Skip to main content

A Survey on Business Cycles: History, Theory and Empirical Findings

  • Conference paper
  • First Online:
Consequences of Social Transformation for Economic Theory (EASET 2022)

Abstract

This work summarizes recent advances in modelling and econometrics for alternative directions in macroeconomics and cycle theories. Starting from the definition of a cycle and continuing with a historical overview, some basic nonlinear models of the business cycle are introduced. Furthermore, some dynamic stochastic models of general equilibrium (DSGE) and autoregressive models are considered. Advances are then provided in recent applications to economics such as recurrence quantification analysis and numerical tools borrowed from other scientific fields such as physics and engineering. The aim is to embolden interdisciplinary research in the direction of the study of business cycles and related control techniques to broaden the tools available to policymakers.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Adachi, M. (1993). Embeddings and immersions. American Mathematical Society.

    Google Scholar 

  • Anisiu, M.-C. (2014). Lotka, Volterra and their model. Didáctica Mathematica, 32, 9–17.

    Google Scholar 

  • Araujo, R. A., & Moreira, H. N. (2021). Testing a Goodwin’s model with capacity utilization to the US economy. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 295–313). Springer.

    Chapter  Google Scholar 

  • Bastos, J., & Caiado, J. (2011). Recurrence quantification analysis of global stock. Physica A-Statistical Mechanics and Its Applications, 390.

    Google Scholar 

  • Brock, W. A., & Dechert, W. D. (1991). Non-linear dynamical systems: Instability and chaos in economics. In W. Hildenbrand & H. Sonnenschein (Eds.), Handbook of mathematical economics (vol. 4, pp. 2209–2235).

    Google Scholar 

  • Buizza, R. (2018). Ensemble forecasting and the need for calibration. Statistical postprocessing of ensemble forecasts (pp. 15–48). Elsevier.

    Chapter  Google Scholar 

  • Chen, P., & Semmler, W. (2021). Financial stress, regime switching and macrodynamics. In G. Orlando, A. N. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics: An interdisciplinary approach to economic dynamics, growth and cycles (pp. 315–335). Springer International Publishing.

    Chapter  Google Scholar 

  • Chiarella, C., Flaschel, P., Groh, G., & Semmler, W. (2013). Disequilibrium, growth and labor market dynamics: Macro perspectives. Springer Science & Business Media.

    Google Scholar 

  • Chiarella, C., & Flaschel, P. (1996). Real and monetary cycles in models of Keynes-Wicksell type. Journal of Economic Behavior & Organization, 30(3), 327–351.

    Article  Google Scholar 

  • Claessens, S., Kose, M. A., & Terrones, M. E. (2021). Financial cycles: What? How? When? NBER International Seminar on Macroeconomics.

    Google Scholar 

  • Crowley, P. M. (2008). Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots. The European Physical Journal Special Topics, 164(1), 67–84.

    Article  Google Scholar 

  • Day, R. H. (1994). Complex economic dynamics: An introduction to macroeconomic dynamics (vol. 2). MIT Press.

    Google Scholar 

  • Eckmann, J.-P., Kamphorst, S. O., & Ruelle, D. (1987). Recurrence plots of dynamical systems. EPL (Europhysics Letters), 4(9), 973.

    Google Scholar 

  • Fabretti, A., & Ausloos, M. (2005). Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. examples from financial market indices. International Journal of Modern Physics C, 16(05), 671–706.

    Google Scholar 

  • Fanti, L. (2003). Labour contract length, stabilisation and the growth cycle. Rivista internazionale di scienze sociali, pp. 1000–1024.

    Google Scholar 

  • Giacomini, R. (2013). The relationship between DSGE and VAR models. VAR models in macroeconomics–new developments and applications: Essays in honor of Christopher A. Sims.

    Google Scholar 

  • Ginoux, J.-M., & Letellier, C. (2012). Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept. Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(2), 023120.

    Google Scholar 

  • Gonze, D., & Ruoff, P. (2021). The Goodwin oscillator and its legacy. Acta Biotheoretica, 69(4), 857–874.

    Article  Google Scholar 

  • Goodwin, R. M. (1982). A growth cycle. essays in economic dynamics (pp. 165–170). Palgrave Macmillan.

