Latin America’s Renewable Energy Impact: Climate Change and Global Economic Consequences

Abstract

In the context of the imperative global shift towards renewable energy to mitigate climate change, Latin America (LATAM) emerges as a region of immense untapped potential. However, there is no formal quantification of the effects of developing this potential. This study analyzes the economic and climate impacts of developing renewable energy in LATAM and the Asia–Pacific region using an integrated economic and climate assessment model (IAM). The key findings are as follows. First, exporting renewable energy from LATAM and the Asia–Pacific region yields economic benefits across all regions. However, this surge in renewable energy exacerbates rather than alleviates global warming. Second, the implementation of policy measures accompanying renewable energy exports, aimed at discouraging the use of polluting energy sources, proves effective in mitigating global warming while sustaining significant economic gains globally. Third, LATAM stands to gain substantially from this development. Fourth, due to the gradual process of capital accumulation, any delays in initiating the development of renewable energy exports not only diminish economic gains during the postponement but also in the years following the commencement of exports. These results are robust to several additional simulations and sensitivity analyses. The results align with the goals of the Paris Agreement.

1. Introduction

Can the renewable energy potential of Latin America help curb climate change? This study formally analyzes this question estimating the economic and climate impacts of this energy potential. To do this end, we extend the integrated assessment model (IAM) used in [1] to quantify the long-term climate and economic consequences of developing the huge renewable energy potential of Latin America. Including this renewable energy potential in an IAM as a substitute for the use of fossil fuels offers analytical advantages. In fact, this modeling strategy allows us to determine simultaneously the efficiency gains in terms of production in different regions from this development, but also its effects on the climate change captured by its consequences in terms of changes in the global temperature.

There are several reasons to view Latin America as a crucial player to combat the climate change. Note that climate change mainly originates by carbon emissions. Moreover, the origins of these emissions are mainly attributed to the energy sector. In fact, according to [2], in 2016, around 73% of global carbon emissions were caused by the energy sector, whereas only 18% were attributed to agriculture and land use change. Moreover, emissions from the energy sector are greatly due to the burning of fossil fuels. It is therefore imperative to reduce the use of this type of fuel in order to comply with the limit of 1.5 ºC temperature increase by 2100. In this context, Latin America offers huge potential in terms of renewable and green sources of energy.

Hence, one significant opportunity to decarbonize the energy matrix worldwide is to change the use of fossil fuels for renewable energies such as solar or wind energy. These sources of renewable energy have reduced the levelized cost of energy (LCOE) ($LCO{E}_i=\frac{{\sum }^n\frac{I_t+V{C}_t}{{(1+r)}^t}}{{\sum }^n\frac{E_t}{{(1+r)}^t}}$, where $I_t$ is investment expenditures in year t, $V{C}_t$ is the variable costs in year t, $E_t$ is the electrical energy generated in year t, and r is the discount rate) by almost 90% and 70%, respectively, in the last ten years, reaching global weighted average values of below 50 (USD/MWh) (see

Table 1. Summary of the evolution of investment prices, capacity factor and levelized cost of energy for different types of renewable technologies. Source: [3].

	Total Installed Costs (USD/kW)			Capacity Factor (%)			LCOE (USD/MWh)
	2010	2022	Change	2010	2022	Change	2010	2022	Change
Bioenergy	2.904	2.162	$-26\%$	72	72	−2%	82	61	−25%
Geothermal	2.904	3.478	20%	87	85	−5%	53	56	6%
Hydropower	1.407	2.881	105%	44	46	4%	42	61	47%
Solar PV	5.124	876	−83%	14	17	17%	445	49	−89%
CSP	10.082	4.274	−58%	30	36	40%	380	118	−69%
Onshore wind	2.179	1.274	−42%	27	37	31%	107	33	−69%
Offshore wind	5.217	3.461	−34%	38	42	6%	197	81	−59%

). Such a reduction in costs make these technologies much more competitive, since a fossil fuel power plant has an average LCOE of about 60 (USD/MWh) before taxes [3].

Although there is a heterogenous distribution of renewable energy potential across the world, Latin America has the biggest one. For instance, in the case of solar energy, it has the highest practical solar PV potential, which corresponds to the average radiation which includes physical and technical restrictions, as well as restrictions associated with regulating access to protected areas or land used for agriculture (see [4]). This is found in the Atacama Desert in northern Chile, where the practical solar PV potential reaches values close to 6.4 (kWh/kWp), followed by Africa or the Middle East region with 5.6 (kWh/kWp) and some other regions like California or Australian Desert with 5.2 (kWh/kWp), as we show in Figure 1.

With this potential, Latin America could satisfy the entire world’s energy demand. For instance, if Chile, Argentina, Bolivia, and Peru could develop only 25% of their practical solar potential level, they would generate around 139.000 (TWh/year) based on [4] (this value was calculated using a conversion efficiency of 15%, a percentage of the territory associated with practical solar potential level 2 of 10%, and an average daily practical potential of 4.71 (kWh/m²)). This figure is in the same order of magnitude as the global primary energy demand, which was 162.673 (TWh/year) in 2019. If we also consider the potential of the rest of LATAM countries and the huge potential from wind energy and other renewable energy sources, these numbers could substantially exceed the energy demand projected in the medium and long term in the region.

Moreover, this renewable energy potential in LATAM could be converted into different kinds of energy like electricity or synthetic fuels (power-to-X) in order to store and transport energy to other regions. The production of power-to-X fuels is based on the generation of green hydrogen through water electrolysis using renewable energies (see [5]). This hydrogen can be used directly, further processed, or synthesized, for example, by adding carbon dioxide (CO ₂) or nitrogen (N₂). This allows for the production of various power-to-X fuel variants, ranging from gaseous and liquid hydrogen to synthetic natural gas (SNG), synthetic kerosene, diesel, methanol, or ammonia. Since the production of power-to-X is highly energy-intensive (40–70 (USD/kgH₂)) and associated with high losses, even with future efficiency improvements, it seems economically sensible to produce it only in regions with excellent renewable energy resources and corresponding land availability. For countries that have such potential in large quantities, exceeding their own needs, power-to-X provides an entry into an attractive future market in the transformation of a global energy system. This possibility is supported by [6], which argues that those regions in the world with the greatest potential to develop a green synthetic fuels export industry are the Atacama Desert, Southern Patagonia, and Australia. This, together with the National Green Hydrogen Strategy [7] promoted by Chile, makes the materialization of this export opportunity more feasible. In the same line, electricity could exported from Latin America to other regions through feasible electrical interconnections. One great example of this worldwide is ENTSO-E, the European Network of Transmission System Operators for electricity. This association makes it possible to interconnect the European electricity systems with those of North African countries, Great Britain, Nordic countries, Eurasia, and the Middle East. Alternatively, this energy potential could be used to produce synthetic fuels (e.g., green hydrogen) and export them to any region of the world.

Therefore, the objective of this research is to quantify and evaluate what renewable energy potential Latin America can offer both in terms of economic benefits and curbing climate change. Given the lack of previous studies on the subject, the main goal is to have an analytical model to understand and quantify the economic and climatic effects of developing and exporting the renewable energy from LATAM. As described above, to perform this analysis, we extend the integrated assessment model developed to include the renewable energy potential from LATAM and the Asia–Pacific region.

The main results of our analysis are as follows. First, renewable energy exports from LATAM generate economic benefits for all regions, but do not reduce the effects of global warming and, on the contrary, exacerbate the problem. Second, if the renewable energy exports are accompanied by policy measures that discourage the use of fossil fuel (e.g., carbon taxes), greater economic benefits can be obtained together with a reduction in global warming. This last result is independent of the allocation of the global demand for renewable energy exports between LATAM and Asia–Pacific regions. Third, the economic gains in LATAM could be as big as about five times the global average due to its exporting nature and the relatively low (per capita) income in comparison with most other regions. Fourth, due to the gradual capital accumulation process, delaying the development of exports reduces economic gains not only during the delay period, but also in the years following the commencement of exports. Finally, stochastic simulations suggest that uncertainties related to the renewable energy development are better attenuated when policy measures that discourage carbon emissions are deployed.

• Related literature and contribution. Our research is related to the three main strands of the previous literature. First, there are studies that focus on quantifying the economic consequences of imposing policies to reduce carbon emissions. Second, other studies analyzing how production changes towards greener technologies can contribute to a more sustainable economic development. Finally, other works formalize the economic externalities from carbon emissions, explicitly incorporating the carbon cycles and its temperature consequences in macro-economic models, which have been named integrated assessment models (IAMs).

Regarding the first strand of the literature, some recent papers, like [8,9], studied the macroeconomic effects of the imposition of a carbon tax in Europe, finding opposite results in terms of GDP or unemployment. In the same line, refs. [10,11,12] analyze the effects of the carbon tax on the Chilean economy showing the trade-off between the effectiveness in reducing emissions and the contractionary effects on macroeconomic results (lower growth and higher inflation).

