Skip to main content
Log in

Solving Infinite Horizon Growth Models with an Environmental Sector

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

This paper concerns computational models in environmental economics andpolicy, particularly so-called integrated assessment models. For themost part, such models are simply extensions of standard neoclassicalgrowth models, extended by including the environment and pollutiongeneration. We review the structure of integrated assessment models,distinguishing between finite horizon and infinite horizon models, bothdeterministic and stochastic. We present a new solution algorithm forinfinite horizon integrated assessment models, relying on a neural netapproximation of the value function within an iterative version of theBellman equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Blitzer, Charles R., Clark, Peter B. and Taylor, Lance (1975). Economy-Wide Models and Development Planning, World Bank, Washington, DC.

    Google Scholar 

  • Cass, D. (1965). Optimum growth in aggregate model of capital accumulation. Review of Economic Studies, 32, 233–246.

    Google Scholar 

  • Christiano, L. (1987). Is consumption insufficiently sensitive to innovations in income? American Economic Review Papers and Proceedings, 77, 337–341.

    Google Scholar 

  • Christiano, L. (1988). Why does inventory investment fluctuate so much? Journal of Monetary Economics, 21, 247–280.

    Google Scholar 

  • Christiano, L. and Eichenbaum, M. (1988). Is theory really ahead of measurement? Current real business cycle theories and aggregate labor market fluctuations. Technical Report 2700, National Bureau of Economic Research Working Paper.

  • Cooley, T. and Hansen, G. (1989). The inflation tax in a real business cycle model. American Economic Review, 79, 733–748.

    Google Scholar 

  • Den Haan, W. J. and Marcet, A. (1990). Solving the stochastic growth model by parameterizing expectations. Journal of Business Economics and Statistics, 8(1), 99–113.

    Google Scholar 

  • Dennis, J. (1977). Nonlinear least squares. In D. Jacobs (ed.), State of the Art in Numerical Analysis. Academic Pess, pp. 269–312.

  • Grossman, G. and Krueger, P. (1995). Economic growth and the environment. Quarterly Journal of Economics, 112.

  • Hansen, G. (1985). Indivisible labor and the business cycle. Journal of Monetary Economics, 16, 309–327.

    Google Scholar 

  • Hansen, G. and Sargent, T. (1988). Straight time and overtime in equilibrium. Journal of Monetary Economics, 21, 281–308.

    Google Scholar 

  • Judd, Kenneth L. (1991). Minimum weighted residual methods for solving dynamic economic models. Unpublished manuscript, Hoover Institution, Stanford University.

  • Kelly, David L. (1998a). On Kuznets curves arising from stock externalities. Mimeo, University Miami Economics Department.

    Google Scholar 

  • Kelly, David L. (1998b). Convergence results for dynamic programming using neural networks. Mimeo, Department of Economics, University of Miami.

    Google Scholar 

  • Kelly, David L. and Kolstad, Charles D. (2001). Malthus and climate: Betting on a stable population. Journal of Environmental Economics and Management, 41, 135–161.

    Google Scholar 

  • Kelly, David L. and Kolstad, Charles D. (1999a). Bayesian learning, growth, and pollution. J. Econ. Dynamics and Control, 23(4), 491–518.

    Google Scholar 

  • Kelly, David L. and Kolstad, Charles D. (1999b). Integrated assessment models for climate change control. In Henk Folmer and Tom Tietenberg (eds.), International Yearbook of Environmental and Resource Economics 1999/2000: A Survey of Current Issues. Edward Elgar, Cheltenham, U.K.

    Google Scholar 

  • Kelly, David L., Kolstad, Charles D., Schlesinger, Michael E., and Andronova, Natalia G. (1998). Learning about climate sensitivity from the instrumental temperature record. Mimeo, UCSB Economics Department.

    Google Scholar 

  • Kolstad, Charles D. (1993). Looking vs. leaping: The timing of CO2 control in the face of uncertainty and learning. In Y. Kaya, N. Nakicenovic, W.D. Nordhaus and F.L. Toth (eds.), Costs, Impacts and Benefits of CO2 Mitigation. IIASA, Austria, pp. 63–82.

    Google Scholar 

  • Kolstad, Charles D. (1994). The timing of CO2 control in the face of uncertainty and learning. In E. van Ireland (ed.), International Environmental Economics. Elsevier, Amsterdam, Ch. 4.

    Google Scholar 

  • Kolstad, Charles D. (1996). Learning and stock effects in environmental regulation: The case of greenhouse gas emissions. Journal of Environmental Economics and Management, 31, 1–18.

    Google Scholar 

  • Koopmans, T.C. (1965). On the concept of optimal economic growth. In An Economic Approach to Development Planning. North Holland.

  • Kydland, F. and Prescott, E. (1982). Time to build and aggregate fluctuations. Econometrica, 50, 1345–1370.

    Google Scholar 

  • Manne, A.S. and Richels, R.G. (1992). Buying Greenhouse Insurance: The Economic Costs of CO2 Emission Limits. MIT Press, Cambridge.

    Google Scholar 

  • Manne, A.S., Mendelsohn, R. and Richels, R. (1995). A model for evaluating regional and global effects of GHG reduction policies. Energy Policy, 23, 17–34.

    Google Scholar 

  • Meadows, D. et al. (1972). The Limits to Growth. Universe Books, New York.

    Google Scholar 

  • Nordhaus, W.D. (1994). Managing the Global Commons: The Economics of Climate Change. MIT Press, Cambridge, Mass.

    Google Scholar 

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

    Google Scholar 

  • Peck, S.C., Chao, H.P. and Teisberg, T.J. (1989). Optimal control and learning strategies when environmental costs are cumulative. Proc. IFAC/IFORS/IAEE International Symposium on Energy Systems, Management and Economics, Oct. 25–27, Tokyo.

  • Peck, S.C. and Teisberg, T.J. (1992). CETA: A model for carbon emissions trajectory assessment. Energy Journal, 13(1), 55–77.

    Google Scholar 

  • Peck, S.C. and Teisberg, T.J. (1993). Global warming uncertainties and the value of information: An analysis using CETA. Resource and Energy Economics, 15, 71–98.

    Google Scholar 

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

    Google Scholar 

  • Stokey, Nancy L. and Lucas, Robert E. Jr. (1989). Recursive Methods in Economic Dynamics. Harvard, Cambridge, Mass.

    Google Scholar 

  • Trick, M. and Zin, S. (1993). A linear programming approach to solving stochastic dynamic programs. Mimeo, Carnegie Mellon University.

    Google Scholar 

  • Trick, M. and Zin, S. (1995). Adaptive spline generation: A new algorithm for solving stochastic dynamic programs. Mimeo, Carnegie Mellon University.

    Google Scholar 

  • Weyant, J.P. et al. (1996). Integrated assessment of climate change: An overview and comparison of approaches and results. In J.P. Bruce et al. (eds.), Climate Change 1995: Economic and Social Dimensions of Climate Change. Cambridge University Press, Cambridge, pp. 367–439.

    Google Scholar 

  • White, H. (1992). Artificial Neural Networks. Blackwell Publishers, Cambridge, Mass.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kelly, D.L., Kolstad, C.D. Solving Infinite Horizon Growth Models with an Environmental Sector. Computational Economics 18, 217–231 (2001). https://doi.org/10.1023/A:1021018417052

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021018417052

Navigation