    Chapter  Google Scholar 

  • Goodwin, R. M. (1951). The nonlinear accelerator and the persistence of business cycles. Econometrica: Journal of the Econometric Society, 1–17.

    Google Scholar 

  • Gorban, A. N., Smirnova, E. V., & Tyukina, T. A. (2010). Correlations, risk and crisis: From physiology to finance. Physica A: Statistical Mechanics and Its Applications, 389(16), 3193–3217.

    Article  Google Scholar 

  • Haddad, E. A., Cotarelli, N., Simonato, T. C., Vale, V. A., & Visentin, J. C. (2020). The grand tour: Keynes and Goodwin go to Greece. Economic Structures, 9(1), 1–21.

    Article  Google Scholar 

  • Harding, D., & Pagan, A. (2002). Dissecting the cycle: A methodological investigation. Journal of Monetary Economics, 49(2), 365–381.

    Article  Google Scholar 

  • Hicks, J. R. (1946). Value and capital: An inquiry into some fundamental principles of economic theory. Clarendon Press.

    Google Scholar 

  • Jevons, W. S. (1879). The theory of political economy. Macmillan and Company.

    Google Scholar 

  • Jouan, G., Cuzol, A., Monbet, V., & Monnier, G. (2022). Gaussian mixture models for clustering and calibration of ensemble weather forecasts. Discrete and Continuous Dynamical Systems - S. https://doi.org/10.3934/dcdss.2022037

    Article  Google Scholar 

  • Kalecki, M. (1971). Selected essays on the dynamics of the capitalist economy 1933–1970. Cambridge University Press.

    Google Scholar 

  • Keynes, J. M. (1936). 1973, the general theory of employment, interest, and money (vol. 7). Macmillan for the Royal Economic Society.

    Google Scholar 

  • Kousik, G., Basabi, B., & Chowdhury, A. R. (2010). Using recurrence plot analysis to distinguish between endogenous and exogenous stock market crashes. Physica a: Statistical Mechanics and Its Applications, 389(9), 1874–1882.

    Article  Google Scholar 

  • Kuznets, S. (1930). Static and dynamic economics. The American Economic Review, 20(3), 426–441.

    Google Scholar 

  • Lampart, M., Lampartová, A., & Orlando, G. (2022). On extensive dynamics of a Cournot heterogeneous model with optimal response. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(2), 023124.

    Google Scholar 

  • Le Corbeiller, P. (1933). Les systèmes autoentretenus et les oscillations de relaxation. Econometrica: Journal of the Econometric Society, 1, 328–332.

    Google Scholar 

  • Letellier, C., & Rossler, O. E. (2006). Rossler attractor. Scholarpedia, 1(10), 1721.

    Google Scholar 

  • Li, T., & Yorke, J. A. (1975). Period three implies chaos. American Mathematical Monthly, 82, 985–992.

    Google Scholar 

  • Liénard, A. (1928). Etude des oscillations entretenues. Revue Générale De L’électricité, 26, 901–912.

    Google Scholar 

  • Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences, 20, 130–141.

    Article  Google Scholar 

  • Lorenz, H.-W. (1992). Complex dynamics in low-dimensional continuous-time business cycle models: The Šil nikov case. System Dynamics Review, 8(3), 233–250.

    Article  Google Scholar 

  • Lorenz, H. W. (1993). Nonlinear dynamical economics and chaotic motion. Springer Verlag.

    Google Scholar 

  • Lowe, A. (2017). On economic knowledge: Toward a science of political economics. Routledge.

    Book  Google Scholar 

  • Mackey, M. C., & Glass, L. (1977). Oscillation and chaos in physiological control systems. Science, 197(4300), 287–289.

    Article  Google Scholar 

  • Marx, K., & McLellan, D. (2008). Capital: An abridged edition. Oxford University Press.

    Google Scholar 

  • May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560), 459–467.

    Article  Google Scholar 

  • May, R. M. (2004). Simple mathematical models with very complicated dynamics. In: B. R. Hunt, T. Y. Li, J. A. Kennedy & H. E. Nusse (Eds.), The theory of chaotic attractors. Springer. https://doi.org/10.1007/978-0-387-21830-4_7

  • Metzler, L. A. (1941). The nature and stability of inventory cycles on JSTOR. Review of Economics and Statistics, 23(3), 113–129.

