The climate rent curse: new challenges for burden sharing

Abstract

The literature on the “resource curse” has strongly emphasized that large incomes from resource endowments may have adverse effects on the growth prospects of a country. Conceivably the income generated from emission permit allocations, as suggested in the context of international climate policy, could have a comparable impact. Effects of a “climate rent curse” have so far not been considered in the design of permit allocation schemes. In this study, we first determine when to expect a climate rent curse conceptually by analyzing its potential channels. We then use a numerical model to explore the extent of consequences that a climate rent curse would have on international climate agreements. We show that given the susceptibility to a curse, permit allocation schemes may fail to encourage the participation of recipient countries in an international mitigation effort. We present transfer schemes that enhance cooperation and limit adverse effects on recipients.

Appendices

Appendix 1: Institutional quality of selected countries

See Table 5.

Table 5 Governance indicators in 2014 for countries that have not experienced negative growth effects from large resource inflows (top rows) and that have suffered from the resource curse in the past (bottom rows).

Appendix 2: Analysis with regionally-specific strengths of the curse

In our main text, we assumed the same strength of adverse effects in all regions that are vulnerable to the curse (namely, AFR, LAM, IND, MEA, OAS and RUS). We made this simple yet strong assumption to study the effects of curse strength in isolation, and to present our finding in the clearest way possible. This section presents an exploratory analysis with regionally-specific values for $\varphi$ to check whether we are missing a critical aspect in our main results. We calculate a region-specific average value for institutional quality based on the six indicators of Table 2 (first set of rows). The region with the lowest average value experiences the highest strength of the curse of $\varphi =9.43$, while the value decreases linearly for the other vulnerable regions (see Table below). We do not assume the curse to apply ($\varphi =0$) if institutional quality on average is larger than zero (the World Development Indicators are normalized so that their average value is equal to zero). The analysis is therefore only indicative as our derivation of the regionally-specific strengths is crude because (1) taking the average of the indicators for institutional quality assumes that the strength of the curse is determined equally by all indicators, (2) we leave out indicators for volatility of a country, (3) assuming a linear decline is an ad hoc approximation.

We apply the equal-per-capita transfer scheme and calculate how often the curse discourages participation for each region (a region-specific analysis as in Fig. 2). The results are summarized in Table 6. The table shows that the results we present in Fig. 2 of the main part are to a large degree consistent with the data we derived with regionally-specific strengths: Destabilization is high for large $\varphi =9.43$ and decreases significantly as the strength decreases. In particular, we do not find any large interacting effects among regions.

Table 6 Percentage of affected regions encouraged to participate by the transfer scheme without any adverse effect and destabilized under regionally-specific strengths of the climate rent curse (for $\varphi$ see Eq. 1) and with the equal-per-capita transfer scheme in place

Appendix 3: Model equations

In this section, we present the details of our numerical model. The model builds on Lessmann et al. (2009) and Lessmann and Edenhofer (2011) but uses eleven world regions as players, instead of nine symmetric players in cited studies. In the following, we first describe the model equations, their calibration, and the numerical procedure to solve the model.

1.1 Preferences

We model the world economy as a set of $N=11$ regions (or players), see Table 7. Players decide in an intertemporal setting which share of income to consume today and which share to save and invest for future consumption. Intertemporal welfare $W_i$ and instantaneous utility function U based on per-capita consumption are given by:

$$\begin{aligned} W_i= \int _0^\infty p_{it}\, U(c_{it}/p_{it})\, e^{-\rho t}\,\hbox {d}t \end{aligned}$$

(2)

$$\begin{aligned} U(c_{it}/p_{it})= \log (c_{it}/p_{it}) . \end{aligned}$$

(3)

Here, $c_{it}$ and $p_{it}$ denote consumption and population in region i at time t, respectively. Parameter $\rho$ is the pure rate of time preference.

Table 7 Regions as defined in MICA and corresponding world regions

1.2 Technology

The economic output $y_{it}$ in each region is produced with a constant elasticity of substitution (CES) production technology F with share parameter $\gamma$ and elasticity of substitution $\rho _F$. $\alpha _{it}$ is the total factor productivity. Climate change damages (defined below in Eq. 15) destroy a fraction $\varOmega _{it}$ of the production. Economic output is further reduced by abatement costs $\varLambda _{it}$ (defined in Eq. 8). F is calibrated using the initial values of output, labor productivity, labor and capital ($y_{i0}$, $\lambda _{i0}$, $l_{i0}$ and $k_{i0}$).

$$\begin{aligned} y_{it}= & {} (1-\varLambda _{it}\,-\varOmega _{it}\, )\, F(l_{it},k_{it}) \end{aligned}$$

