Startseite Fractional calculus in economic growth modelling of the group of seven
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Fractional calculus in economic growth modelling of the group of seven

  • Inés Tejado EMAIL logo , Emiliano Pérez und Duarte Valério
Veröffentlicht/Copyright: 19. März 2019
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

This paper presents models of economic growth for all the countries of the Group of Seven (G7) in the 1973–2016 period. The models consist of differential equations, of both integer and fractional order, where the gross domestic product (GDP) is a function of the country’s land area, arable land, population, school attendance, gross capital formation (GCF), exports of goods and services, general government final consumption expenditure (GGFCE), and broad money (M3). Results show that fractional models have a better performance, measured by several summary statistics, without increasing the number of parameters, or sacrificing the ability to predict GDP evolution in the short term. A standard validation procedure for economic growth models is presented for the assessment of future models.

Acknowledgements

This work was partially supported by FEDER Funds (Programa Operativo FEDER de Extremadura 2014-2020) through the grant “Ayuda a Grupos de Investigación” (ref. GR15178) of the Junta de Extremadura and by FCT, through IDMEC, under LAETA, project UID/EMS/50022/2019. Inés Tejado would like to thank the Junta de Extremadura its support through the scholarship granted within the mobility program of 2017.

References

[1] B. Baeumer, M.M. Meerschaert, Fractional diffusion with two time scales. Physica A: Stat. Mech. Appl. 373 (2007), 237–251; 10.1016/j.physa.2006.06.014.Suche in Google Scholar

[2] J. Blackledge, Application of the fractal market hypothesis for modelling macroeconomic time series. ISAST Trans. Electronics Sig. Proc. 2, No 1 (2008), 89–110; 10.21427/D7091P.Suche in Google Scholar

[3] J. Blackledge, Application of the fractional diffusion equation for predicting market behaviour. IAENG Int. J. Appl. Math. 40, No 3 (2010), 130–158; 10.21427/D7HK8R.Suche in Google Scholar

[4] D.E. Bloom, D. Canning, J. Sevilla, Technological diffusion, conditional convergence, and economic growth. Working Paper # 8713, National Bureau of Economic Research (2002), 27 pp.; 10.3386/w8713; Available at: https://www.nber.org/papers/w8713.Suche in Google Scholar

[5] M. Boleantu, Fractional dynamical systems and applications in economy. Diff. Geom. – Dyn. Syst. 10 (2008), 62–70.Suche in Google Scholar

[6] M. Caputo, J.M. Carcione, M.A.B. Botelho, Modeling extreme-event precursors with the fractional diffusion equation. Fract. Calc. Appl. Anal. 18, No 1 (2015), 208–222; 10.1515/fca-2015-0014; https://www.degruyter.com/view/j/fca.2015.18.issue-1/issue-files/fca.2015.18.issue-1.xml.Suche in Google Scholar

[7] Á. Cartea, D. del Castillo-Negrete, Fractional diffusion models of option prices in markets with jumps. Physica A: Stat. Mech. Appl. 374, No 2 (2007), 749–763; 10.1016/j.physa.2006.08.071.Suche in Google Scholar

[8] W.C. Chen, Nonlinear dynamics and chaos in a fractional order financial system. Chaos Solitons Fract. 36, No 5 (2008), 1305–1314; 10.1016/j.chaos.2006.07.051.Suche in Google Scholar

[9] S. Dadras, H.R. Momeni, Control of a fractional-order economical system via sliding mode. Physica A: Stat. Mech. Appl. 389, No 12 (2010), 2434–2442; 10.1016/j.physa.2010.02.025.Suche in Google Scholar

[10] E.F. Denison, Why Growth Rates Differ. Brooking Institutions, Washington (1967).Suche in Google Scholar

[11] Federal Reserve Bank of St. Louis, Federal Reserve Economic Data (2018). Accessed March 2018; [Online]. Available at: https://fred.stlouisfed.org/.Suche in Google Scholar

[12] R. Gorenflo, F. Mainardi, E. Scalas, M. Raberto, Fractional calculus and continuous-time finance III: The diffusion limit. In: Mathematical Finance Trends in Mathematics, Workshop of the Mathematical Finance Research Project, Konstanz (2001), 171–180.10.1007/978-3-0348-8291-0_17Suche in Google Scholar

[13] Z. Hu, X. Tu, A new discrete economic model involving generalized fractal derivative. Adv. Differ. Eq. 65 (2015), 1–11; 10.1186/s13662-015-0416-8.Suche in Google Scholar