    Article  Google Scholar 

  • Mill, J. S. (1848). Principles of political economy with some of their applications to social philosophy. John W. Parker.

    Google Scholar 

  • Mittnik, S., & Semmler, W. (2012). Regime dependence of the fiscal multiplier. Journal of Economic Behavior & Organization, 83(3), 502–522.

    Article  Google Scholar 

  • OECD. (2016). Quarterly GDP (indicator). https://doi.org/10.1787/b86d1fc8-en

  • Orlando, G. (2016). A discrete mathematical model for chaotic dynamics in economics: Kaldor’s model on business cycle. Mathematics and Computers in Simulation, 125, 83–98.

    Article  Google Scholar 

  • Orlando, G. (2022). Simulating heterogeneous corporate dynamics via the Rulkov map. Structural Change and Economic Dynamics, 61, 32–42.

    Article  Google Scholar 

  • Orlando, G., & Bufalo, M. (2022). Modelling bursts and chaos regularization in credit risk with a deterministic nonlinear model. Finance Research Letters, 47, 102599.

    Article  Google Scholar 

  • Orlando, G., & Della Rossa, F. (2019). An empirical test on Harrod’s open economy dynamics. Mathematics, 7(6), 524.

    Article  Google Scholar 

  • Orlando, G., & Sportelli, M. (2021). Growth and cycles as a struggle: Lotka-Volterra, Goodwin and Phillips. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 191–208). Springer.

    Chapter  Google Scholar 

  • Orlando, G., & Taglialatela, G. (2021a). An example of nonlinear dynamical system: The logistic map. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 39–50). Springer.

    Chapter  Google Scholar 

  • Orlando, G., & Taglialatela, G. (2021b). Dynamical systems. In G. Orlando, A. N. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics: An interdisciplinary approach to economic dynamics, growth and cycles (pp. 13–37). Springer International Publishing.

    Chapter  Google Scholar 

  • Orlando, G., & Zimatore, G. (2017). RQA correlations on real business cycles time series. Proceedings of the Conference on Perspectives in Nonlinear Dynamics, 2016(1), 35–41.

    Google Scholar 

  • Orlando, G., & Zimatore, G. (2018). Recurrence quantification analysis of business cycles. Chaos, Solitons & Fractals, 110, 82–94.

    Article  Google Scholar 

  • Orlando, G., & Zimatore, G. (2020b). Recurrence quantification analysis on a Kaldorian business cycle model. Nonlinear Dynamics, 100(1), 785–801.

    Article  Google Scholar 

  • Orlando, G., & Zimatore, G. (2021). Recurrence quantification analysis of business cycles. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 269–282). Springer.

    Chapter  Google Scholar 

  • Orlando, G., Pisarchik, A. N., & Stoop, R. (Eds.). (2021a). Nonlinearities in economics: An interdisciplinary approach to economic dynamics, growth and cycles. Springer International Publishing.

    Google Scholar 

  • Orlando, G., Stoop, R., & Taglialatela, G. (2021b). Bifurcations. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 51–72). Springer.

    Chapter  Google Scholar 

  • Orlando, G., Stoop, R., & Taglialatela, G. (2021c). Chaos. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 87–103). Springer.

    Chapter  Google Scholar 

  • Orlando, G., Stoop, R., & Taglialatela, G. (2021d). Embedding dimension and mutual information. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 105–108). Springer.

    Chapter  Google Scholar 

  • Orlando, G., Zimatore, G., & Giuliani, A. (2021e). Recurrence quantification analysis: Theory and applications. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 141–150). Springer.

    Chapter  Google Scholar 

  • Orlando, G., Bufalo, M., & Stoop, R. (2022). Financial markets’ deterministic aspects modeled by a low-dimensional equation. Science and Reports, 12(1693), 1–13.

    Google Scholar 

  • Orlando, G., & Zimatore, G. (2020a). Business cycle modeling between financial crises and black swans: Ornstein–Uhlenbeck stochastic process vs Kaldor deterministic chaotic model. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(8), 083129.