(4)

$$\begin{aligned} F(l_{it},k_{it})= & {} \alpha _{it} y_{i0} \left[ (1-\gamma ) \left( \frac{\lambda _{it}l_{it}}{\lambda _{i0}l_{i0}}\right) ^{\rho _F} + \gamma \left( \frac{k_{it}}{k_{i0}}\right) ^{\rho _F} \right] ^{(1/\rho _F)} \end{aligned}$$

(5)

Labor $l_{it}$ is given exogenously, as is labor productivity $\lambda _{it}$. Capital $k_{it}$ accumulates with investments $i_{it}$ and is depreciated at rate $\delta _i$.

$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t}{k}_{it}= & {} i_{it} - \delta _i k_{it} \end{aligned}$$

(6)

1.3 Emissions and emission allowances

Greenhouse gas emissions $e_{it}$ are a by-product of economic activity $y_{it}$. We assume that the emission intensity $\sigma _{it}$ falls exogenously due to technological progress: $\sigma _{it}=\sigma _0(i) \left[ \cdot (1-\sigma _{min}(i))\exp ^{\nu _1(i)\cdot t+\nu _2(i)\cdot t^2} +\sigma _{min}(i) \right]$. Beyond this, emissions may be reduced by abatement $a_{it}$ at the cost of $\varLambda _{it}$, where the generic functional form is taken form Nordhaus and Yang (1996).

$$\begin{aligned} e_{it}&= {} y_{it}\,\sigma _{it}\,(1-a_{it}) \end{aligned}$$

(7)

$$\begin{aligned} \varLambda _{it}&= {} b^1_{it} \cdot \left( a_{it}\right) ^{b^2_i} \end{aligned}$$

(8)

Emission allowances may be traded internationally ($z_{it}$ denotes import or exports of allowances by region i), but we exclude intertemporal banking and borrowing of allowances, i.e., total imported and exported allowances must be balanced in every period, with initial allowances equal to $q_{it}$.

$$\begin{aligned} e_{it}\le & {} q_{it} - z_{it} \end{aligned}$$

(9)

$$\begin{aligned} \sum _j z_{jt}&= {} 0,\quad \forall t \end{aligned}$$

(10)

1.4 Climate dynamics

Global warming is driven by total global emissions of $CO_2$ into the atmosphere, which are equal to cumulative total emission allowances $Q_{t}$.

$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t} C_t= & {} \zeta Q_t - \kappa (C_t-C_0) + \psi \,E_t \end{aligned}$$

(11)

$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t} E_t= & {} Q_t \end{aligned}$$

(12)

$$\begin{aligned} Q_t= & {} \sum _i q_{it} \end{aligned}$$

(13)

Equation 11 translates global emissions into carbon concentration in the atmosphere C. Concentration C rises with global allowances (same as emissions), where $\zeta$ converts emissions into a change in concentration, and it decreases due to the carbon uptake of the oceans proportional ($\kappa$) to the increase above the preindustrial level $C_0$. The final term limits the ocean carbon uptake (to the fraction $1-\psi /\zeta \kappa$ in equilibrium). For more details on the climate equations see Petschel-Held et al. (1999).

$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t} T_t= & {} \mu \log (C_t/C_0)-\phi (T_t-T_0) \end{aligned}$$

(14)

Equation 14 transforms concentration levels into a global mean atmospheric temperature increase T. Here, parameter $\mu$ controls the strength of the temperature reaction to a change in concentration, whereas parameter $\phi$ is related to its timing. Together, they have an interpretation as the “climate sensitivity” ($\mu /\phi \cdot \log 2$), i.e., the equilibrium temperature increase for a doubling of the concentration. In view of the inertia of the climate system, we run the model for 200 years in steps of 10 years.

The climate change damage function is taken from Dellink et al. (2004):

$$\begin{aligned} \varOmega _{it}&=\theta _{2i}(T_t)^2 \end{aligned}$$

(15)

Two sets of “book keeping” equations complete the model: The budget constraints for consumption and investments for each region at every point in time, as well as the intertemporal budget constraint ensuring that over the entire time horizon, the import value must equal the export value in each region.

$$\begin{aligned} y_{it} + m_{it}= c_{it} + i_{it} + b_{it} + x_{it} \end{aligned}$$

(16)

$$\begin{aligned} \int _0^\infty p_t\, m_{it} \ \hbox {d}t= & {} \int _0^\infty p_t\, x_{it} + p^z_t\, z_{it} \hbox {d} t \end{aligned}$$

(17)

Variables $m_{it}$ and $x_{it}$ are imports and exports of region i, respectively, and $p_t$ and $p^z_t$ are the prices of goods and allowances, respectively.