[14] J. Korbel, Y. Luchko, Modeling of financial processes with a space-time fractional diffusion equation of varying order. Fract. Calc. Appl. Anal. 19, No 6 (2016), 1414–1433; 10.1515/fca-2016-0073; https://www.degruyter.com/view/j/fca.2016.19.issue-6/issue-files/fca.2016.19.issue-6.xml.Suche in Google Scholar

[15] N. Laskin, Fractional market dynamics. Physica A: Stat. Mech. Appl. 287 (2000), 482–492; 10.1016/S0378-4371(00)00387-3.Suche in Google Scholar

[16] J.W. Lee, H. Lee, Lee and Lee Long-run Education Dataset (2016). Accessed March 2018; Available at: http://www.barrolee.com/Lee_Lee_LRdata_dn.htm.Suche in Google Scholar

[17] R.E. Lucas, On the mechanics of economic development. J. Monet. Econ. 22 (1988), 3–42; 10.1016/0304-3932(88)90168-7.Suche in Google Scholar

[18] A. Maddison, Explaining the economic performance of nations, 1820–1989. In: Convergence of Productivity, W.J. Baumol WJ et al. (Eds), Oxford University Press, Oxford (1994), 20–61.Suche in Google Scholar

[19] R.L. Magin, Fractional Calculus in Bioengineering. Begell House (2004).Suche in Google Scholar

[20] F. Mainardi, M. Raberto, R. Gorenflo, E. Scalas, Fractional calculus and continuous-time finance II: The waiting-time distribution. Physica A: Stat. Mech. Appl. 287 (2000), 468–481; 10.1016/S0378-4371(00)00386-1.Suche in Google Scholar

[21] O. Marom, E. Momoniat, A comparison of numerical solutions of fractional diffusion models in finance. Nonlin. Anal.: Real World Appl. 10 (2009), 3435–3442; 10.1016/j.nonrwa.2008.10.066.Suche in Google Scholar

[22] M.M. Meerschaert, E. Scalas, Coupled continuous time random walks in finance. Physica A: Stat. Mech. Appl. 370 (2006), 114–118; 10.1016/j.physa.2006.04.034.Suche in Google Scholar

[23] M.M. Meerschaert, A. Sikorskii, Stochastic Models for Fractional Calculus. Walter de Gruyter (2012).10.1515/9783110258165Suche in Google Scholar

[24] Ministero degli Affari Esteri e della Cooperazione Internazionale, History of the G7/G8 (2018). Accessed April 2018; Available at: https://www.esteri.it/mae/en/politica_estera/g8/storia-del-g7-g8.html.Suche in Google Scholar

[25] OECD, OECDiLibrary (2018). Accessed March 2018; Available at: http://dx.doi.org/10.1787/1036a2cf-en.10.1787/1036a2cf-enSuche in Google Scholar

[26] I. Petrás, I. Podlubny, State space description of national economies: The V4 countries. Comput. Statist. Data Anal. 52, No 2 (2007), 1223–1233; 10.1016/j.csda.2007.05.014.Suche in Google Scholar

[27] S. Sassia, M. Goaied, Financial development, ICT diffusion and economic growth: Lessons from MENA region. Telecom. Pol. 37, No 4–5 (2013), 252–261; 10.1016/j.telpol.2012.12.004.Suche in Google Scholar

[28] E. Scalas, R. Gorenflo, F. Mainardi. Fractional calculus and continuous-time finance. Physica A: Stat. Mech. Appl. 284, No 1-4 (2000), 376–384; 10.1016/S0378-4371(00)00255-7.Suche in Google Scholar

[29] E. Scalas, The application of continuous-time random walks in finance and economics. Physica A: Stat. Mech. Appl. 362 (2006), 225–239; 10.1016/j.physa.2005.11.024.Suche in Google Scholar

[30] A. Seck, International technology diffusion and economic growth: Explaining the spillover benefits to developing countries. Struct. Change Econ. Dyn. 23, No 4 (2012), 437–451; 10.1016/j.strueco.2011.01.003.Suche in Google Scholar

[31] T. Skovranek, I. Podlubny, I. Petrás, Modeling of the national economies in state-space: A fractional calculus approach. Econ. Model. 29, No 4 (2012), 1322–1327; 10.1016/j.econmod.2012.03.019.Suche in Google Scholar

[32] V.E. Tarasov, Long and short memory in economics: Fractional-order difference and differentiation. Int. J. Bus. Manag. Soc. Res. 5, No 2 (2016), 327–334; 10.21013/jmss.v5.n2.p10.Suche in Google Scholar

[33] V.V. Tarasova, V.E. Tarasov, Exact discretization of an economic accelerator and multiplier with memory. Fractal Fract. 1, No 6 (2017), 1–14; 10.3390/fractalfract1010006.Suche in Google Scholar