However, our work is also related to the second type of literature, which is the one that studies technological change. The first study in this context is [13] which introduces endogenous and directed technical change in an environmentally constrained growth model to argue that, when inputs are substitutable, sustainable growth can be achieved with temporary policies that redirect innovation towards clean inputs. Recently, refs. [14,15,16] added to the evidence of this phenomenon and showed the implications of certain technological developments. Specifically, ref. [17] studied the shale gas phenomenon and its long-term effects but without explicitly modeling the climate and carbon cycle. Therefore, we understand our work like a new technological innovation. Specifically, a new kind of energy (electricity or synthetic fuels from Latin America) for the world that explicitly models the climate and carbon cycle.

Finally, our work is closely related to the growing literature of using IAMs to study climate change and its effects on the economy. Preliminary works in this area are DICE/RICE models [18,19,20] which extend the neoclassical economic framework with carbon cycle dynamics, temperature, and damage function, aiming to find the social cost of carbon emissions (SCC). More recently, ref. [21] constructed a parsimonious framework to find, under certain assumptions, an analytical expression for the SCC. Others examples such as the PAGE model [22] was used in The Stern Review [23] which argues that the benefits of strong and early action on climate change outweigh the costs. Similarly, the FUND model [24] was used to calculate the social cost of carbon (SCC) [25], or [26] focused on the effects of uncertainty in the parameter to calculate the SCC. Recently, the new GTAP-InVEST model [27] has been used to map the planet’s critical natural assets, as [28] understood the relationship between biodiversity and society [29] to highlight the lack of relationship between markets and biodiversity [30]. All of these last questions fall beyond the issue of climate change.

In sum, our work is related to analyze the worldwide economic consequences of changes in the energy matrix. In this line, our work is related to [31], which uses the G-Cube model explained in [32], in which they study the effects of demographic transition, long-term slowdown in productivity growth, and the disruption in the global economy due to increasing climate shocks with an emphasis on the short-term macroeconomics adjustment. However, we keep an aggregate approach of the different regions of the world in order to explicitly model the carbon cycle and temperature determination like [1]. At the same time, we extend the work by [1] to include additional energy sources to explicitly assess the joint economic and climate consequences of developing that new source of renewable energy. This allows us to quantify the effects of developing the huge renewable energy potential of LATAM and Asia–Pacific region, having a long-term perspective that simultaneously assesses the worldwide impacts on the main macroeconomic variables and the climate.

It should be noted that we want to be clear in terms of our work not taking into account the friction in the industrial organization of the market for this new kind of energy, or the friction in terms of international trade even though we try to internalize these frictions in the path of the prices of energies. Despite the above, we believe that this work is the first step and a novel contribution to quantify the long-term economic and climatic consequences of exploiting Latin America’s renewable potential. In this way, it addresses the lack of studies on the subject by highlighting the heterogeneity of the availability of renewable resources and new opportunities to curb climate change.

• Road Map. The rest of this paper is organized as follows. The description of the model, with a special emphasis on novel extensions, is presented in Section 2, followed by the calibration of the model in Section 3. The results are discussed in Section 4, whereas a robustness analysis of the results is presented in Section 5. The conclusions and ideas for future work are presented in Section 6. Finally, the analytical derivations of the model and additional details on the calibration and simulations for each region are provided in the Appendix A.

2. Model to Incorporate Renewable Energy Exports

Our model is closely based on the works by [1,33]. The multi-region setting consists of having one oil-producing region, and arbitrarily, many oil-importing regions. Each oil-importing region has a representative firm that uses capital, labor, and energy input to produce final goods. The energy input in each region is produced through a composition of different imperfectly substitutable energy sources. One of these energy sources is oil, which is sold internationally in the world market. The remaining energy sources are all produced regionally at given prices that vary across regions. This variation captures the difference in the capacity to produce alternative sources of energy as a substitute for oil. Each region features a government that sets the climate policy within that region. Finally, and importantly, the model features an explicit representation of the climate as well as a carbon cycle. As the final production demands energy input, which employs the sources that generate carbon emissions, this process affects the stock of CO₂ and the global temperature. The global temperature, in turn, negatively affects the productivity to produce the final goods. These negative effects are modeled through a damage function in each region and their effects are not internalized by households and firms. This implies that imposing a tax on the energy sources that generate carbon emissions can improve the welfare of the economy, as proven by [21]. The detailed description of the baseline model is relegated to the Appendix A, where oil is the only energy source that can be traded internationally. This type of model was developed to consider formal general equilibrium effects in a dynamic and long-term perspective.

In this section, we present two extensions to the baseline model that modify the energy production in each region to allow for energy exports from Latin America (LATAM). Formally, we allow for two types of energy exports from LATAM, namely synthetic fuel and electricity. In the case of electricity exports from LATAM, we restrict their reach exclusively to its closer regions. Our approach to adding alternative energy sources closely follows [1], who considered fracking as a technology to produce a large amount of unconventional oil and gas in the United States.

2.1. Electricity Exports from LATAM

One way to take advantage of the renewable energy potential that exists in Latin America is by converting primary energies (solar, wind, biomass, geothermal, etc.) into electricity and exporting it through electrical interconnections with other regions. Without loss of generality, we will assume that $k=3$ corresponds to renewable energy. In turn, Latin America (region $i=r$) will have the option of exporting this renewable energy. Accordingly, we will define $e_{3,i,t}^x$ as renewable energy exportable through electricity, which corresponds to the renewable energy exported as electricity by Latin America during the period t. It is worth noting that, in the calibration section, we will specify which regions will be able to import this type of energy and how the prices of this new energy source will evolve, where such prices include the costs associated with the transportation of electricity. Also, the total supply of electricity produced by Latin America will be denoted by $e_{3,i,t}^r$.

This new energy source exported from Latin America is a substitute for the domestic production of renewable energy in region $i\ne r$, which is defined by $e_{3,i,t}^d$. To capture this possibility, we define the aggregate renewable energy in region $i\ne r$ as

$$\begin{array}{c}\hfill {\mathbf{e}}_{3,i,t}=2{\left({\lambda }_{3,1,i}{\left(e_{3,i,t}^d\right)}^{{\rho }_r}+{\lambda }_{3,2,i}{\left(e_{3,i,t}^x\right)}^{{\rho }_r}\right)}^{\frac{1}{{\rho }_r}}\end{array}$$

(1)

where ${\lambda }_{3,1,i}$ and ${\lambda }_{3,2,i}$ determine the relative efficiency of domestic and imported renewable energy in region i. Parameter ${\lambda }_{3,2,i}$ also determines the factibility of exporting electricity from LATAM to region i. Thus, when ${\lambda }_{3,2,i}=0$, exporting electricity from LATAM to region i is not feasible. Below, in the calibration section, we will make a precise assumption regarding the regions to which LATAM can feasibly export electricity. In the above expression, ${\rho }_r$ controls the elasticity of substitution between these two types of renewable energy sources. In the case of LATAM, the renewable energy is just ${\mathbf{e}}_{3,r,t}=e_{3,r,t}^d$. After having this renewable energy source in each region, the aggregate energy input for final good production in region i is given by:

$$E_{i,t}={\left(\sum _{k\ne 3}{\lambda }_k{\left(e_{k,i,t}\right)}^{\rho }+{\lambda }_3{\left({\mathbf{e}}_{3,i,t}\right)}^{\rho }\right)}^{\frac{1}{\rho }}$$

(2)

This aggregation is the same specification considered in Proposition A1. A relevant assumption is that the elasticity of substitution between domestic and imported renewable energy is higher than the one among different types of energy sources, such as ${\rho }_r>\rho$. With this modification in the process to aggregate energy sources, energy firms in region $i\ne r$ will first determine the combination of domestic and imported renewable energy, which consists of solving

$$\begin{array}{c}\hfill {\min }_{e_{3,i,t}^d,e_{3,i,t}^x}\left[{\widehat{p}}_{3,i,t}^d{e}_{3,i,t}^d+{\widehat{p}}_{3,i,t}^x{e}_{3,i,t}^x\right]\\ \hfill \mathrm{s}.\mathrm{t}.\mathrm{Equation}\left(1\right)\end{array}$$

(3)

where ${\widehat{p}}_{3,i,t}^d$ and ${\widehat{p}}_{3,i,t}^x$ are, respectively, the prices of domestic and imported renewable energy during region i in period t (in Latin America, we will just have ${\widehat{p}}_{3,i,t}={\widehat{p}}_{3,r,t}^d$). The aggregate price of renewable energy in region i will be given by:

$${\widehat{p}}_{3,i,t}=\frac{1}{2}{\left({\left({\lambda }_{3,1,i}\right)}^{\frac{1}{1-{\rho }_r}}{\left({\widehat{p}}_{3,i,t}^d\right)}^{\frac{{\rho }_r}{{\rho }_r-1}}+{\left({\lambda }_{3,2,i}\right)}^{\frac{1}{1-{\rho }_r}}{\left({\widehat{p}}_{3,i,t}^x\right)}^{\frac{{\rho }_r}{{\rho }_r-1}}\right)}^{\frac{{\rho }_r-1}{{\rho }_r}}$$

(4)

The optimal combination of all energy sources in region i is obtained by solving:

$$\begin{array}{c}\hfill {\min }_{e_{k,i,t}k\ne 3,{\mathbf{e}}_{3,i,t}}\left[\sum _{k\ne 3}^n{\widehat{p}}_{k,i,t}{e}_{k,i,t}+{\widehat{p}}_{3,i,t}{\mathbf{e}}_{3,i,t}\right]\\ \hfill \mathrm{s}.\mathrm{t}.\mathrm{Equation}\left(2\right)\end{array}$$

(5)

which is equivalent to the optimization problem defined in (A9) and (A10).

