Skip to main content

The climate rent curse: new challenges for burden sharing


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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  1. Note that in this study, we assume that governments aim to maximize the long-term benefit of their countries. This might arguably not always be the case; governments that maximize their personal profit and rent seeking might be tempted by additional transfers. We revisit this point in more detail in our conclusions and outlook in the final section of this study.

  2. The results of Brunnschweiler and Bulte have subsequently been rejected by Van der Ploeg and Poelhekke (2010), and the more recent literature indeed shows that whether resources have a negative or positive influence on long-term growth depends largely on numerous circumstances (Van der Ploeg 2011).

  3. See Jakob et al. (2015) for a detailed discussion of rents in various climate finance settings.

  4. We distinguish these climate rents from any rent in a carbon market in which the initial allocation is cost-efficient and rents occur due to the scarcity of permits.

  5. This is a crucial difference to, e.g., a carbon tax: while for the implementation of a tax on emissions financial transfers could be implemented through direct transfers of money, in an emissions trading scheme the sale of surplus permits induces financial flows indirectly.

  6. Jacks et al. (2011) show that world market integration has a positive impact on the stability of commodity prices.

  7. In the case of the EU-ETS, a remarkable decrease of the permit price was observed toward the end of the first commitment period.

  8. Exporting allocated permits above the level of uncontrolled emissions exhibits only transaction costs. When exporting permits below that level, the costs of extracting include mitigation costs.

  9. We do not consider external stability as we are interested in the incentive of regions to participate and receive transfers.

  10. MICA has been introduced and used in Lessmann et al. (2009); in this paper we present an updated version with heterogeneous players calibrated to eleven world regions.

  11. The linear relationship between decreases in growth rates and export shares assumes that the first dollar induces adverse effects on recipients, which is a questionable assumption. As the relationship is most likely nonlinear, our modeling approach most likely overestimates the adverse effect of small inflows and might, in turn, underestimate the negative effect of large transfers.

  12. This modeling assumption is in line with the most prominent channels inducing the curse: unproductive rent seeking as well as low investment due to credit constraints. In addition, unsustainable investment decisions from governments can also be attributed to less total factor productivity.

  13. Rodrik (2007) discusses in great detail how policy reforms should be designed in order to enhance the growth prospects in the face of various economic and institutional constraints. In our model, an endogenous choice of the strength of the resource curse is not considered.

  14. Developing regions are identified according to the list given by ISI (2012). A region in MICA counts as “developing” if more than 50% of its GDP is made up of developing countries.

  15. Looking at the timing of transfer payments as a share of GDP, conventional transfers schemes that encourage participation are on average especially high within the twenty-first century, with significant declines from 2050 on. The historic-responsibility and the equal-per-capita scheme on average attain the highest value in the beginning of the time horizon, while the peak is in 2050 for the per-capita-convergence scheme.

  16. The timing of the optimal transfer schemes that encourage participation varies, but as a trend for the average higher shares of GDP are attained in the twenty-second century.

  17. The negative contribution from damages is due to the fact that without a climate rent curse, production in vulnerable regions is higher. This, in turn, leads to higher damages as these are proportional to the output, see Eq. (5).

  18. Additionally, as highlighted above, we do not find the optimal transfers with anticipation of the climate rent curse taken.

  19. The best performing internally stable coalition under the OT-scheme that is not affected by the curse achieves an abatement of 19.3% of the social optimum.

  20. Note that the intertemporal budget constraint Eq. (17), which contains the (a priori unknown) market clearing prices is omitted from the model.


  • Alfaro, L., Chanda, A., Kalemli-Ozcan, S., & Sayek, S. (2004). FDI and economic growth: The role of local financial markets. Journal of International Economics, 64(1), 89–112.

    Article  Google Scholar 

  • Altamirano-Cabrera, J., & Finus, M. (2006). Permit trading and the stability of international climate agreements. Journal of Applied Economics, 9(1), 19–47.

    Google Scholar 

  • Barrett, S. (1994). Self-enforcing international environmental agreements. Oxford Economic Papers, 46, 878–894.

    Article  Google Scholar 

  • Barrett, S. (2003). Environment and statecraft: The strategy of environmental treaty-making. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Benz, E., & Trück, S. (2009). Modeling the price dynamics of CO\(_2\) emission allowances. Energy Economics, 32, 4–15.