1.5 Algorithm to implement the curse

We calculate the unaffected growth rates $g_0(i,t)$ by extracting the time path of $\mathrm{GDP}(i,t)$ as the sum of production $(1-\varLambda _{it})\, F(l_{it},k_{it})$ and the revenues from permit trade $\pi (i,t)$. The average growth rate per economically active person over twenty years is then determined. The target growth rate $g^*(i,t)$ can be calculated according to Eq. (1). For time period t, we adjust the total factor productivity twenty years ahead $\alpha (i,t+20)$ to reduce $\mathrm{GDP}(i,t+20)$ such that the growth rate drops to $g^*(i,t)$. The growth rates $g_0(i,t'>t)$ are updated to take this new value into account. We find that adjusting $\alpha (i,t)$ has only a small influence on the growth rate of the previous steps, and we can therefore apply this algorithm successively for all times t. The specified way implicitly assumes that the reduction in total factor productivity is not permanent but that countries recover from it fully within a decade after the revenue from resources vanishes. This view is optimistic and represents a lower bound to the negative effects of the climate rent curse.

For the optimal transfer scheme, the revenues $\pi (i,t)$ are given exogenously through the algorithm described in Sect. 5.1. We do not change the transfers $\pi (i,t)$ from their calculation without the climate rent curse and add the transfers to the consumption paths of each region outside of the MICA model in line with the algorithm proposed in Kornek et al. (2014).

1.6 Model calibration

The focus of this model is on the incentive of regions to participate in the international abatement effort. For the calibration of the model, two aspects are therefore of primary importance: the costs of emissions reductions and associated benefits, i.e., foregone damages.

For an estimate of mitigation costs, we calibrate our model to a large-scale integrated assessment model, REMIND-R (Leimbach et al. 2010). MICA and REMIND-R share some important features, resulting in similar economic dynamics: Both are multiregion optimal growth models driven by the maximization of intertemporal utility, and both allow for intertemporal trade. Thus, when using the same initial values ($k_{i0}$, $l_{i0}$, $y_{i0}$), exogenous population scenario ($l_{it}$), and parameter values where possible (i.e., in the utility function: $\rho$, $\eta$, in the production function: $\gamma$, $\rho _F$, and in capital dynamics: $\delta _i$), and calibrating the labor productivity ($\lambda _{it}$), the economic dynamics in the absence of climate policy or climate change damages are in “good agreement.” We measure this agreement by computing the coefficient of determination $R^2$ for $y_{it}$, and $c_{it}$ over the first 10 decades. With rare exceptions, the resulting $R^2$ are large (columns 1–2 of Table 8). The exogenous decline in emission intensity $\sigma _{it}$ was chosen by calibrating the parameters ($\sigma _0(i)$, $\sigma _{min}(i)$, $\nu _1(i)$, $\nu _2(i)$) such that emissions over the century coincide. Here we report remaining difference as the deviation of cumulative emissions over the first century, with values around 5% in all regions (see column 4 in Table 8).

The actual costs of reducing emission by $a_{it}$ percent versus these baseline dynamics are defined by the cost function $\varLambda$ (Eq. 8). We calibrate its parameters, $b^1_{it}$ and $b^2_i$, to reproduce the abatement costs in REMIND-R, such that both models reduce emissions by the same amount over the century under the two carbon tax scenarios (high tax and low tax). For this, the $b^1_{it}$ follow the generic equation $(b^1_{it}= b^0_{i} \cdot e ^{\vartheta _i \cdot t}+b_{i}^{\hbox {inf}})$, whose parameters ($b^0_{i}$, $\vartheta _i$, $b_{i}^{\hbox {inf}})$ are then found to best fit to the abatement of REMIND-R. The remaining difference is reported in columns 5–6 in Table 8.

Table 8 Remaining errors in the calibration of MICA. We measure the goodness-of-fit by the $R^2$ value, except for emissions where the difference in their cumulative amount over the century is reported

Information on climate change damages is available in the literature in form of damage functions. We use the damage function from Dellink et al. (2004), which we rescale to the spacial layout of our eleven regions [see Nordhaus (2002) for a discussion of spatial rescaling].

1.7 Solving the model for the game’s equilibrium

We are considering a two-stage game of, first, membership in an international environmental agreement (IEA), and second, an emission game where players choose their emission allowances.