Similarly to the case of oil, we assume that there is a single world market for this new renewable energy traded internationally. Moreover, we will consider that the electricity capacity in LATAM is sufficiently large such that its supply by period is infinitely price elastic with a price that evolves exogenously. Exporting electricity from LATAM to region i faces an additional cost of ${\mu }_{i,t}$ per exported unit and is expressed in terms of final goods. Hence, the price ${\widehat{p}}_{3,i,t}^x={\widehat{p}}_{3,r,t}^d(1+{\mu }_{i,t})$ for $i\ne r$. The technology in the electricity sector will exogenously determine the evolution for ${\widehat{p}}_{3,r,t}^d$ and ${\mu }_{i,t}$ (this factor $1+{\mu }_{i,t}$ can be interpreted as an iceberg cost widely used in modern trade models). Hence, the total supply of electricity provided by LATAM will be defined by the demand side of renewable energy, given the path of these technological factors (${\widehat{p}}_{3,r,t}^d$ and ${\mu }_{i,t}$) in the electricity sector. The income obtained from the exportation of this electricity is added to the net product previously defined in subsection (v) of Proposition A1 for region $i=r$ (e.g., LATAM). As in the base model, the equilibrium conditions are summarized in Proposition A2.

We can note that this extension of the model does not modify the equilibrium conditions for the households since the saving rate in each region $s_{i,t}$ remains constant and the oil supply during each period keeps being inelastically given by $R_{i,t}(1-\beta )$. This conclusion is obtained because the proposed extension only corresponds to a change in the static problem of the energy-aggregating firms and final goods, but not a change in the dynamic problems of the representative households in each region. Hence, finding the equilibrium period-by-period still solves an algebraic Equation (obviously different from Proposition A1) that clears the global oil market.

2.2. Export of Synthetic Fuels from LATAM and Asia–Pacific

Another way to take advantage of the renewable potential in Latin America is through the development and export of synthetic fuels such as green hydrogen. To include green hydrogen in our model, and in a similar way to what we proposed in the case of exports of electricity, we define a new energy source $e_{n+1,i,t}$ that we will call synthetic fuel and that can be traded internationally as oil. This synthetic fuel will be a close substitute for oil given its physical characteristics (see [6]). Thus, we define a new fuel aggregate that combines oil and synthetic fuel in each region i as

$$\begin{array}{c}\hfill {\mathbf{O}}_{i,t}\equiv 2{\left({\lambda }_{1,n}{\left(e_{1,i,t}\right)}^{{\rho }_H}+{\lambda }_{2,n}{\left(e_{n+1,i,t}\right)}^{{\rho }_H}\right)}^{\frac{1}{{\rho }_H}}\end{array}$$

(6)

where $e_{1,i,t}$ and $e_{n+1,i,t}$ are, respectively, the demand for oil and synthetic fuel used to generate the aggregate fuel (${\mathbf{O}}_{i,t}$) in region i during period t. In contrast to the case of electricity exports, we will assume that the parameters that determine the relative efficiency of these two types of fuels (${\lambda }_{1,n}$ and ${\lambda }_{2,n}$) are equalized across regions. The synthetic fuel can be exported to any region as oil, so there will be no feasibility considerations that prevent its trading across regions. Importantly, as described in the introduction, the advantage of solar power producing green hydrogen is highly concentrated in LATAM and Australia. Therefore, the production and exports of synthetic fuels will only be from these two regions (LATAM and Asia–Pacific).

As in the case of adding the export of electricity, the aggregation in (6) will assume that ${\rho }_H>\rho$ characterizes the greater degree of substitution between oil and the exportable synthetic fuel compared to the substitution between oil and the other existing energy sources. We now define the aggregate energy input $E_{i,t}$ in region i as:

$$E_{i,t}={\left({\lambda }_1{\left({\mathbf{O}}_{i,t}\right)}^{\rho }+\sum _{k=2}^n{\lambda }_k{\left(e_{k,i,t}\right)}^{\rho }\right)}^{\frac{1}{\rho }}$$

(7)

To determine the optimal combination of oil and synthetic only in each region i, the energy firms first need to solve the following optimization problem:

$$\begin{array}{c}\hfill \underset{e_{1,i,t}}{min}\left[{\widehat{p}}_{1,i,t}{e}_{1,i,t}+{\widehat{p}}_{n+1,i,t}{e}_{n+1,i,t}\right]\\ \hfill \mathrm{s}.\mathrm{t}.\mathrm{Equation}\left(6\right)\end{array}$$

(8)

where ${\widehat{p}}_{1,i,t}$ and ${\widehat{p}}_{n+1,i,t}$ are, respectively, the prices of oil and the synthetic fuel in region i during period t after taxes. In turn, and in line with the export of oil, we assume that there is a single worldwide market for this synthetic fuel, implying that its price before taxes is equalized across regions: $p_{n+1,i,t}=p_{n+1,t}$. However, in contrast to oil, synthetic fuel is a renewable energy source and its price is determined by the cost of production, which will be a technological assumption in the model. Accordingly, we will consider that the price $p_{n+1,t}$ evolves exogenously and, therefore, the global production is infinitely price elastic. The demand for synthetic fuel will be divided between the Latin America and Asia–Pacific regions since these are the only two regions capable of producing this new fuel. The global demand of synthetic fuel will be denoted by $e_{n+1,t}^T={\sum }_{i=1}^r{e}_{n+1,i,t}$ and in line with [6]; we will assume that LATAM and Asia–Pacific produce half of this global production in each period. Hence, the proceeds of these exports from LATAM and Asia–Pacific are added to their respective net incomes:

$${\widehat{Y}}_{i,t}=(1-\nu )A_{i,t}{L}_{i,t}^{1-\alpha -\nu }{K}_{i,t}^{\alpha }{E}_{i,t}^{\nu }+e_{n+1,t}^T·p_{n+1,t}/2$$

(9)

with $i\in \left\{\mathrm{LATAM},\mathrm{Asia}–\mathrm{Pacific}\right\}$. It is important to mention that, in Section 5, we will modify this assumption in order to assess the robustness of our simulated scenarios. After determining the demand for each component of the fuel aggregate, energy firms find the demand for the other type of energy sources ($e_{k,i,t}$) based on the aggregate demand for energy $E_{i,t}$ by solving (A9) and (A10). Again, we can note that, under this model extension, the dynamic optimization of households is not modified. Hence, the characterization of the equilibrium conditions can be stated in Proposition A3.

2.3. Exports of Electricity and Synthetic Fuel

A final extension could simultaneously explore the incorporation of the exports of electricity and synthetic fuel described in the last two subsections. In consequence, the aggregate production of the energy input will be given by:

$$E_{i,t}={\left({\lambda }_1{\left({\mathbf{O}}_{i,t}\right)}^{\rho }+{\lambda }_2{\left(e_{2,i,t}\right)}^{\rho }+{\lambda }_3{\left({\mathbf{e}}_{3,i,t}\right)}^{\rho }\right)}^{\frac{1}{\rho }}$$

(10)

where the aggregate fuel (${\mathbf{O}}_{i,t}$) and the aggregate electricity (${\mathbf{e}}_{3,i,t}$) are obtained as:

$${\mathbf{O}}_{i,t}=2{\left({\lambda }_{1,n}{\left(e_{1,i,t}\right)}^{{\rho }_H}+{\lambda }_{2,n}{\left(e_{n+1,i,t}\right)}^{{\rho }_H}\right)}^{\frac{1}{{\rho }_H}}$$

(11)

$${\mathbf{e}}_{3,i,t}=2{\left({\lambda }_{3,1,i}{\left(e_{3,i,t}^d\right)}^{{\rho }_r}+{\lambda }_{3,2,i}{\left(e_{3,i,t}^x\right)}^{{\rho }_r}\right)}^{\frac{1}{{\rho }_r}}$$

(12)

Like in the previous extension, we can state a proposition that summarizes the equilibrium conditions under this joint modification in the combination of energy sources, as shown in Proposition A4.