    Article  Google Scholar 

  • Boschini, A., Pettersson, J., & Roine, J. (2007). Resource curse or not: A question of appropriability. The Scandinavian Journal of Economics, 109(3), 593–617.

    Article  Google Scholar 

  • Bosetti, V., & Frankel, J. (2011). Sustainable cooperation in global climate policy: Specific formulas and emission targets to build on Copenhagen and Cancun. Discussion Paper: Harvard Project on Climate Agreements, Belfer Center for Science and International Affairs, Harvard Kennedy School, 46.

  • Bowen, A., Campiglio, E., & Herreras Martinez, S. (2015). An “equal effort” approach to assessing the North-south climate finance gap. Climate Policy. doi:10.1080/14693062.2015.1094728.

  • Bowen, A., Campiglio, E., & Tavoni, M. (2014). A macroeconomic perspective on climate change mitigation: Meeting the financing challenge. Climate Change Economics, 5, 1440005.

    Article  Google Scholar 

  • Brechet, T., Gerard, F., & Tulkens, H. (2011). Efficiency vs stability in climate coalitions: A conceptual and computational appraisal. The Energy Journal, 32, 49–75.

    Article  Google Scholar 

  • Brunnschweiler, C. N., & Bulte, E. H. (2008). The resource curse revisited and revised: A tale of paradoxes and red herrings. Journal of Environmental Economics and Management, 55, 248–64.

    Article  Google Scholar 

  • Calvin, K., Clarke, L., Krey, V., Blanford, G., Kejun, J., Kainuma, M., et al. (2012). The role of Asia in mitigating climate change: Results from the Asia modeling exercise. Energy Economics, 34, S251–S260.

    Article  Google Scholar 

  • Carraro, C., Eyckmans, J., & Finus, M. (2006). Optimal transfers and participation decisions in international environmental agreements. Review of International Organizations, 1(4), 379–96.

    Article  Google Scholar 

  • Carraro, C., & Siniscalco, D. (1993). Strategies for the international protection of the environment. Journal of Public Economics, 53(3), 309–328.

    Article  Google Scholar 

  • Chander, P., & Tulkens, H. (1995). A core-theoretic solution for the design of cooperative agreements on transfrontier pollution. International Tax and Public Finance, 2, 279–93.

    Article  Google Scholar 

  • Collier, P., & Hoeffler, A. (2004). Greed and grievance in civil war. Oxford Economic Papers, 56(4), 563–595.

    Article  Google Scholar 

  • Corden, W. M. (1984). Booming sector and Dutch disease economics: Survey and consolidation. Oxford Economic Papers, 36, 359–380.

    Article  Google Scholar 

  • Corden, W. M., & Neary, J. P. (1982). Booming sector and de-industrialisation in a small open economy. Economic Journal, 92, 825–848.

    Article  Google Scholar 

  • de Ree, J., & Nillesen, E. (2009). Aiding violence or peace? The impact of foreign aid on the risk of civil conflict in sub-Saharan Africa. Journal of Development Economics, 88(2), 301–313.

    Article  Google Scholar 

  • Dellink, R. (2011). Drivers of stability of climate coalitions in the STACO model. Climate Change Economics, 2(2), 105–128.

    Article  Google Scholar 

  • Dellink, R., Finus, M., van Ierland, E., & Altamirano, J. (2004). Empirical background paper of the STACO model. Available on the STACO website, Wageningen University.

  • ECX. (2012). Data from: Accessed 3 Sept 2012.

  • Edenhofer, O., Knopf, B., Barker, T., Baumstark, L., Bellevrat, E., Chateau, B., et al. (2010a). The economics of low stabilization: Model comparison of mitigation strategies and costs. The Energy Journal, 31(1), 11–48.

    Google Scholar 

  • Edenhofer, O., Lotze-Campen, H., Wallacher, J., & Reder, M. (2010b). Global aber gerecht: Klimawandel bekämpfen. CH Beck: Entwicklung ermöglichen.

    Google Scholar 

  • Fankhauser, S., & Hepburn, C. (2010a). Designing carbon market, part I: Carbon markets in time. Energy Policy, 37, 1637–1647.

    Google Scholar 

  • Fankhauser, S., & Hepburn, C. (2010b). Designing carbon market, Part II: Carbon markets in space. Energy Policy, 38, 4381–4387.

    Article  Google Scholar 

  • Flachsland, C., Marschinski, R., & Edenhofer, O. (2009). Global trading versus linking: Architectures for international emissions trading. Energy Policy, 38, 4363–4370.