The game is solved numerically by backward induction, i.e., first we compute partial agreement Nash equilibria (PANE, cf. Chander and Tulkens 1995) for all possible coalitions, and then we test these coalitions for internal and external stability according to the following criteria:

$$\begin{aligned} \left. W_i\right| _S\ge & {} \left. W_i\right| _{S\setminus \{i\}}\hbox { for }i\in S \quad \hbox {(internal stability)} \end{aligned}$$

(18)

$$\begin{aligned} \left. W_j\right| _S> & {} \left. W_j\right| _{S\cup \{j\}}\hbox { for }j\notin S \quad \hbox {(external stability)} \end{aligned}$$

(19)

The computation of the PANE for the second stage is complicated by the fact that we are looking at an intertemporal optimization model featuring an environmental externality as well as international trade. To our knowledge, there are no out-of-the-box solvers available to solve such a model in primal form. Lessmann et al. (2009) suggest an iterative approach based on Negishi’s (1972) approach. For this study, we use a modified version of the iterative algorithm, which works as follows:

Negishi’s approach searches for the social planner solution that corresponds to a competitive equilibrium by varying the weights $\omega _i$ in the joint welfare maximization:²⁰

$$\begin{aligned}&\displaystyle \max _{\{i_{jt},a_{jt},m_{jt},x_{jt},z_{jt}\ :\ j=1\dots N\}} \quad \sum _{i=1}^N \omega _i\, W_i \end{aligned}$$

(20)

$$\begin{aligned}&\hbox {subject to Eqs}.\,2{-}17 \end{aligned}$$

(21)

Since this exploits the fundamental theorems of welfare economics, the approach cannot be applied for an economy with externalities. In principle, this problem is circumvented by making any external effect on other players exogenous to model (turning variables into parameters that are adjusted in an iteration).

Here, the externalities are climate change damages through aggregate global emissions. In Nash equilibrium, players will only anticipate the effect that their emissions have on their own economic output, not the effect onto other players’ output. We can mimic this in a social planner solution by giving each player his own perception of the causal link between emissions and global warming. Instead of Eq. (11), which describes one trajectory of concentration $C_t$, we introduce N equations for $C_{it}$:

$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t} C_{it}&\ =\ \zeta \left( q_{it} + \sum _{j \ne i} \overline{q_{jt}}\right) - \kappa (C_t-C_0) + \psi \,E_t&\quad \forall _{i \notin S} \end{aligned}$$

(22)

$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t} C_{it}&\ =\ \zeta \left( \sum _{k \in S} q_{kt} + \sum _{j \notin S} \overline{q_{jt}}\right) - \kappa (C_t-C_0) + \psi \,E_t&\quad \forall _{i \in S} \end{aligned}$$

(23)

Here, the allowance choices of other players enter as a fixed value (a parameter, indicated by the bar), set to the levels of the corresponding variables during the previous iteration (or some initial value). The sum of allowances in Eq. (12) needs to be adjusted analogously, and the temperature Eq. (14) will consequently have N instances for $T_{it}$, too. The temperature change $T_{it}$, anticipated by player i, will then enter in Eq. (15) instead of $T_t$.

The thusly modified model is then solved in a nested iteration: In the inner iteration, we solve the model for a given vector $\overline{q} = (\overline{q_{it}})$ of allowance choices repeatedly, updating $\overline{q_{it}}=q_{it}$ at the end of each iteration, i.e., we perform a fixed point iteration of the mapping $q = G(q)$ where G is the best response of players to the exogenously given strategy $\overline{q_{it}}$ of the other players. If the inner iteration converges, it converges to a Nash equilibrium in allowance choices. However, the international markets for allowances and private goods may not be a competitive equilibrium. This is what the outer iteration achieves.

The outer iteration follows the standard Negishi approach: We adjust the welfare weights $\omega _i$ in the joint welfare function (Eq. 20) until the intertemporal budget constraint (Eq. 17) is satisfied. The resulting equilibrium is the desired PANE.

1.8 Numerical verification of the equilibrium

We verify the resulting candidate PANE equilibrium strategies in emissions and trade numerically by comparing them to the results of the following maximization problems:

$$\begin{aligned} \begin{aligned} \forall _i&\displaystyle \max _{\{i_{it},a_{it},m_{it},x_{it},z_{it}\}} W_i\\&\hbox {subject to Eqs.}\,2{-}18 \hbox{ and prices }\ p_{t}, p_{t}^z \end{aligned} \end{aligned}$$

(24)

Deviations of this model from our solution should be within the order of magnitude of numerical accuracy only, which is what we find (not shown). In particular, simultaneous clearance of all international markets confirms the competitive equilibrium in international trade.