3. Calibration

Since our model is closely based on [1], most of the parameters’ values are taken from that study. This calibration strategy guarantees an adequate comparison of our scenarios with the baseline simulations and previous studies. As described below and in contrast to [1], we use the update information from LCOE to estimate the energy aggregation parameters and the expected path of prices for different types of energy sources.

We start by defining that each simulation period corresponds to 10 years. There are eight regions ($r=8$) that constitute the global economy, representing an oil-producing region, North America, Europe, China, Africa, South Asia, Asia–Pacific (excluding China), and Latin America. For the model extensions, we assume that only Latin America will export energy to North America in the case of electricity exports, while for synthetic fuel exports, we assume that Latin America and the Asia–Pacific can produce this fuel based on solar energy. This last assumption is consistent with [6]. In contrast to electricity exports, synthetic fuel can be exported to all regions of the world.

In the following subsections, we define the value of the different parameters that we will use to simulate the model scenarios described below.

3.1. Functional Forms of Preferences and Technologies

One of the central points in deriving Propositions A1–A4 is the assumption of logarithmic utilities, Cobb–Douglas production functions, and a depreciation rate equal to one for the study period. As mentioned above, the logarithmic utility corresponds to the CRRA family of functions with the elasticity of intertemporal substitution equal to one, which for the 10-year study horizon is a good approximation in line with [21].

Regarding the depreciation rate, a value of $\delta =1$ is still a considerably high value, even if one period is 10 years, since, among other aspects, the evaluation horizon for energy projects is 40 years. However, due to the analytical solution of the model, we decided to maintain this assumption. Additionally, an annual depreciation rate of 10 percent corresponds to a depreciation rate of around 65 percent over a 10-year period.

With respect to the functional form of the production function, let us note that the Cobb–Douglas function is a special case of the CES function when the elasticity of substitution is equal to one. This is in line with [34,35,36], who argue that this type of modeling is correct when the elasticity of substitution is less than one for short periods. However, in the long run, a Cobb–Douglas function is a reasonable assumption. Therefore, following [33], we use $\alpha =0.3$ and $\nu =0.055$.

Finally, there is a great deal of discussion in the literature related to the calculation of the social cost of carbon with regard to the value of the intertemporal discount rate, as it has important effects on the value of the social cost of carbon (see [37]). This is why we distinguish between two main approaches: the first one from [23] and their later works, who argue that the discount rate should actually be an effective $0\%$ ($\beta =1$); and the second one, which is the one we will use, namely the approach from Nordhaus’ works which uses a discount rate of $1.5\%$ per decade, which corresponds to $\beta =0.985$. It should be noted that, since our focus is not on calculating the optimal tax or social cost of carbon, using a lower discount rate would only reinforce the long-term results obtained, which will be discussed in detail in Section 4.

3.2. Energy Sector

First, we will assume that there will be $n=3$ types of energy for the case without exports, corresponding to oil, coal, and renewable energies. In turn, for the extensions of the model, we will assume that only two types of energy will exist for each of the defined energy aggregates: for the fuel aggregate, we consider that it will be composed of oil and synthetic fuel; and for the renewable aggregate, it will be composed of domestic and imported renewable energy (electricity), when importing is feasible.

Regarding the aggregation function, we use the elasticity substitution of [38] equal to $0.95$, corresponding to the unweighted average between the elasticities of substitution between coal–oil, coal–electricity, and electricity–oil, which implies that $\rho =-0.058$ ($\rho =\frac{\epsilon -1}{\epsilon }$ with $\epsilon$ the elasticity of substitution). Furthermore, since we define the synthetic fuel and exported renewable energy as close substitutes for oil and domestic renewable energy, respectively, we assume that ${\rho }_r={\rho }_H=0.2$.

Concerning the relative efficiencies among energies, we use condition (iv) of Proposition A1 to obtain

$$\begin{array}{c}\hfill \frac{{\lambda }_1}{{\lambda }_k}={\left(\frac{e_{1,t}}{e_{k,t}}\right)}^{1-\rho }\frac{p_{1,t}}{p_{k,t}}\end{array}$$

(13)

Thus, taking the global demand for different energy and fossil fuel prices from [39], together with the LCOE of renewable technologies from [3] and the assumption that ${\sum }_k{\lambda }_k=1$, we obtain that ${\lambda }_1=0.434$, ${\lambda }_2=0.111$, and ${\lambda }_3=0.453$. It is worth noting that the use of LCOE to parameterize the energy aggregation function is an improvement over the previous works by [1,21,33], since, as shown in [3], LCOEs have been a very good approximation of the clearing prices of the different energy tenders worldwide. This is why, in the aforementioned works, it was arbitrarily assumed that the relative price between oil and renewable energy is equal to one. This made the efficiency of renewable energy, ${\lambda }_3$, lower, and therefore, its contribution in the aggregation function underestimated.

For the relative efficiencies of the fuel aggregate, we use the same methodology, obtaining ${\lambda }_{1,n}=0.83$ and ${\lambda }_{2,n}=0.17$. For the case of the renewable aggregate, due to the non-existence of exported electricity between the regions involved, we assume that both types of renewable energy have the same efficiency (${\lambda }_{3,1,i}={\lambda }_{3,2,i}$) for the regions that can import them.

Finally, to determine energy prices: for fossil fuels, we use the average of the last 10 years from [39]; for the price of renewable energies, we obtain it as the simple average of the LCOE for small-scale hydropower, solar photovoltaic and onshore wind technologies, for the year 2018. We do not consider offshore wind sources due to their low participation in the world energy matrix; for synthetic fuel, we use the LCOE of green hydrogen taken from [3]; and the price of the exported renewable energy corresponds to the mean between the price of the renewable energies of the regions involved in trading this energy input. This last assumption is made in order to have a higher price of the exported energy with respect to that consumed in the exporting region, which is needed to cover for the costs associated with the transportation of that renewable energy. It should be noted that, since the unit of measurement of our model is tons of carbon equivalent, we use the methodology proposed by [21] to use the energy efficiencies of each of the technologies and the associated expenditure in terms of GDP by the energy sector. With this, we transform the prices measured in typical units ($\frac{\mathrm{Energy}\mathrm{Metric}\mathrm{Units}}{\mathrm{Monetary}\mathrm{Units}}$.) into units of carbon equivalent per units of GDP; the price summary is attached in

Table A2. Initial prices by type of energy measured in final goods.

Region	Coal	Renewable Energies	Synthetic Fuel	Exportable Electricity
North America	0.1148	0.939	-	-
Europe	0.1148	1.248	-	-
China	0.1148	0.676	-	-
Africa	0.1148	0.898	-	-
South Asia	0.1148	0.966	-	-
Asia–Pacific	0.1148	1.152	0.778	-
Latin America	0.1148	0.631	0.778	0.7850

.

3.3. Climate and Damage Function

For the carbon cycle model, we base our model directly on what is proposed in [21], so $\phi =0.0228$, ${\phi }_L=0.2$, and ${\phi }_0=0.393$, where, in addition, the concentration of carbon in the atmosphere in the pre-industrial era is 581 gigatons of carbon.

Also, with respect to emissions, we use $g_k=1$ for fossil fuels and $g_k=0$ for renewable technologies. It should be noted that heterogeneity in emissions by technological type is assumed, since, as mentioned in Section 3.2, energy prices are measured in units of final goods, including efficiency.

With respect to the temperature model, we directly use the parameterization used in [19], so ${\sigma }_1=0.098$, ${\sigma }_2=0.088$, ${\sigma }_3=0.025$, $\eta =3.8$, and $\kappa =1.31$. Finally, to parameterize ${\gamma }_{i,t}$, we follow [1], who proposed the following functional form

$${\gamma }_i=-\frac{ln\left(1-\left({\varphi }_{1,i}T+{\varphi }_{2,i}{T}^2\right)\right)}{S_0\left(e^{\frac{Tln\left(2\right)}{\xi }}-1\right)}$$

(14)

where $\xi$ is the climate sensitivity, which is equal to 3 °C for each doubling in the carbon concentration. The parameter values of ${\varphi }_{1,i}$ and ${\varphi }_{2,i}$ are shown in

Table A1. Productivity parameters.

