Optimum Growth and Carbon Policies with Lags in the Climate System



We study the optimal carbon tax in an economy in which climate change, stemming from polluting non-renewable resource, affects the economy’s growth potential. Our main contribution is to introduce and explore the natural time lag of the climate system between emissions and damages to capital accumulation in an endogenous growth setting. This allows us to investigate how optimal climate policy, and its interplay with climate dynamics, affect long-run growth and the transition of the economy towards it. Without pollution decay, a higher speed of emissions diffusion steepens the growth profile of the economy. With pollution decay, this leads to lower short-run but higher long-run economic growth during transition. Poor understanding of the emissions diffusion process leads to suboptimal carbon taxes, resource extraction and growth.


Climate policy Non-renewable resource dynamics Pollution diffusion lag Optimum growth 

JEL Classification

Q54 O11 Q52 Q32 



This study has benefitted greatly by the comments and suggestions of Julien Daubanes, Alexandra Vinogradova and Andreas Schäfer. Moreover we are grateful for the suggestions of Sjak Smulders and two anonymous referees. We also thank the discussants at the SURED 2014 conference, Ascona–Switzerland, and at the 5th World Congress of Environmental and Resource Economists (2014), Istanbul–Turkey, for their valueable contribution.


  1. Barro RJ, Sala-i-Martin X (2003) Economic growth, 2nd Edn. Vol 1 of MIT Press Books. The MIT PressGoogle Scholar
  2. Bovenberg A, Smulders S (1995) Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model. J Public Econ 57:369–391CrossRefGoogle Scholar
  3. Bretschger L, Valente S (2011) Climate change and uneven development. Scand J Econ 113:825–845CrossRefGoogle Scholar
  4. Brock WA, Taylor MS (2005) Chapter 28 economic growth and the environment: a review of theory and empirics. In: Aghion P, Durlauf SN (eds) Handbook of economic growth, vol 1, part B of handbook of economic growth. Elsevier, pp 1749–1821Google Scholar
  5. Dasgupta P, Heal G (1979) Economic theory and exhaustible resources. Cambridge University Press, CambridgeGoogle Scholar
  6. Daubanes J, Grimaud A (2010) Taxation of a polluting non-renewable resource in the heterogeneous world. Environ Res Econ 47:567–588CrossRefGoogle Scholar
  7. EIA (2015) Energy consumption, expenditures, and emissions indicators estimates, 1949–2011. http://www.eia.gov/totalenergy
  8. EM-DAT The International Disasters Database (2015). http://www.emdat.be
  9. Gaudet G, Lasserre P (2013) The taxation of nonrenewable natural resources. Cahiers de recherche 2013-10, Universite de Montreal, Departement de sciences economiquesGoogle Scholar
  10. Gerlagh R, Liski M (2012) Carbon prices for the next thousand years. CESifo Working Paper Series 3855, CESifo Group MunichGoogle Scholar
  11. Golosov M, Hassler J, Krusell P, Tsyvinski A (2014) Optimal taxes on fossil fuel in general equilibrium. Econometrica 82:41–88CrossRefGoogle Scholar
  12. Grimaud A, Rouge L (2005) Polluting non-renewable resources, innovation and growth: welfare and environmental policy. Res Energy Econ 27(2):109–129CrossRefGoogle Scholar
  13. Grimaud A, Rouge L (2014) Carbon sequestration, economic policies and growth. Res Energy Econ 36:307–331CrossRefGoogle Scholar
  14. Groth C, Schou P (2007) Growth and non-renewable resources: the different roles of capital and resource taxes. J Environ Econ Manag 53:80–98CrossRefGoogle Scholar
  15. Hoel M, Kverndokk S (1996) Depletion of fossil fuels and the impacts of global warming. Res Energy Econ 18:115–136CrossRefGoogle Scholar
  16. IEA (2015) Monthly oil price statistics, 2006–2015. http://www.iea.org/statistics/relatedsurveys/monthlyenergyprices
  17. Ikefuji M, Horii R (2012) Natural disasters in a two-sector model of endogenous growth. J Public Econ 96:784–796CrossRefGoogle Scholar
  18. IPCC (2013) Climate change 2013: the physical science basis, WG I Contribution to the IPCC 5, summary for policy makers. Cambridge University Press, Cambridge. http://www.climatechange2013.org
  19. MacDonald N (1978) Time lags in biological models. Springer, BerlinCrossRefGoogle Scholar
  20. Michel P, Rotillon G (1995) Disutility of pollution and endogenous growth. Environ Res Econ 6:279–300Google Scholar
  21. Nordhaus WD (Jun. 1992) Rolling the ’dice’: an optimal transition path for controlling greenhouse gases. Cowles Foundation Discussion Papers 1019, Cowles Foundation for Research in Economics, Yale UniversityGoogle Scholar
  22. Nordhaus WD (2011) Integrated economic and climate modeling. Cowles Foundation Discussion Papers 1839, Cowles Foundation for Research in Economics, Yale UniversityGoogle Scholar
  23. Rebelo S (1991) Long-run policy analysis and long-run growth. J Polit Econ 99:500–521CrossRefGoogle Scholar
  24. Sinclair PJN (1994) On the optimum trend of fossil fuel taxation. Oxf Econ Papers 46:869–877CrossRefGoogle Scholar
  25. Stern N (2007) The economics of climate change: the Stern review. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  26. Stern N (2013) The structure of economic modeling of the potential impacts of climate change: grafting gross underestimation of risk onto already narrow science models. J Econ Lit 51:838–859Google Scholar
  27. Tahvonen O (1997) Fossil fuels, stock externalities, and backstop technology. Can J Econ 30:855–874CrossRefGoogle Scholar
  28. van den Bijgaart I, Gerlagh R, Liski M (2016) A simple formula for the social cost of carbon. J Environ Econ Manag 77:75–94CrossRefGoogle Scholar
  29. van der Ploeg F, Withagen C (2010) Growth and the optimal carbon tax: when to switch from exhaustible resources to renewables? OxCarre Working Papers 055, Oxford Centre for the Analysis of Resource Rich Economies, University of OxfordGoogle Scholar
  30. Withagen C (1994) Pollution and exhaustibility of fossil fuels. Res Energy Econ 16:235–242CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.CER-ETH Center of Economic Research at ETH ZurichZurichSwitzerland

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