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Dynamic Input–Output Models in Environmental Problems: A Computational Approach with CAS Software

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Abstract

The study of interactions between the economy and the environment has always been an interesting subject. Apart from static input–output (IO) models, environmentally extended IO analysis has resulted in dynamic IO models as well. Dynamic models are built of differential equations and, in the case of discrete models with the help of difference equations. The dynamic approach requires advanced mathematical skills especially in cases where the stability of the system under study is considered. In this paper we state some applied environmental models in discrete time based on dynamic IO analysis and we propose a computational approach in computer algebra system environments that investigates the extent and the nature of their stability. The computer codes are fully presented and can be reproduced as they are in computational-based research practice and education.

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Notes

  1. Mathematica software is tradable from Wolfram Research, Inc.

  2. Xcas is a Computer Algebra System available free in http://www-fourier.ujf-grenoble.fr/~parisse/giac.html.

References

  • Amman, H. M., & Kendrick, D. A. (1998). Computing the steady state of linear quadratic optimization models with rational expectations. Economics Letters, 58, 185–191.

    Article  Google Scholar 

  • Amman, H. M., & Kendrick, D. A. (1999). Linear-quadratic optimization for models with rational expectations. Macroeconomic Dynamics, 3, 534–543.

    Article  Google Scholar 

  • Amman, H.M., Kendrick, D.A., & Neudecker, H. (1996). Numerical steady state solutions for nonlinear dynamic optimisation models. In Conference on Computing in Economics and Finance, Society of Computational Economics.

  • Arbex, M., & Perobelli, F. S. (2010). Solow meets Leontief: economic growth and energy consumption. Energy Economics, 32(1), 43–53.

    Article  Google Scholar 

  • Brenner, A., Shacham, M., & Cutlip, M. B. (2005). Applications of mathematical software packages for modeling and simulations in environmental engineering education. Environmental Modelling & Software, 20, 1307–1313.

    Article  Google Scholar 

  • Cathers, B., Boyd, M.J., Craig, E., & Chadwick, M. (1996). Modelling for environmental engineering students using MATLAB and SIMULINK. 0–7803-3 173–7/96 IEEE.

  • Chiang, A. (1984). Fundamental methods of mathematical economics (3rd ed.). Singapore: McGraw-Hill Book.

    Google Scholar 

  • Dobos, I., & Floriska, A. (2009). A dynamic Leontief pollution model with environmental standards. Journal of Applied Input-Output Analysis, 15, 40–49.

    Google Scholar 

  • Dobos, I., & Tallos, P. (2013). A dynamic input-output model with renewable resources. Central European Journal of Operations Research, 21(2), 295–305.

    Article  Google Scholar 

  • Duchin, F. & Steenge, A.E. (2007). Mathematical models in input-output economics. Rensselaer Working paper in Economics. http://www.economics.rpi.edu/workingpapers/rpi0703.pdf. Accessed 4 January 2015.

  • Halkos, G.E., & Tsilika, K.D. (2011). Xcas as a programming environment for stability conditions of a class of linear differential equation models in economics. In Proceedings of the 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011). AIP Conference Proceedings, 1389, 1769–1772. doi:10.1063/1.3636951. DVD ISBN: 978-0-7354-0954-5.

  • Halkos, G. E., & Tsilika, K. D. (2012a). Computational techniques for stability analysis of a class of discrete time discrete state dynamic economic models. American Journal of Applied Sciences, 9(12), 1944–1952.

    Article  Google Scholar 

  • Halkos, G.E., & Tsilika, K.D. (2012b). Stability analysis in economic dynamics: A computational approach. MPRA paper. http://mpra.ub.uni-muenchen.de/41371/. Accessed 4 January 2015.

  • Hoekstra, R., & Janssen, M. A. (2006). Environmental responsibility and policy in a two-country dynamic input-output model. Economic Systems Research, 18(1), 61–84.

    Article  Google Scholar 

  • Idenburg, A. M., & Wilting, H. C. (2004). DIMITRI: a dynamic input-output model to study the impacts of technology related innovations. In J. C. J. M. van den Bergh & M. A. Janssen (Eds.), Economics of industrial ecology: Materials, structural change and spatial scales (pp. 223–252). Cambridge: MIT Press.