Region	Linear ${\mathit{\varphi }}_1$ 1	Quadratic ${\mathit{\varphi }}_2$ 1	${\mathit{z}}_{\mathit{i},0}$2	Percentage Gap 3
North America	0.000 × ${10}^{-2}$	0.1414 × ${10}^{-2}$	4.55	-
Europe	0.000 × ${10}^{-2}$	0.1591 × ${10}^{-2}$	3.9	90%
China	0.0758 × ${10}^{-2}$	0.1259 × ${10}^{-2}$	3.62	80%
Africa	0.3410 × ${10}^{-2}$	0.1983 × ${10}^{-2}$	2.87	60%
South Asia	0.4385 × ${10}^{-2}$	0.1689 × ${10}^{-2}$	2.9	70%
Asia–Pacific	0.0785 × ${10}^{-2}$	0.1259 × ${10}^{-2}$	3.65	80%
Latin America	0.000 × ${10}^{-2}$	0.1259 × ${10}^{-2}$	3.55	70%

¹ Parameters damage function. ² Initial productivities. ³ Percentage of gap covered with respect to North America.

.

3.4. Initial and Long-Term Conditions

To parameterize the initial values of the model variables, we use the methodology proposed in [40] Chapter 3, which consists of taking the variables with a lag period (10 years for our model) and leaving the productivity level free, so as to set the initial productivity level in such a way that the model correctly predicts the values of the state variables in the initial period. In this way, the values of the initial productivities are shown in Table A1.

For this exercise, we use GDP values measured in current dollars in base 2010, and labor force as a percentage of current population for all regions, taken from [41]. This population evolves as described in Equations (A4) and (A5), where $g_{L,t}$ evolves according to

$$g_{L,t+1}=g_{L,t}-a(g_{L,t}-g_{L,BGP})$$

(15)

where $g_{L,0}=$ 0.08, $a=$ 0.4, and $g_{L,BGP}=$ 0 corresponds to the long-term population growth rate or on a balanced growth path. This parameterization is in line with the [42] report that projects a population of 9.7 billion in 2050 and 11 billion in 2100.

Another important point to parameterize is how the productivities of the regions will evolve in the long run in the balanced growth path (BGP). For this, following the development of [1], we propose the existence of an effective productivity $z_{i,t}$ and a productivity for the BGP ${\widehat{z}}_{i,t}$ such that it evolves as follows:

$$\begin{array}{cc}\hfill z_{i,t+1}& =z_{i,t}+10ln\left(g_{A_{BGP},i}\right)+\frac{1}{4}({\widehat{z}}_{i,t}-z_{i,t})\hfill \end{array}$$

(16)

$$\begin{array}{cc}\hfill {\widehat{z}}_{i,t+1}& ={\widehat{z}}_{i,t}+10ln\left(g_{A_{BGP},i}\right)\hfill \end{array}$$

(17)

where $g_{A_{BGP},i}$ is the productivity growth in BGP, which we will assume $g_{A_{BGP},i}=2\%$, for all regions following [21]. Equations (16) and (17) describe the regions that are closing the gap with respect to the BGP, so that regions that are further away from the state that will have higher productivity growth, and hence higher output growth. This is in line with the neoclassical growth models [43,44], as well as with the concept of convergence proposed in [45].

Finally, to parameterize the initial productivities in the BGP for the different regions, we assume that the North American region is at $10\%$ above the effective productivity. In turn, we assume that the other regions will only reach a certain percentage of North America’s productivity as shown in Table A1, in line with [40].

4. Results

In this section, we present the results obtained for the model and parameterization presented above. For this purpose, we start by characterizing the different scenarios of the evolution of the global economy, and then, by showing the quantitative results for these scenarios and different tax levels. It is worth noting that we focus on carbon tax policies below as one particular instrument to reduce the use of fossil fuels. However, there are other policies that could generate the same incentive to use less intensively fossil fuels such as carbon markets, which are very well explained in [46]. Hence, this part of the results can be thought of as any type of policy that discourage the use of polluting energy sources.

4.1. Scenario Definition

The central point of our study is knowing how the environment of our model will evolve. For this purpose, we defined three variables that would allow us to characterize the different future scenarios for our environment in a good way, which would correspond to the level of taxes per region, the price of renewable energies, and the price of coal. Theoretically, the price of oil should also be considered within the variables of interest that define the evolution of the environment, but let us remember that the price of oil is endogenous in our model, as discussed in Appendix A.

4.1.1. Tax Level

An important characteristic that defines the evolution of the economy corresponds to the capacity of agents to internalize the negative externality of using energy that produces carbon emissions. For this, the first possible scenario is the definition of a tax that allows an efficient allocation of resources. Following [21], we define a tax on all regions in such a way that it allows a reallocation that is equivalent to that of a social planner that internalizes the externality, i.e., a pareto-efficient allocation. The model used in [21] corresponds to a global economy. For this reason, the tax is the same for all regions. Moreover, the derivation of this tax is with a lump-sum payoff and not as a revenue amplifier as in Equation (A13), but since the potential revenue from these taxes would be very small, and hence the amplifier, the quantitative differences will not be important. Specifically, it corresponds to a tax ${\tau }_{i,2020}$ that satisfies:

$${\tau }_{i,2020}={\tau }_{2020}=\gamma {\widehat{Y}}_{i,2020}\left[\frac{{\varphi }_L}{1-\beta }+\frac{(1-{\varphi }_L){\varphi }_0}{1-(1-\varphi )\beta }\right]=85[USD/tC]$$

(18)

which means that, for each unit of carbon tones emitted into the atmosphere, USD 85 will have to be paid. At the same time, we continue with the assumptions of growing at a rate of $2.2\%$ per annum, which is approximately the average annual product growth rate.

However, it may be difficult for less developed regions of the world to implement a high carbon tax. For example, in Latin America, Africa, or South Asia countries, only a few of them have emission taxes, and if they do, they do not exceed 10 (USD/ton$C_{eq}$) as shown in [47]. Therefore, the second scenario consists of a heterogeneous tax per region, which specifically corresponds to a tax equal to half of the optimum for less developed regions (LATAM, Africa, and South Asia), and an optimum tax for the other regions. Finally, the third possible scenario is the case in which no tax is applied worldwide.

4.1.2. Renewable Energy Price

Along with the application of carbon taxes, the reduction in production costs for the different types of renewable energies can help promote a change in the energy matrix at a global level and, therefore, could also help combat climate change. For this reason, one scenario for the price of renewable energies responds to the following equation

$$\begin{array}{cc}\hfill p_{i,k,t+1}& =p_{i,k,t}{(1+{\gamma }_{k,t})}^t\hfill \end{array}$$

(19)

$$\begin{array}{cc}\hfill {\gamma }_{k,t+1}& ={\gamma }_{k,t}-b_k({\gamma }_{k,t}-{\gamma }_{k,\infty })\hfill \end{array}$$

(20)

where $p_{i,k,t}$ and ${\gamma }_{k,t}$ are the price and growth rate of energy k at time t, respectively, with ${\gamma }_{k,\infty }$ denoting the long-term growth rate of technology k, which we will assume to be zero for all technologies, and $b_k$ denotes the period-by-period closing fraction of the gap between growth rates.

Specifically, for the first scenario, a low price is considered, which means that the growth rate will be $-20\%$ per decade and a gap closure equal to $b_k=1/3$ for domestic renewable energies and that exported through electricity, and $b_k=1/4$ for synthetic fuel. The above is to capture the maturity level of the technologies, since synthetic fuel, being a relatively new technology, has more years to go before it reaches the long-term growth rate ${\gamma }_{k,\infty }$.

Finally, as well as for the tax level, another scenario will be characterized by no price decrease, i.e., ${\gamma }_{k,t}=0,\forall t,k$.

4.1.3. Coal Price

In addition to the two previously described variables, the evolution of the price of coal could affect the effectiveness of the price decrease in renewable energies as a tool to curb climate change. Given this, in a first scenario, we use the same dynamics for the price of renewable energies, as described in (19) and (20), where we specifically use a growth rate of $5\%$ per decade and a value of $b=1/10$.

It should be noted that the assumption that the price of coal increases by 5% is relative to the efficiency in final good production. Thus, if coal production has a productivity that grows at a rate lower than the one of final good production, it would also imply a rise in the coal price relative to final goods.

4.1.4. Scenarios

Given the possible cases for the described variables, 12 possible scenarios can be generated. However, for our work, we will only analyze the five following scenarios for energy prices:

• Business as usual: This scenario is characterized by constant renewable energy and coal prices, and without taxes by region.
• Renewable development: This scenario is characterized by low renewable energy prices, constant coal prices, and no taxes per region. These correspond to a feasible scenario when the energy prices predicted by [3] are achieved.
• Renewable massification: This scenario, apart from a low price for renewables, is characterized by a high carbon price and no taxation. This tries to reflect the scenario where there is relative innovation in favor of clean energy in line with [13].
• Optimal global tax: As the name implies, this scenario is characterized by applying the optimal tax defined in Section 4.1.1, along with a low price for renewables and a constant price for coal. It corresponds to a scenario in which a worldwide climate policy is feasible.
• Heterogeneous tax: It is characterized in the same way as the previous scenario, only with the heterogeneous tax per region that we defined in Section 4.1.1. It tries to reflect a more feasible worldwide climate policy.