    Google Scholar 

  • Fuss, S., Chen, C., Jakob, M., Marxen, A., Rao, N., & Edenhofer, O. (2016). Could resource rents finance universal access to infrastructure? A first exploration of needs and rents. Environment and Development Economics, 21(6), 691–712. doi:10.1017/S1355770X16000139.

    Article  Google Scholar 

  • Gollier, C., & Tirole, J. (2015). Negotiating effective institutions against climate change. Economics of Energy and Environmental Policy, 4, 5–28.

    Article  Google Scholar 

  • Index Mundi. (2012). Data from: Accessed 1 Sept 2012.

  • ISI. (2012). Developing regions 2012. International Statistical Institute.

  • Jacks, D. S., O’Rourke, K. H., & Williamson, J. G. (2011). Commodity price volatility and world market integration since 1700. The Review of Economics and Statistics, 93(3), 800–813.

    Article  Google Scholar 

  • Jacoby, H. D., Babiker, M. M., Paltsev, S., & Paltsev, J. M. (2008). Sharing the burden of GHG reductions. MIT joint program on the science and policy of global change: Technical report.

  • Jakob, M., Steckel, J., Flachsland, C., & Baumstark, L. (2015). Climate finance for developing country mitigation: Blessing or curse? Climate and Development, 7(1), 1–15.

    Article  Google Scholar 

  • Jakob, M., & Steckel, J. C. (2014). How climate change mitigation could harm development in poor countries. Wiley Interdisciplinary Reviews: Climate Change, 5(2), 161–168.

    Google Scholar 

  • Jakob, M., Steckel, J. C., Klasen, S., Lay, J., Grunewald, N., Martónez-Zarzoso, I., et al. (2014). Feasible mitigation actions in developing countries. Nature Climate Change, 4, 961–968.

    Article  Google Scholar 

  • Jones, B., Keen, M., & Strand, J. (2013). Fiscal implications of climate change. International Tax and Public Finance, 20(1), 29–70.

    Article  Google Scholar 

  • Koch, N., Grosjean, G., Fuss, S., & Edenhofer, O. (2016). Politics matters: Regulatory events as catalysts for price formation under cap-and-trade. Journal of Environmental Economics and Management, 78, 121–139.

    Article  Google Scholar 

  • Kornek, U., Lessmann, K., & Tulkens, H. (2014). Transferable and non transferable utility implementations of coalitional stability in integrated assessment models. CORE Discussion Paper, vol. 35.

  • Kriegler, E., Weyant, J. P., Blanford, G. J., Krey, V., Clarke, L., Edmonds, J., et al. (2014). The role of technology for achieving climate policy objectives: Overview of the EMF 27 study on global technology and climate policy strategies. Climatic Change, 123(3–4), 353–367.

  • Leimbach, M., Bauer, N., Baumstark, L., & Edenhofer, O. (2010). Mitigation costs in a globalized world: Climate policy analysis with REMIND-R. Environmental Modeling and Assessment, 15(3), 155–173.

    Article  Google Scholar 

  • Lessmann, K., & Edenhofer, O. (2011). Research cooperation and international standards in a model of coalition stability. Resource and Energy Economics, 33(1), 36–54.

    Article  Google Scholar 

  • Lessmann, K., Kornek, U., Bosetti, V., Dellink, R., Emmerling, J., Eyckmans, J., et al. (2015). The stability and effectiveness of climate coalitions. Environmental and Resource Economics, 62(4), 811–836.

    Article  Google Scholar 

  • Lessmann, K., Marschinski, R., & Edenhofer, O. (2009). The effects of tariffs on coalition formation in a dynamic global warming game. Economic Modelling, 26(3), 641–649.

    Article  Google Scholar 

  • Luderer, G., Bosetti, V., Jakob, M., Leimbach, M., Steckel, J., Waisman, H., et al. (2012a). The economics of decarbonizing the energy system-results and insights from the RECIPE model intercomparison. Climatic Change, 114, 9–37.

    Article  Google Scholar 

  • Luderer, G., DeCian, E., Hourcade, J., Leimbach, M., Waisman, H., & Edenhofer, O. (2012b). On the regional distribution of mitigation costs in a global cap-and-trade regime. Climatic Change, 114, 59–78.