[34] V.V. Tarasova, V.E. Tarasov, Economic interpretation of fractional derivatives. Progress Fract. Different. Appl. 1 (2017), 1–6; 10.18576/pfda/030101.Suche in Google Scholar

[35] I. Tejado, D. Valério, E. Pérez, N. Valério, Fractional calculus in economic growth modelling: The economies of France and Italy. In: International Conference on Fractional Differentiation and its Applications, Novi Sad (2016).Suche in Google Scholar

[36] I. Tejado, D. Valério, E. Pérez, N. Valério, Fractional calculus in economic growth modelling. The Spanish and Portuguese cases. Int. J. Dyn. Control5, No 1 (2017), 208–222; 10.1007/s40435-015-0219-5.Suche in Google Scholar

[37] I. Tejado, E. Pérez, D. Valério, Economic growth in the European Union modelled with fractional derivatives: First results. Bull. Pol. Acad. Sci.-Tech. Sci. 66, No 4 (2018), 455–465; 10.24425/124262.Suche in Google Scholar

[38] I. Tejado, E. Pérez, D. Valério, Economic Data for the G7 Group (2018). Available at: https://github.com/UExtremadura/Economic/blob/master/G7Data_Tejado_et_al2018.xls.Suche in Google Scholar

[39] I. Tejado, E. Pérez, D. Valério, Results for Predictions of the Future Evolution of the GDP for the G7 Group (2018). Available at: https://github.com/UExtremadura/Economic/blob/master/G7Results_Tejado_et_al2018.rar.Suche in Google Scholar

[40] J.A. Tenreiro Machado, A.M. Lopes, Analysis of natural and artificial phenomena using signal processing and fractional calculus. Fract. Calc. Appl. Anal. 18, No 2 (2015), 459–478; 10.1515/fca-2015-0029; https://www.degruyter.com/view/j/fca.2015.18.issue-2/issue-files/fca.2015.18.issue-2.xml.Suche in Google Scholar

[41] J.A. Tenreiro Machado, M.E. Mata, Pseudo phase plane and fractional calculus modeling of western global economic downturn. Commun. Nonlinear Sci. Numer. Simul. 22, No 1-3 (2015), 396–406; 10.1016/j.cnsns.2014.08.032.Suche in Google Scholar

[42] J.A. Tenreiro Machado, M.E. Mata, A.M. Lopes, Fractional state space analysis of economic systems. Entropy17 (2015), 5402–5421; 10.3390/e17085402.Suche in Google Scholar

[43] theGlobalEconomy.com, Economic Indicators for Over 200 Countries (2018). Accessed March 2018; Available at: https://www.theglobaleconomy.com/Germany/data_money_supply/, https://www.theglobaleconomy.com/France/data_money_supply/, https://www.theglobaleconomy.com/Italy/data_money_supply/.Suche in Google Scholar

[44] The World Bank, World Bank Open Data (2018). Accessed March 2018; Available at: https://data.worldbank.org.Suche in Google Scholar

[45] D. Valério, J. Sá da Costa, Introduction to single-input, single-output Fractional Control. IET Control Theory Appl. 5, No 8 (2011), 1033–1057: 10.1049/iet-cta.2010.0332.Suche in Google Scholar

[46] Z. Wang, X. Huang, G. Shi, Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay. Comput. Math. Appl. 62, No 3 (2011), 1531–1539. 10.1016/j.camwa.2011.04.057.Suche in Google Scholar

[47] West Germany (2018). Accessed August 2018; Available at: https://en.wikipedia.org/wiki/West_Germany.Suche in Google Scholar

[48] Wittgenstein Centre for Demography and Global Human Capital, Wittgenstein Centre Data Explorer Version 1.2 (2015). Accessed March 2018; Available at: http://dataexplorer.wittgensteincentre.org/shiny/wic/.Suche in Google Scholar

[49] Y. Xu, Z. He, Synchronization of variable-order fractional financial system via active control method. Cent. Eur. J. Phys. 11, No 6 (2013), 824–835; 10.2478/s11534-013-0237-x.Suche in Google Scholar

[50] Y. Yue, L. He, G. Liu, Modeling and application of a new nonlinear fractional financial model. J. Appl. Math. (2013), ID 325050; 10.1155/2013/325050.Suche in Google Scholar

Received: 2018-10-01
Published Online: 2019-03-19
Published in Print: 2019-02-25

© 2019 Diogenes Co., Sofia

Heruntergeladen am 7.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/fca-2019-0009/html
Button zum nach oben scrollen