With only these five scenarios, we characterize the different possible feasible futures in order to understand the long-term consequences of the development of Latin America’s renewable energy potential and the possibility space of the results.

4.2. Scenario Results

In this subsection, we show the climatic and economic results of implementing different types of renewable energy exports from Latin America to the other regions of the world, in the possible future scenarios. Figure 2 shows the evolution of the temperature increase with respect to the pre-industrial period for the each of the scenarios, where the first important result of this study can be observed, which is that the export of renewable energy, whether as electricity interconnections or synthetic fuels, does not solve the problem of climate change. In fact, the renewable energy development itself may even exacerbate the global warming problem, as is it observed for the scenarios business as usual and renewable development.

However, and in line with [1,21,37], we can see the effectiveness of taxes in efforts to mitigate climate change, where both the optimal tax and heterogeneous tax scenarios achieve a considerable reduction in the temperature rise at a global level. In this sense, there are no major differences in the evolution of temperature for these scenarios due to the fact that the main global pollutants are the regions of North America, the European Union, and China, for which the heterogeneous tax scenario continues with the optimum tax level.

In turn, observing the results of the renewable massification scenario, we can see that the increase in the price of coal by $5\%$ per decade generates results that are equivalent to the application of a tax. Therefore, given that the evolution of prices is exogenous, it gives grounds to extend the methodological framework described in Appendix A. Specifically, to develop an endogenous growth model in line with [48], and thus, to understand the causes that allow such price evolution, as well as the design of market instruments that allow one to internalize the positive externality of the investment in R+D in the firms, typically, a subsidy must be implemented to facilitate the use of renewable energies. However, that would be analogous to a price reduction that has already been shown to have no climatic effects.

These results are obtained due to the inclusion of these new exportable energies that predominate the income effect versus the substitution effect in the optimization decisions of the energy aggregators, which is in line with [1,33,49]. This is because the aggregate price of energy $P_{i,t}$, in any of the cases defined above, decreases when including these exportable energy sources, which generates an increase in the aggregate amount of energy demanded $E_{i,t}$. In turn, this generates a higher demand for all types of energy, including polluting fossil fuels. Finally, the position of the global energy matrix changes to a more renewable one, but in absolute terms. the amount of fossil fuels used is greater than in the case without exports when the cost of these fuels is not increased.

In addition, Figure 3 shows the global economic results for the cases shown above. The vertical axis shows the percentage of increase in final goods consumption at the global level with respect to the case without exports. The brown curves corresponding to the case without exports are horizontal and equal to 100 percent, so that values greater than 100 percent correspond to economic gains and vice versa. Also, the dotted lines correspond to the same results only in the case where export development is delayed by 50 years. It should be noted that no differences were observed in the curves describing the time evolution for temperature in the different scenarios (Figure 2); for this reason, the dotted lines were not included in the graphs.

From Figure 3, we can see that the export of electricity between LATAM and the US does not have effects on aggregate welfare with respect to the case without exports. These remain practically constant in the evaluation period, independently of the future scenario. However, we can see that, for all cases, the export of synthetic fuels and both types of exports at the same time, generates short- and long-term benefits at the global level.

Specifically, for the renewable development scenario, there is a reduction in the possible long-term economic benefits, reaching a maximum of 5.7% in the year 2160. This long-term phenomenon is due to the fact that, as we saw in Figure 2, the export of both electricity and synthetic fuels increases the temperature at the global level if there is no increase in the price of fossil fuels, either exogenously as in the renewable massification scenario or through the application of taxes. Therefore, this increases the factor ${\gamma }_i$ for all regions, which in turn decreases the aggregate productivity of the regions according to Equation (A19), generating a decrease in production and therefore in the consumption of final goods. For this same reason, we can see that the application of taxes not only slows down climate change, but also increases the long-term benefits for all regions, going from values of 4.3–9.71% in the year 2220, for the scenarios renewable development and optimal tax, respectively.

It is worth noting that a delay in the implementation of exports would generate a loss of the potential benefit that could be obtained. Not only in the years in which the implementation of exports was delayed, but also in the following 20 years, due to the fact that the dynamics of capital adjustment is not instantaneous. This result is due to the neoclassical feature of the model, where the convergence to the new balance growth path with renewable energy development is not immediate. Capital accumulation requires savings, and this amount is small when income per capita is smaller in the scenario with delay development. It is important to emphasize that the economic benefits shown previously are the unweighted sum of the benefits of each of the regions that make up this economy, so the gains are not the same for all regions.

It should be noted, although we have developed and shown arguments in favor of the climatic and economic effectiveness of the application of emission taxes, we would like to emphasize that this is not the only way to achieve favorable economic and climate results in the long term. This is because the way in which the Pigouvian tax was constructed, according to the Equations (A12) and (A13), only has effects on the preference of fuel types and not on household wealth. Hence, a policy of a regulatory nature, such as a ban on the operation of fossil fuel-based industries, would have effects analogous to those of the tax, except that the optimal nature of the instrument would not be as direct.

Therefore, even if the export of renewable energy from LATAM and/or Asia–Pacific to other regions of the world does not solve the problem of climate change by itself, if combined with other public policies aimed at reducing the use of fossil fuels, virtuous scenarios will be obtained. In these scenarios, global warming is reduced along with an increase in economic welfare not only for the exporting regions but for all regions of the world, as summarized in

Table 2. Summary of world-aggregated results.

Scenario	Variables *	2040	2070	2120	2170	2220
Without tax	Temperature	1.1 °C	1.7 °C	3.4 °C	6.1 °C	9.2 °C
	Consumption gains	1.8%	3.0%	5.1%	5.7%	4.3%
With optimal tax	Temperature	1.1 °C	1.4 °C	1.9 °C	2.4 °C	2.9 °C
	Consumptions g	1.7%	3.0%	5.3%	7.4%	9.7%

* Temperature measured as an increase compared to pre-industrial times. Consumption gains measured as a percentage increase over business as usual.

.

Economic Results by Region

As previously mentioned, the economic results shown in Figure 3 correspond to the unweighted sum of the economic benefits of each region. In addition, Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6 and Figure A7 in the Annex show the distribution of economic benefits obtained across regions under each alternative scenario.

As can be seen in these Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6 and Figure A7, all regions follow the same behavior described above for the global economic benefits, but we can observe that the level of benefits obtained differs between regions. For example, for the LATAM region, given the exporting nature, it can be seen that there are economic benefits for the entire study horizon for having electricity exports, which on average are around 2.6% with a maximum value of 3.2% in the year 2040 for the optimal tax scenario. In addition, the economic benefits are five times greater in relation to the global benefits for the first 100 years of the study horizon (5.3% at the global level compared to 26.2% for LATAM), and four times greater for the rest of the horizon (9.67% at the global level compared to 38.8% for LATAM in the year 2220) for the optimal tax scenario. This is not the case for the Asia–Pacific region, which, although its economic benefits increase in relation to global benefits, they do so by only 1.7 times for the first 100 years and 1.6 times for the rest of the period (economic benefits of 9.02% and 15.47%, respectively). This is because the increase in consumption caused by the extra income from exports, which is the same for both regions, corresponds to a smaller proportion for Asia–Pacific than for LATAM, given its initial level of development and consumption.

It is worth noting that all the analyses made with respect to economic benefits by region are under the assumption described by Equation (9), which states that the revenues obtained from synthetic fuel are equally distributed between the LATAM and Asia–Pacific regions. This assumption will be relaxed in Section 5.

5. Sensitivity Analysis

The results shown previously in Section 4 provide a clear message about the potential economic benefits of renewable energy exports, and the importance of complementing this with policies that discourage fuel consumption to curb climate change. In this section, we assess how our main results are modified if some aspects of the model are altered. First, we analyze the effects of different levels of taxation. Second, we study alternative assumptions for the distribution of the exports of synthetic fuels between LATAM and Asia–Pacific regions. Finally, we perform a stochastic analysis that allows us to have a simple approach to understand how uncertainty affects the results.

5.1. Different Tax Levels

As we showed in the previous section, the combination of renewable energy exports, in conjunction with the application of taxes for all regions, generates scenarios of considerable economic benefits and global temperature reduction. Therefore, in this section, we want to evaluate what the environmental and economic results will be if different levels of taxation are applied for the scenario renewable development. Specifically, we consider homogeneous carbon taxes for all the regions, starting with ${\tau }_{i,0}={\tau }_0=0$ up to ${\tau }_0=250$ (USD/tC), increasing 5 (USD/tC) in each simulation. It should be noted that all taxes follow the same behavior of the optimal tax proposed by [21], i.e., they start at the different values mentioned above and grow at a rate of $2.2\%$ per year.