    Article  Google Scholar 

  • Lutz, B. J., Pigorsch, U., & Rotfuss, W. (2013). Nonlinearity in cap-and-trade system: The EUA price and its fundamentals. Energy Economics, 40, 222–232.

    Article  Google Scholar 

  • Mattauch, L., Creutzig, F., & Edenhofer, O. (2015). Avoiding carbon lock-in: Policy options for advancing structural change. Economic Modelling, 50, 49–63.

    Article  Google Scholar 

  • Mavrotas, G., Murshed, S., & Torres, S. (2011). Natural resource dependence and economic performance in the 1970–2000 period. Review of Development Economics, 15(1), 124–138.

    Article  Google Scholar 

  • McGinty, M. (2007). International environmental agreements among asymmetric nations. Oxford Economic Papers, 59, 45–62.

    Article  Google Scholar 

  • Meckling, J., & Hepburn, C. (2013). Economic instruments for climate change. In R. Falkner (Ed.), The Handbook of Global Climate and Environment Policy. London: Wiley.

  • Mehlum, H., Moene, K., & Torvik, R. (2006a). Cursed by resources or institutions? World Economy, 29(8), 1117–1131.

    Article  Google Scholar 

  • Mehlum, H., Moene, K., & Torvik, R. (2006b). Institutions and the resource curse. The Economic Journal, 116(508), 1–20.

    Article  Google Scholar 

  • Meinshausen, M., Meinshausen, N., Hare, W., Raper, S. C. B., Frieler, K., Knutti, R., et al. (2009). Greenhouse-gas emission targets for limiting global warming to 2C. Nature, 458, 1158–1162.

    Article  CAS  Google Scholar 

  • Messner, D., Schellnhuber, J., Rahmstorf, S., & Klingenfeld, D. (2010). The budget approach: A framework for a global transformation toward a low-carbon economy. Journal of Renewable and Sustainable Energy, 2(3), 1–14.

    Article  Google Scholar 

  • Murphy, K. M., Shleifer, A., & Vishny, R. W. (1989). Industrialization and the big push. The Journal of Political Economy, 97, 1003–1026.

    Article  Google Scholar 

  • Murphy, K. M., Shleifer, A., & Vishny, R. W. (1993). Why is rent-seeking so costly to growth? American Economic Review Papers and Proceedings, 83(2), 409–414.

    Google Scholar 

  • Negishi, T. (1972). General equilibrium theory and international trade. Amsterdam: North-Holland Pub Co.

    Google Scholar 

  • Newell, R. G., Pizer, W. A., & Raimi, D. (2013). Carbon markets 15 years after Kyoto: Lessons learned, new challenges. The Journal of Economic Perspectives, 27(1), 123–146.

    Article  Google Scholar 

  • Nordhaus, W. D. (2002). Alternative approaches to spatial rescaling. new haven: Yale University.

    Google Scholar 

  • Nordhaus, W. D. (2007). To tax or not to tax: Alternative approaches to slowing global warming. Review of Environmental Economics and Policy, 1(1), 26–44.

    Article  Google Scholar 

  • Nordhaus, W. D., & Yang, Z. (1996). A regional dynamic general-equilibrium model of alternative climate-change strategies. The American Economic Review, 86(4), 741–765.

    Google Scholar 

  • Petschel-Held, G., Schellnhuber, H. J., Bruckner, T., Tóth, F. L., & Hasselmann, K. (1999). The tolerable windows approach: Theoretical and methodological foundations. Climatic Change, 41(3), 303–331.

    Article  CAS  Google Scholar 

  • Rajan, R. G., & Subramanian, A. (2008). Aid and growth: What does the cross-country evidence really show? The Review of economics and Statistics, 90(4), 643–665.

    Article  Google Scholar 

  • Rajan, R. G., & Subramanian, A. (2011). Aid, Dutch disease, and manufacturing growth. Journal of Development Economics, 94(1), 106–118.

    Article  Google Scholar 

  • Ramey, G., & Ramey, V. A. (1995). Cross-country evidence on the link between volatility and growth. The American Economic Review, 85(5), 1138–1151.

    Google Scholar 

  • Ramsey, F. (1928). A mathematical theory of saving. Economic Journal, 38, 543–559.

    Article  Google Scholar 

  • Robinson, J. A., Torvik, R., & Verdier, T. (2006). Political foundations of the resource curse. Journal of Development Economics, 79(2), 447–468.

