Giải tích phân phân đoạn trong mô hình tăng trưởng kinh tế của Nhóm Bảy quốc gia

Fractional Calculus and Applied Analysis - Tập 22 - Trang 139-157 - 2019
Inés Tejado1, Emiliano Pérez1, Duarte Valério2
1Industrial Engineering School, University of Extremadura, Badajoz, Spain
2IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

Tóm tắt

Bài báo này trình bày các mô hình tăng trưởng kinh tế cho tất cả các quốc gia trong Nhóm Bảy (G7) trong giai đoạn 1973–2016. Các mô hình bao gồm các phương trình vi phân, với cả bậc nguyên và bậc phân đoạn, trong đó tổng sản phẩm quốc nội (GDP) là một hàm của diện tích đất, đất canh tác, dân số, tỷ lệ đi học, hình thành vốn cố định gộp (GCF), xuất khẩu hàng hóa và dịch vụ, chi tiêu tiêu dùng cuối cùng của chính phủ (GGFCE), và cung tiền rộng (M3). Các kết quả cho thấy các mô hình phân đoạn có hiệu suất tốt hơn, được đo lường bằng nhiều thống kê tóm tắt, mà không làm tăng số lượng tham số, hoặc hy sinh khả năng dự đoán sự phát triển của GDP trong ngắn hạn. Một quy trình xác nhận tiêu chuẩn cho các mô hình tăng trưởng kinh tế được trình bày để đánh giá các mô hình trong tương lai.

Từ khóa

#tăng trưởng kinh tế #mô hình vi phân #Nhóm Bảy (G7) #tổng sản phẩm quốc nội (GDP) #diện tích đất #đất canh tác