In addition, we define the economic benefit $\Delta W_t^x$ at year t, doing the type of export x as the difference measured in percentages between the present value of the consumption at year t for doing the energy export of type x with respect to the present value of the consumptions when not doing energy exports (NE). Mathematically, this corresponds to

$$\Delta W_t^x=\frac{VP{C}_t^x-VP{C}_t^{NE}}{VP{C}_t^{NE}}$$

(21)

with

$$VP{C}_t^i=\sum _{j=2020}^t{\beta }^{j-2020}\sum _k{C}_{j,k}^i$$

(22)

where i represents the type of export to be performed, with $NE$ denoting the case of no exports, k is the region, j is the corresponding year, and the results are shown in Figure 4. The axes correspond to the temperature increase, the economic benefit measured in the present value defined in (21) and the tax level, where the optimal tax level is highlighted in red (18).

With respect to the temperature analysis, we can see how increasing the level of taxation generates a reduction in the long-term temperature increase, regardless of the type of export. Whilst we understand marginal benefit as the additional temperature reduction by increasing the level of taxation, the marginal benefit is decreasing; thus, it makes sense that the optimal tax coincides with the value when the marginal benefit is close to zero. In addition, we can see that the application of different tax levels has no apparent effect in first 100 years or so, which brings back into discussion the fact that the negative externality of carbon emissions is a sluggish process, which emphasizes the intergenerational aspect of the climate change problem.

For the case of economic benefits, we can see that there are practically no differences for the case of electricity exports, since its marginal benefit is practically constant, as shown in Figure 4. Furthermore, we can see for the case of synthetic fuel exports, as for both types of exports, whether there are economic benefits resulting from applying higher tax levels. Here, again, the marginal benefit is decreasing and becoming close to zero for values equal to the optimal tax or higher.

These results can be seen for specific years, as shown in Figure 5, where the vertical axis shows the temperature increase, and the horizontal axis shows the economic benefit for different types of exports in the years 2070, 2120, 2170, and 2220. In addition, the upper points of each curve correspond to the cases where the starting point is ${\tau }_0=0$; the intermediate points correspond to the increase in the initial value by 5 (USD/tC) up to 250 (USD/tC); and the highlighted points correspond to the optimal tax level of 85 (USD/tC). We can see that, for the first 50 years, and in line with the above, there are no substantial changes in temperature increase or economic benefits. This is not the case for the following years where different tax levels are applied, although these have a small effect on the temperature decrease and economic welfare, generating large benefits in 200 years in climatic and economic terms, independently of the decision to export energy.

However, we can see how the strategy of exporting both types of renewable energies dominates the strategies of only electricity exports or no exports. This is because the best results are located in the lower right corner (lower temperature increase and higher economic benefit), where, for the same tax, there are no substantial differences in the temperature increase, but there are substantial differences in the economic benefits in both the short term (increase of 3%) and long term (increase of almost 10%).

Finally, it should be noted that, as in Section 4, the same conclusion of dominance of the strategy of both exports applies, when combined with a policy of emissions reduction equivalent to the application of taxes. So, this analysis could be viewed as an analysis for different levels of emission reduction, rather than a tax level discussion.

5.2. Different Allocation of Synthetic Fuel Exports

As mentioned in Section 4, the results by region and hence the equilibrium of the economy described in the different propositions depend on the assumption stated in the Equation (9), which assumes that the rents from the export of synthetic fuels are shared equally between LATAM and Asia–Pacific regions.

To relax this assumption, we define the parameter $\Theta \in [0,1]$ and we now consider that the equations for net income for the Asia–Pacific and LATAM regions are as follows:

$$\begin{array}{cc}\hfill {\widehat{Y}}_{7,t}& =(1-\nu )A_{7,t}{L}_{7,t}^{1-\alpha -\nu }{K}_{i,t}^{\alpha }{E}_{7,t}^{\nu }+e_{n+1,t}^T·p_{n+1,t}·(1-\Theta )\hfill \end{array}$$

(23)

$$\begin{array}{cc}\hfill {\widehat{Y}}_{8,t}& =(1-\nu )A_{8,t}{L}_{8,t}^{1-\alpha -\nu }{K}_{8,t}^{\alpha }{E}_{8,t}^{\nu }+e_{n+1,t}^T·p_{n+1,t}·\Theta \hfill \end{array}$$

(24)

with $i=7$ and $i=8$ for the Asia–Pacific and LATAM, respectively. With this new formulation, we evaluate the different distributions between these regions, taking values from $\Theta =0$ to $\Theta =1$, with a 0.1 increase between each simulation.

First, we can see in the Figure A8 and Figure A9 that at the global variable show no differences for the alternative values of $\Theta$. This can be explained due to the fact that the representative household in each region is characterized by the same homothetic utility function. There was only one change among the exporting regions of synthetic fuels, which changed the steady state for those regions, but kept consumption at the global level constant. Hence, the global amount of total emissions for each scenario does not change and, therefore, the economic benefit of the other regions does not change.

Now, analyzing the results obtained for LATAM with the different values of $\Theta$ in Figure 6, we can see that the range of possible additional economic gains from the appropriation of synthetic fuel rents oscillates between 0.51 and 18.3% in 20 years, 2.1 and 41.2% in 80 years, and finally between 3.6 and 66.6% in 200 years depending on the scenario. In turn, we can observe that even if the assumption of Equation (9) is not met and LATAM manages to produce $20\%$ of the world demand for synthetic fuel, it would generate additional benefits of around $7\%$, $13\%$, and $21\%$ in 50, 100, and 200 years, respectively. This shows that the economic benefits for LATAM are sizable even if it does not have the largest share of the synthetic fuel market.

In the case of Asia–Pacific, as shown in Figure 7, although they generate additional benefits from the appropriation of synthetic fuel revenues, their income gains are below the one obtained by LATAM. This is because the (per capita) income in Asia–Pacific is higher than that in LATAM, implying that the rents of synthetic fuel exports relative to the income are bigger in LATAM than in the Asia–Pacific.

As expected, it is worth noting that the cases in which LATAM obtains the highest additional benefits is when $\Theta =1$, as in this case, LATAM produces all the synthetic fuel supply worldwide; and in the opposite case, for the Asia–Pacific, this is when $\Theta =0$. It should be noted that, for both cases, the corner solutions are feasible in terms of supply capacity, according to the [4] study, taking into account that, in the case of LATAM, Brazil should be included in the energy potential, as opposed to what is stated in Section 1. Therefore, even if the equilibrium between the distribution of synthetic fuel rents is an exogenous assumption; this exercise allows us to show that, at a global level, the main results do not change, either from a climatic or economic point of view. Also, this exercise highlights that it allows us to understand that the potential benefits for exporting synthetic fuels is relatively more relevant for income in LATAM than it is in the Asia–Pacific.

5.3. Stochastic Simulation

To date, all the descriptions we have made have been based on a deterministic neoclassical model, where energy prices, with the exception of oil, evolve exogenously. In addition, there are some parameters of the model for which there are no precise agreements for their values. For example, the elasticity of substitution between energy sources, which, according to [38], is equal to 0.95, while [50], using sectorial panel data between countries, argue that this elasticity of substitution should be greater than unity and close to 1.25.

This uncertainty among the possible evolution of energy prices, added to that of the structural parameters of the model, could change agents’ investment decisions. Therefore, given the good computational performance of the model that we developed, an alternative to understanding how this uncertainty would affect the evolution of temperature and the possible economic benefits of making energy exports would be running Monte Carlo simulations that stochastically perturb some critical parameters and the paths for productivity levels and energy prices. Remember that the solution in each time period, independent of the scenarios and type of export being studied, corresponds to solving an algebraic equation that cleans the oil market.

These simulations correspond to the drawing of the realizations of the structural stochastic variables of the model at the beginning of each simulation, and drawing, period by period, the possible evolutions of energy prices. The variables that we include in this analysis, how they are distributed, and the way they evolve are summarized in

Table 3. Stochastic parameter characterization.