    Google Scholar 

  • Pan, X., & Kraines, S. (2001). Environmental input-output models for life-cycle analysis. Environmental and Resource Economics, 20(1), 61–72.

    Article  Google Scholar 

  • Proops, J., & Safonov, P. (Eds.). (2004). Modeling in Ecological Economics. Northampton, Massachusetts: Edward Elgar Publishing.

  • Safonov, P. (1996a). Dynamic ecology-economy interactions modeling: some experience and perspectives of application in Russian and German context. In Proceedings of the International Conference Ecology, Society, Economy: in Pursuit of Sustainable Development, University of Versailles Saint-Quentin, France. http://www.ulb.ac.be/ceese/STAFF/safonov/ZEW.pdf. Accessed 4 January 2015.

  • Safonov, P. (1996b). A system of dynamic models for ecological-economic regional development. In S. Faucheux, D. Pearce, & J. Proops (Eds.), Models of sustainable development (pp. 302–318). Cheltenham: Edward Elgar.

    Google Scholar 

  • Shmelev, S.E. (2009). Environmentally extended input-output analysis of the UK economy: key sector analysis. 17th International Conference on Input-Output Techniques, Sao Paulo, Brazil, July 13–17.

  • Strang, G. (1988). Linear algebra and its applications (3rd ed.). Philadelphia: Harcourt Brace Jovanovich College.

    Google Scholar 

  • Tamura, H., & Ishida, T. (1985). Environmental-economic models for total emission control of regional environmental pollution—input-output approach. Ecological Modelling, 30(3–4), 163–173.

    Article  Google Scholar 

  • Wiedmanna, T., Lenzenb, M., Turnerc, K., & Barrett, J. (2007). Examining the global environmental impact of regional consumption activities—Part 2: Review of input-output models for the assessment of environmental impacts embodied in trade. Ecological Economics, 61, 15–26.

    Article  Google Scholar 

  • Wu, S., Lei, Y., & Li, L. (2014). Resource distribution, interprovincial trade, and embodied energy: A case study of China. Advances in Materials Science and Engineering, 17, 73–86.

    Google Scholar 

  • Zhang, G., & Liu, M. (2014). The changes of carbon emission in China’s industrial sectors from 2002 to 2010: a structural decomposition analysis and input-output subsystem. Discrete Dynamics in Nature and Society, 39, 11. doi:10.1155/2014/798576.

    Google Scholar 

  • Zhang, G., Liu, M., & Gao, X. (2014). Dynamic characteristic analysis of indirect carbon emissions caused by Chinese urban and rural residential consumption based on time series input-output tables from 2002 to 2011. Mathematical Problems in Engineering, 2014, doi:10.1155/2014/297637.

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Authors and Affiliations

  1. Department of Economics, Laboratory of Operations Research, University of Thessaly, Korai 43, 38333, Volos, Greece

    George Halkos & Kyriaki Tsilika

Authors
  1. George Halkos
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  2. Kyriaki Tsilika
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Correspondence to George Halkos.

Appendix: Mathematica and Xcas Programmed Functions

Appendix: Mathematica and Xcas Programmed Functions

In this appendix we provide a brief overview of the code we used for the examples in this paper.

The first argument of steadytate function in Mathematica contains system’s coefficient matrix (a) and the second argument system’s initial state (initial) in a column matrix form. steadytate function calculates the asymptotic behavior of the system in a column matrix form.

figure a

distributionk function, takes as arguments system’s coefficient matrix (a) and system’s initial state (initial).

figure b

In Xcas environment, stability conditions are examined using stabilitytest2 function taking system’s coefficient matrix as argument (x). steadystate function takes as arguments system’s coefficient matrix (a) and the system’s initial state (initialstate) in a column matrix form.

figure c

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Halkos, G., Tsilika, K. Dynamic Input–Output Models in Environmental Problems: A Computational Approach with CAS Software. Comput Econ 47, 489–497 (2016). https://doi.org/10.1007/s10614-015-9497-4

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