A survey on macroeconomic data and trends in the Eurozone and a control dashboard model based on the KAM and Nekhoroshev theorems and the Hénon attractor

Desogus, Marco and Casu, Elisa (2021): A survey on macroeconomic data and trends in the Eurozone and a control dashboard model based on the KAM and Nekhoroshev theorems and the Hénon attractor. Published in: Journal of Academy of Business and Economics , Vol. 21, No. 3 (2021): pp. 67-85.

Abstract

Starting from the examination of the main macroeconomic parameters that have characterized the structure of the Eurozone in the last decade – and their systemization – our aim was to apply a model suitable for describing its dynamics. In particular, the Kolmogorov-Arnold-Moser theorem was adapted to the question, up to low level perturbations caused by negative economic conditions, the first symptoms of financial or exogenous crises, and other turbulence affecting the economy. We then applied Nekhoroshev's theorem to represent the phenomena characterized by the occurrence of stronger resonance as well as the reactions of the system to the control and recovery measures implemented by the ECB Governing Council. The goal of the paper is to propose the adoption of a systemic stability planning and control dashboard – also suitable for the support and stimulation of growth cycles – with attention to optimal performance, which can be identified in compliance with (or restoration of) the macroeconomic trajectories determined in the model by the Hénon Attractor. The proposed scheme may find useful application – both for evaluation and operational purposes – in the current period, characterized by the complex and compromised scenario brought about by the SARS-COVID2 pandemic emergency, which has obviously imposed structured measures to support the economy.

• Item Type: MPRA Paper
• Language: English
• Keywords: Macroeconomic Cycles; Monetary Policy Analysis; Optimizing Dynamic Models; Eurozone; Hamiltonian; Quasi-periodic Solution; Covid19 Crisis
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E58 - Central Banks and Their Policies; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E66 - General Outlook and Conditions; H - Public Economics > H1 - Structure and Scope of Government > H12 - Crisis Management

References

Andrade P., Cahn C., Fraisse H., Mésonnier J.S., Can the Provision of Long-Term Liquidity Help to Avoid a Credit Crunch? Evidence from the Eurosystem’s LTRO, Journal of the European Economic Association, 17 (4), (2019), 1070–1106. URL: https://doi.org/10.1093/jeea/jvy020

Asai T., Tanaka K., Oishi S., Numerical verification for asymmetric solutions of the Hénon equation on bounded domains, Journal of Computational and Applied Mathematics, 399 (113708), (2022), 1–13. URL: https://doi.org/10.1016/j.cam.2021.113708

Ben Bouheni F., Hasnaoui A., Cyclical behavior of the financial stability of eurozone commercial banks, Economic Modelling, 67, (2017), 392–408. URL: https://doi.org/10.1016/j.econmod.2017.02.018

Benettin G., Applicazioni del teorema di Nekhoroshev alla meccanica celeste, Bollettino dell’Unione Matematica Italiana, Serie 8, 4-B [in Italian], (2001), 71–95. URL: http://www.bdim.eu/item?id=BUMI_2001_8_4B_1_71_0

Centro studi e ricerche Intesa Sanpaolo Group [in Italian], accessed Jun-Jul 2021. URL: https://group.intesasanpaolo.com/it/research/macroeconomic-analysis-new

Cong H., Liu C., Wang P., A Nekhoroshev type theorem for the nonlinear wave equation, Journal of Differential Equations, 269 (4), (2020), 3853–3889. URL: https://doi.org/10.1016/j.jde.2020.03.015

Crescenzi R., Giua M., Sonzogno G.V., Mind the Covid-19 crisis: An evidence-based implementation of Next Generation EU, Journal of Policy Modeling, 43 (2), (2021), 278–297. URL: https://doi.org/10.1016/j.jpolmod.2021.03.002

Curcuru S.E., Kamin S.B., Li C., Rodriguez M., International Spillovers of Monetary Policy: Conventional Policy vs. Quantitative Easing, International Finance Discussion Paper - Board of Governors of the Federal Reserve System, 1234 (2018). URL: http://dx.doi.org/10.17016/IFDP.2018.1234

Data center Eurostat, accessed Jan 2021 to Jun 2021. URL: https://ec.europa.eu/eurostat/data/database

Data center World Bank, accessed Mar 2021 to May 2021. URL: https://data.worldbank.org/