Parameter	Function	Shock Distribution	Shock Media	${\mathit{\sigma }}_{\mathit{i}}$
Substitution elasticity	$\rho =\overline{\rho }+{\epsilon }_1$	Normal	0	0.05
Weights of energetics	${\lambda }_2={\overline{\lambda }}_2-{\epsilon }_2$	Normal	0	0.005
	${\lambda }_3={\overline{\lambda }}_3+{\epsilon }_2$
Long-term growth of $A_{t,i}$	$g_{A_{i_{LP}}}={\overline{g}}_{A_{i_{LP}}}+{\epsilon }_3$	Normal	0	0.02
Initial asymptotic productivity	${\widehat{z}}_{i,0}={\overline{\widehat{z}}}_{i,0}+{\epsilon }_4$	Normal	0	0.005
Population growth	$g_L={\overline{g}}_L+{\epsilon }_5$	Normal	0	0.001
Decrease price renewable energy	$g_{p_3}={\overline{g}}_{p_3}+{\epsilon }_{6,t}+0.2{\epsilon }_{6,t-1}$	Normal	0	0.02
Decrease in price of exported electricity	$g_{p_4}={\overline{g}}_{p_4}+{\epsilon }_{7,t}+0.2{\epsilon }_{7,t-1}+{\epsilon }_{6,t}+0.2{\epsilon }_{6,t-1}$	Normal	0	0.01
Decrease synthetic fuel price	$g_{p_H}={\overline{g}}_{p_H}+{\epsilon }_{8,t}+0.2{\epsilon }_{8,t-1}+{\epsilon }_{6,t}+0.2{\epsilon }_{6,t-1}$	Normal	0	0.01

.

However, before showing the results obtained, it is necessary to mention that the methodology of Monte Carlo simulations is not robust according to Lucas’s critique [51]. Given that households are risk-averse, i.e., the utility functions are concave, we have

$$\underset{\mathrm{Current}\mathrm{case}\mathrm{with}\mathrm{Monte}\mathrm{Carlo}\mathrm{simulations}}{\underbrace{\underset{{\left\{c_t\right\}}_{t=0}^{\infty }}{max}\sum _{t=0}^{\infty }{\beta }^{t}u\left({\mathbb{E}}_t\left[c_t\right]\right)}}\le \underset{\mathrm{Robust}\mathrm{case}\mathrm{in}\mathrm{front}\mathrm{of}\mathrm{the}\mathrm{Lucas}\mathrm{critique}}{\underbrace{\underset{{\left\{c_t\right\}}_{t=0}^{\infty }}{max}{\mathbb{E}}_0\left[\sum _{t=0}^{\infty }{\beta }^{t}u\left(c_t\right)\right]}}$$

Therefore, households could have precautionary savings to hedge against this uncertainty, by changing the policy function of the previous propositions and preferring mature technologies such as fossil fuels to smooth their consumption curve. However, ref. [20] uses this methodology in a RICE model to find confidence intervals for the social cost of carbon, as does the neoclassical growth model with the stochastic productivity shocks proposed by [52] under the same assumptions as ours, which also obtains a constant savings rate for all periods. Therefore, we will consider the results obtained as a true equivalent of the problem that is robust to the Lucas’s critique.

For our results, we used a number of $n=1.000$ Monte Carlo simulations, where the results are shown in Figure 8 and Figure 9. These figures show how the temperature evolves under the different export scenarios for the cases without and with optimal taxes, respectively, where the blue curves represent the mean of the temporal temperatures, and the orange curves show the possibility space of results at $99\%$. (This assumes that the results are normally distributed, so we calculate the standard deviation for each of the periods, and then add and subtract three times this value from the mean to obtain the orange curves. Additionally, in Figure 8, we can see that the dominance of the income effect over the substitution effect in renewable energy exports is still evident, since the mean values and stochasticity bands for renewable energy exports are higher than in the case without exports. Furthermore, we can observe that, in the first 100 years the confidence band is very small. This is not the case for the long term, where, depending on the scenario, the band of possibilities for temperature can range from 4 to 5 degrees Celsius in 200 years.

In turn, in Figure 9, we can see that, in addition to the tax being effective in reducing the average temperature in the long term for all scenarios, it considerably reduces the band of possible outcomes for the evolution of temperature for all export scenarios. Thus, the band of possibilities is reduced from 4 to only 1 degree Celsius for the case without exports and with electricity exports, and from 5 to only 2 degrees Celsius for the exports of synthetic fuels and both types in 200 years.

The results, once again, reinforce the idea of applying a tax at a global level. Regardless of the possible evolution of prices or the structural parameters of the model, by applying this instrument, we not only reduce the average value of the temperature, but also serve as insurance against the uncertainty of the possible realizations of the random variables that could give rise to scenarios in which the negative effects on the environment intensify.

In addition to the above, Figure 10 shows how the average share of renewable energies in the world energy matrix and its volatility evolves, for the case without taxes (continuous lines) and with taxes (dotted lines). Renewable energy is understood as the sum of renewable energy produced in each region and the exports of electricity and synthetic fuels. As expected, the application of the tax accelerates and increases the share of renewable energy for all export scenarios, but at the same time, considerably decreases the volatility of this value. This result indicates that, under tax application, renewable technologies are robust to possible future scenarios, which would give agents certainty to invest in this type of technologies. This is in line with the results of the endogenous growth models proposed by [1,13,14,15,53,54], where they argue that the application of taxes on emissions allows for redirecting the technological change towards clean technologies.

In turn, and in line with previous analyses, not only does the application of Pigouvian taxes allow for redirecting technological change (or failing that, investment in types of technology), but any policy that generates incentives to reduce carbon emissions will do as well. This can be seen in the Chilean case, where the agreement on the retirement of the coal-fired thermoelectric power plants (see [55]), substantially boosted the investment in renewable technologies (mainly solar and wind), which grew by 30% for Chile, compared to an average growth of 20% for the other LATAM countries.

Therefore, the implementation of emission reduction policies is not only effective in reducing global temperature and increasing the economic benefits of renewable energy exports, as seen in the previous section, but also allows hedging against scenarios that lead to a further increase in global temperatures and as a signaling instrument for investment in renewable technologies.

6. Conclusions and Future Work

There is a worldwide consensus that we are at a crucial moment to curb climate change, and the renewable energies are a great alternative to reduce greenhouse gas emissions. Using an integrated evaluation model, this work quantifies the medium- and long-term economic and climatic impacts of the development of the renewable energy potential in Latin America (LATAM). The main lesson to be learned from this analysis is that the development and export of renewable energy from LATAM to the rest of the world alone is unable to slow down the climate change. Moreover, this development could end up aggravating the global warming problem. In fact, as summarized in Table 2, this development can efficiently gain around 5 percent of consumption one hundred years ahead, but with a global temperature of 3.3 °C higher in the same horizon. This is the case since the economic benefits of this energy development lead to more global consumption and demand for energy, generating more carbon emissions.

In contrast to the previous case, if these renewable energy development and exports are combined with policies that discourage the use of polluting technologies, (either through carbon taxes or other regulatory measures), virtuous cycles will be obtained. In these cases, it is possible to slow down climate change and increase economic benefits in the medium and long term for all regions of the world. As shown in Table 2, a scenario that combines renewable development with carbon tax generates economic gains in terms of world consumption of 5.3 percent with a rise of only 1.9 ºC in the global temperature one hundred years ahead. Importantly, this last result is independent of the assumption regarding the distribution of synthetic fuel development between the LATAM and Asia–Pacific regions. Moreover, given the exporting nature of LATAM and its income level, the economic benefits of this renewable energy development could be as big as about five times those of other regions.

Consistently with the existing literature, the application of carbon taxes is highly effective in decreasing global warming and, at the same time, in increasing long-term economic benefits. However, it is important to note that the effectiveness of carbon taxes decreases when its value is fixed above the optimal level. In addition, using a stochastic simulation analysis, we show that the application of taxes enables us to reduce some of the risks involved in the development of renewable energies, since the application of taxes reduces the volatility of the proportion of renewable energy in the composition of the global energy matrix.

Our analysis also highlights the consequences of delaying the development and exports of renewable energy from LATAM to the rest of the world. We show that the potential economic benefits not only decrease during the delay period, but also in the periods after the commencement of exports, which is due to the persistence of several macroeconomic variables such as capital.

There are several avenues for possible future work. For instance, to understand the fundamental causes behind the evolution of energy prices, the model could be extended to include innovation in the energy sector as a source of endogenous growth. This would help to evaluate other types of policy instruments, such as subsidizing renewable technologies, which were proposed in the recent literature [1,53,54]. Another possible extension is to characterize the oil-producing region more strategically, i.e., lift the assumption of perfect competition for the oil market. Also, concerning the economic model, another possible extension is the inclusion of international trade aspects to better capture other comparative advantages and fundamental factors that can endogenously shape the supply of synthetic fuel in each region. Finally, a possible extension would be to compare different climate models, for instance, the carbon cycle model of the DICE model, or more complex versions that take into account the interaction between the temperature cycle and climate, as proposed in [56].

Finally, we can highlight that the problem of decarbonizing the world energy matrix depends not only on developing the supply of renewable energy but also on aggressively tackling the negative externality caused by the use of fossil fuels, which is reinforced by the fact that different sources of energy are not perfect substitutes. Moreover, since the process of carbon emissions is a slow-moving process, a long-term perspective, such as the one proposed in this work, is required to properly understand and evaluate the climate consequences of different policies proposed internationally.