    Article  Google Scholar 

  • Rodrik, D. (2007). One economics. Many recipes. Princeton: Princeton University Press.

    Google Scholar 

  • Rubio, S. J., & Ulph, A. (2006). Self-enforcing international environmental agreements revisited. Oxford Economic Papers, 58, 233–263.

    Article  Google Scholar 

  • Sachs, J. D. & Warner, A. M. (1995). Natural resource abundance and economic growth. Natural Bureau of Economic Research, Working Paper.

  • Sachs, J. D. & Warner, A. M. (1997). Natural resource abundance and economic growth. Center for International Development and Harvard Institute for International Development, Working Paper. Replicated in Davis, G. A. (2013) Replicating Sachs and Warners Working Papers on the Resource Curse, The Journal of Development Studies, 49:12, 1615–1630.

  • Schollaert, A., & Van de Gaer, D. (2009). Natural resources and internal conflict. Environmental and Resource Economics, 44, 145–165.

    Article  Google Scholar 

  • Svensson, J. (2000). Foreign aid and rent-seeking. Journal of International Economics, 51(2), 437–461.

    Article  Google Scholar 

  • Tavoni, M., Kriegler, E., Aboumahboub, T., Calvin, K., Demaere, G., Wise, M., et al. (2013). The distribution of the major economies’ effort in the Durban platform scenarios. Climate Change Economics, 4(4), 1340009.

    Article  Google Scholar 

  • Torvik, R. (2001). Learning by doing and the Dutch disease. European Economic Review, 45, 285–306.

    Article  Google Scholar 

  • UNFCCC. (2015). Adoption of the Paris agreement. Accessed 1 June 2016.

  • Van der Ploeg, F. (2011). Natural resources: Curse or blessing? Journal of Economic Literature, 49(2), 366–420.

    Article  Google Scholar 

  • Van der Ploeg, F., & Poelhekke, S. (2009). Volatility and the natural resource curse. Oxford Economic Papers, 61, 727–760.

    Article  Google Scholar 

  • Van der Ploeg, F., & Poelhekke, S. (2010). The pungent smell of “red herrings”: Subsoil assets, rents, volatility and the resource curse. Journal of Environmental Economics and Management, 60, 44–55.

    Article  Google Scholar 

  • Van der Ploeg, F., & Venables, A. J. (2011). Harnessing windfall revenues: Optimal policies for resource-rich developing economies. The Economic Journal, 121(551), 1–30.

    Article  Google Scholar 

  • van Wijnbergen, S. (1984). The ‘Dutch disease’: A disease after all? The Economic Journal, 94(373), 41–55.

    Article  Google Scholar 

  • Weikard, H.-P. (2009). Cartel stability under an optimal sharing rule. The Manchester School, 77(5), 1463–6786.

    Article  Google Scholar 

  • Wick, K., & Bulte, E. (2006). Contesting resources rent seeking, conflict and the natural resource curse. Public Choice, 128, 457–476.

    Article  Google Scholar 

  • WorldBank. (2016). The worldwide governance indicators, 2016 update. Aggregated indicators of governance 1996–2014. World Bank.

Download references


Funding from the German Federal Ministry of Education and Research (BMBF) (funding code 01UV1008A, EntDekEn) is gratefully acknowledged. The authors want to thank Michael Jakob for helpful comments and suggestions.

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Ulrike Kornek or Jan Christoph Steckel.


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:

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

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 \(k_{i0}\)).

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

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 \(\delta _i\).

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

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).

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

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 \(q_{it}\).

$$\begin{aligned} e_{it}\le & {} q_{it} - z_{it} \end{aligned}$$
$$\begin{aligned} \sum _j z_{jt}&= {} 0,\quad \forall t \end{aligned}$$

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 \(Q_{t}\).

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

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).

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

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):

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

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.

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

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:

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

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:Footnote 20

$$\begin{aligned}&\displaystyle \max _{\{i_{jt},a_{jt},m_{jt},x_{jt},z_{jt}\ :\ j=1\dots N\}} \quad \sum _{i=1}^N \omega _i\, W_i \end{aligned}$$
$$\begin{aligned}&\hbox {subject to Eqs}.\,2{-}17 \end{aligned}$$

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 \(C_{it}\):

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

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:

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

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.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kornek, U., Steckel, J.C., Lessmann, K. et al. The climate rent curse: new challenges for burden sharing. Int Environ Agreements 17, 855–882 (2017).

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


JEL Classification