Dedola L., Georgiadis G., Gräb J., Mehl A., Does a big bazooka matter? Quantitative easing policies and exchange rates, Journal of Monetary Economics, 117, (2021), 489–506. URL: https://doi.org/10.1016/j.jmoneco.2020.03.002

Desogus M., Casu E., On the Monetary Causes of Inequality: A Review of the Literature and an Alternate Way Forward, International Journal of Economics, Finance and Management Sciences, 8 (4), (2020), 156–167. URL: http://dx.doi.org/10.11648/j.ijefm.20200804.14

Dubeibe F.L., Riaño-Doncel A., Zotos E.E., Dynamical analysis of bounded and unbounded orbits in a generalized Hénon–Heiles system, Physics Letters A, 382 (13), (2018), 904–910. URL: https://doi.org/10.1016/j.physleta.2018.02.001

Franceschini V., Sistemi Dinamici e Caos. Lezioni tenute presso la Scuola di Dottorato in Meccanica Avanzata – Faculty of Engineering, University of Modena [in Italian], (A.Y. 2006-2007). URL: https://cdm.unimore.it/home/matematica/franceschini.valter/SD2.pdf

Frieden J., Walter S., Understanding the Political Economy of the Eurozone Crisis, Annual Review of Political Science, 20 (1), (2017), 271–390. URL: https://doi.org/10.1146/annurev-polisci-051215-023101

Genschel P., Jachtenfuchs M., From Market Integration to Core State Powers: The Eurozone Crisis, the Refugee Crisis and Integration Theory, Journal of Common Market Studies, 56 (1), (2018), 178–196. URL: https://doi.org/10.1111/jcms.12654

Giorgilli A., I moti quasi periodici e la stabilità del sistema solare. II: Dai tori di Kolmogorov alla stabilità esponenziale, Bollettino dell'Unione Matematica Italiana, Serie 8, 10-A [in Italian], (2007), 465-495. URL: http://www.bdim.eu/item?id=BUMI_2007_8_10A_3_465_0

Gräbner C., Heimberger P., Kapeller J., Schütz B., Is the Eurozone disintegrating? Macroeconomic divergence, structural polarisation, trade and fragility, Cambridge Journal of Economics, 44 (3), (2020), 647–669. URL: https://doi.org/10.1093/cje/bez059

Guiso L., Herrera H., Morelli M., Sonno T., Global crises and populism: the role of Eurozone institutions, Economic Policy, 34 (97), (2019), 95–139. URL: https://doi.org/10.1093/epolic/eiy018

ISTAT, Rapporto Annuale 2021. La situazione del Paese [in Italian], (2021). URL: https://www.istat.it/it/archivio/259060

Lenza M., Slacalek J., How Does Monetary Policy Affect Income and Wealth Inequality? Evidence from Quantitative Easing in the Euro Area, ECB Working Paper, 2190, (2018). URL: https://ssrn.com/abstract=3275976

Luo C.M., The COVID-19 Crisis: The EU Recovery Fund and its Implications for European Integration – a Paradigm Shift, European Review, 1, (2021), 1–19. URL: https://doi.org/10.1017/S106279872100003X

Palmero M.S., Diaz G.I., McClintock P.V.E., Leonel E.D., Diffusion phenomena in a mixed phase space, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30 (013108), (2020), 1–6. URL: https://doi.org/10.1063/1.5100607

Picek O., Spillover Effects From Next Generation EU. Intereconomics, 55, (2020), 325–331. URL: https://doi.org/10.1007/s10272-020-0923-z

Ralph S. J. Koijen R.S.J., Koulischer F., Nguyen B., Yogo M., Euro-Area Quantitative Easing and Portfolio Rebalancing, American Economic Review, 107 (5), (2017), 621–627. URL: https://doi.org/10.1257/aer.p20171037

Wang Y., Wang H., Zhang M. Rui J., Quasi-periodic solutions for a nonlinear non-autonomous Hamiltonian system, Journal Europeen des Systemes Automatises, 51 (4-6), (2018), 259–271. URL: https://doi.org/10.3166/JESA.51.259-271

Wasserfallen F., Leuffen D., Kudrna Z., Degner H., Analysing European Union decision-making during the Eurozone crisis with new data, European Union Politics, 20 (1), (2018), 3–23. URL: https://doi.org/10.1177/1465116518814954