Tài liệu tham khảo

B. Baeumer, M.M. Meerschaert, Fractional diffusion with two time scales. Physica A: Stat. Mech. Appl., 373 (2007), 237–251; DOI: 10.1016/j.physa.2006.06.014. J. Blackledge, Application of the fractal market hypothesis for modelling macroeconomic time series. ISAST Trans. Electronics Sig. Proc., 2 No 1 (2008), 89–110; DOI: 10.21427/D7091P. J. Blackledge, Application of the fractional diffusion equation for predicting market behaviour. IAENG Int. J. Appl. Math., 40 No 3 (2010), 130–158; DOI: 10.21427/D7HK8R. D.E. Bloom, D. Canning, J. Sevilla, Technological diffusion, conditional convergence, and economic growth. Working Paper # 8713, National Bureau of Economic Research (2002), 27; DOI: 10.3386/w8713; https://www.nber.org/papers/w8713. M. Boleantu, Fractional dynamical systems and applications in economy. Diff. Geom.–Dyn. Syst., 10 (2008), 62–70. 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; DOI: 10.1515/fca-2015-0014; https://www.degruyter.com/view/j/fca.2015.18.issue-1/issue-files/fca.2015.18.issue-1.xml. 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; DOI: 10.1016/j.physa.2006.08.071. W.C. Chen, Nonlinear dynamics and chaos in a fractional order financial system. Chaos Solitons Fract., 36 No 5 (2008), 1305–1314; DOI: 10.1016/j.chaos.2006.07.051. 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; DOI: 10.1016/j.physa.2010.02.025. E.F. Denison, Why Growth Rates Differ. Brooking Institutions, Washington (1967). Federal Reserve Bank of St. Louis Federal Reserve Economic Data (2018) Accessed March 2018 [Online]. Available at: https://fred.stlouisfed.org/. R. Gorenflo, F. Mainardi, E. Scalas, M. Raberto, Fractional calculus and continuous-time finance III: The diffusion limit. Mathematical Finance Trends in Mathematics, Workshop of the Mathematical Finance Research Project. Konstanz (2001), 171–180. Z. Hu, X. Tu, A new discrete economic model involving generalized fractal derivative. Adv. Differ. Eq., 65 (2015), 1–11; DOI: 10.1186/s13662-015-0416-8. 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; DOI: 10.1515/fca-2016-0073; https://www.degruyter.com/view/j/fca.2016.19.issue-6/issue-files/fca.2016.19.issue-6.xml. N. Laskin, Fractional market dynamics. Physica A: Stat. Mech. Appl., 287 (2000), 482–492; DOI: 10.1016/S0378-4371(00)00387-3. J.W. Lee, H. Lee, Lee and Lee Long-run Education Dataset (2016) Accessed March 2018 http://www.barrolee.com/Lee_Lee_LRdata_dn.htm. R.E. Lucas, On the mechanics of economic development. J. Monet. Econ., 22 (1988), 3–42; DOI: 10.1016/0304-3932(88)90168-7. A. Maddison, Explaining the economic performance of nations, 1820–1989. Convergence of Productivity (Eds: W.J. Baumol, WJ et al. Oxford University Press, Oxford (1994), 20–61. R.L. Magin, Fractional Calculus in Bioengineering. Begell House (2004). 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; DOI: 10.1016/S0378-4371(00)00386-1. O. Marom, E. Momoniat, A comparison of numerical solutions of fractional diffusion models in finance. Nonlin. Anal.: Real World Appl., 10 (2009), 3435–3442; DOI: 10.1016/j.nonrwa.2008.10.066. M.M. Meerschaert, E. Scalas, Coupled continuous time random walks in finance. Physica A: Stat. Mech. Appl., 370 (2006), 114–118; DOI: 10.1016/j.physa.2006.04.034. M.M. Meerschaert, A. Sikorskii, Stochastic Models for Fractional Calculus. Walter de Gruyter. (2012). 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. OECD OECDiLibrary (2018) Accessed March 2018; Available at: http://dx.doi.org/10.1787/1036a2cf-en. I. Petrás, I. Podlubny, State space description of national economies: The V4 countries. Comput. Statist. Data Anal., 52 No 2 (2007), 1223–1233; DOI: 10.1016/j.csda.2007.05.014. S. Sassia, M. Goaied, Financial development, ICT diffusion and economic growth: Lessons from MENA region. Telecom. Pol., 37 No 4–5 (2013), 252–261; DOI: 10.1016/j.telpol.2012.12.004. E. Scalas, R. Gorenflo, F. Mainardi, Fractional calculus and continuous-time finance. Physica A: Stat. Mech. Appl., 284 No 1-4 (2000), 376–384; DOI: 10.1016/S0378-4371(00)00255-7. E. Scalas, The application of continuous-time random walks in finance and economics. Physica A: Stat. Mech. Appl., 362 (2006), 225–239; DOI: 10.1016/j.physa.2005.11.024. 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; DOI: 10.1016/j.strueco.2011.01.003. 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; DOI: 10.1016/j.econmod.2012.03.019. 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; DOI: 10.21013/jmss.v5.n2.p10. V.V. Tarasova, V.E. Tarasov, Exact discretization of an economic accelerator and multiplier with memory. Fractal Fract., 1 No 6 (2017), 1–14; DOI: 10.3390/fractalfract1010006. V.V. Tarasova, V.E. Tarasov, Economic interpretation of fractional derivatives. Progress Fract. Different. Appl., 1 (2017), 1–6; DOI: 10.18576/pfda/030101. I. Tejado, D. Valério, E. Pérez, N. Valério, Fractional calculus in economic growth modelling: The economies of France and Italy. International Conference on Fractional Differentiation and its Applications. Novi Sad (2016). I. Tejado, D. Valério, E. Pérez, N. Valério, Fractional calculus in economic growth modelling. The Spanish and Portuguese cases. Int. J. Dyn. Control, 5 No 1 (2017), 208–222; DOI: 10.1007/s40435-015-0219-5. 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; DOI: 10.24425/124262. 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. 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. 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; DOI: 10.1515/fca-2015-0029; https://www.degruyter.com/view/j/fca.2015.18.issue-2/issue-files/fca.2015.18.issue-2.xml. 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 1-3 (2015), 396–406; DOI: 10.1016/j.cnsns.2014.08.032. J.A. Tenreiro Machado, M.E. Mata, A.M. Lopes, Fractional state space analysis of economic systems. Entropy, 17 (2015), 5402–5421; DOI: 10.3390/e17085402. 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/. The World Bank World Bank Open Data (2018) Accessed March 2018; Available at: https://data.worldbank.org. D. Valério, J. Sá da Costa, Introduction to single-input, single-output Fractional Control. IET Control Theory Appl., 5 No 8 (2011), 1033–1057; DOI: 10.1049/iet-cta.2010.0332. 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; DOI: 10.1016/j.camwa.2011.04.057. West Germany (2018) Accessed August 2018; Available at: https://en.wikipedia.org/wiki/West_Germany. 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/. 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; DOI: 10.2478/s11534-013-0237-x. Y. Yue, L. He, G. Liu, Modeling and application of a new nonlinear fractional financial model. J. Appl. Math. (2013) ID 325050: DOI: 10.1155/2013/325050.