2.4).

Link between the NEICs and CCs of both sectors and $Y_{\text{e}}$

$$\begin{aligned} \text {NEICs}+\text {CCs}= \, & {} X_{\text{e}} + \delta _{\text{e}} K_{\text{e}} + X_{\text{f}} + \delta _{\text{f}} K_{\text{f}} \\= \, & {} \left( q_{\text{f}} w_{\text{e}} + \frac{Y_{\text{f}} q_{\text{f}}}{Y_{\text{e}}} w_{\text{f}} \right) \frac{Y_{\text{e}}}{q_{\text{f}}}\\= \, & {} \bigg ( q_{\text{f}} w_{\text{e}} +(1-q_{\text{e}}-\zeta ) w_{\text{f}} \bigg )\frac{Y_{\text{e}}}{q_{\text{f}}} \\ \end{aligned}$$

We indeed find the last terms of (30).

Given the definition of the net domestic product (16), Eq. (30) gives an expression for the NDP as a function of the technical parameters, the fraction $\zeta$, and the production $Y_{\text{e}}$:

$$\begin{aligned} \text{NDP}= \, & {} D_{\text{f}} + pC_{\text{e}} \\=\, & {} \bigg ( (1-w_{\text{f}})(1-q_{\text{e}})- q_{\text{f}} w_{\text{e}} + \zeta (1-w_{\text{f}} + pq_{\text{f}}) \bigg ) \frac{Y_{\text{e}}}{q_{\text{f}}} \end{aligned}$$

which corresponds to equation (17).

Link Between v, g and $g_k$

Using (4), (11) and (3) we write:

$$\begin{aligned} \Delta K = s\text{GDP}-\delta K = \left( \frac{s}{v}-\delta \right) K \end{aligned}$$

Hence the capital growth rate $g_k$ is given by:

$$\begin{aligned} g_{k}=\frac{\Delta K}{K}=\frac{s}{v}-\delta \end{aligned}$$

Be g the GDP growth rate: $g = \frac{\Delta \text{GDP}}{\text{GDP}}$. Starting from (3), one can write at first order $g_{v}=\frac{\Delta v}{v} = \frac{\Delta K}{K} - \frac{\Delta \text{GDP}}{\text{GDP}}$, which implies Eq. (26):

$$\begin{aligned} g = g_{k}-g_{v} =\frac{s}{v}-\delta -g_{v} \end{aligned}$$

GDP growth is decomposed into the growth of the capital stock and the decline in the capital intensity of the economy.

Validation of $g_v=0$

In the reference calibration, the capital intensity of the economy (v=$\frac{K}{\text{GDP}}$) was assumed to be constant, and therefore $g_v$ was zero. This assumption can be validated as follows. One can do the exercise of estimating v for the years 1990 to 2018 via the previous equations. A posteriori, we observe that this parameter is more or less constant, regardless of the hypothesis that we postulated a priori for its rate of variation $g_v$. From then on, the starting postulate $g_v = 0$ is the only valid one.