    Google Scholar 

  • Orlando, G. (2018). Chaotic business cycles within a Kaldor-Kalecki framework. In: Pham, V. T., Vaidyanathan, S., Volos, C., Kapitaniak, T. (eds.). Nonlinear dynamical systems with self-excited and hidden attractors. Studies in systems, decision and control, vol. 133. Springer. https://doi.org/10.1007/978-3-319-71243-7_6

  • Piscitelli, L., & Sportelli, M. C. (2004). A simple growth-cycle model displaying “Sil’nikov Chaos.” Economic complexity (Vol. 14, pp. 3–30). Emerald Group Publishing Limited.

    Chapter  Google Scholar 

  • Prescott, E. C. (1986). Theory ahead of business-cycle measurement. In Carnegie-Rochester conference series on public policy (vol. 25, pp. 11–44). Elsevier.

    Google Scholar 

  • Rivot, S., & Trautwein, H.-M. (2020). Macroeconomic statics and dynamics in a historical perspective. European Journal of the History of Economic Thought, 27(4), 471–475.

    Article  Google Scholar 

  • Della Rossa, F., Guerrero, J., Orlando, G., & Taglialatela, G. (2021). Applied spectral analysis. In G. Orlando, A. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics (pp. 123–139). Springer.

    Chapter  Google Scholar 

  • Rosser, J. B., Jr. (2013). A conceptual history of economic dynamics. Madison University.

    Google Scholar 

  • Rössler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397–398.

    Article  Google Scholar 

  • Semmler, W. (1986). On nonlinear theories of economic cycles and the persistence of business cycles. Mathematical Social Sciences, 12(1), 47–76.

    Article  Google Scholar 

  • Sharkovskij, A. (1964). Co-existence of cycles of a continuous map of the line into itself. Ukranian Math. Z., 16, 61–71.

    Google Scholar 

  • Sherman, H. J. (2014). The business cycle: Growth and crisis under capitalism. Princeton University Press.

    Google Scholar 

  • Slutzky, E. (1937). The summation of random causes as the source of cyclic processes. Econometrica: Journal of the Econometric Society, 5(2), 105–146.

    Google Scholar 

  • Sportelli, M. C. (2000). Dynamic complexity in a Keynesian growth-cycle model involving Harrod’s instability. Zeitschr. f. Nationalökonomie., 71(2), 167–198.

    Article  Google Scholar 

  • Sportelli, M., & De Cesare, L. (2019). Fiscal policy delays and the classical growth cycle. Applied Mathematics and Computation, 354, 9–31.

    Article  Google Scholar 

  • Stiglitz, J. E. (2018). Where modern macroeconomics went wrong. Oxford Review of Economic Policy, 34(1–2), 70–106.

    Google Scholar 

  • Stoop, R. (2021). Signal processing. In G. Orlando, A. N. Pisarchik & R. Stoop (Eds.), Nonlinearities in economics. Dynamic modeling and econometrics in economics and finance (vol. 29). Springer. https://doi.org/10.1007/978-3-030-70982-2_8

  • Taillardat, M., Mestre, O., Zamo, M., & Naveau, P. (2016). Calibrated ensemble forecasts using quantile regression forests and ensemble model output statistics. Monthly Weather Review, 144(6), 2375–2393.

    Article  Google Scholar 

  • Veblen, T. (1904). The theory of business enterprise. Charles Scribner’s Sons.

    Google Scholar 

  • Verhulst, P. (1847). Deuxième mémoire sur la loi d’accroissement de la population. Mémoires De L’académie Royale Des Sciences, Des Lettres Et Des Beaux-Arts De Belgique, 20, 1–32.

    Google Scholar 

  • Wang, K., Steyn-Ross, M. L., Steyn-Ross, D. A., Wilson, M. T., Sleigh, J. W., & Shiraishi, Y. (2014). Simulations of pattern dynamics for reaction-diffusion systems via simulink. BMC Systems Biology, 8(1), 1–21.

    Article  Google Scholar 

  • Wicksell, K. (1898). Geldzins und Güterpreise. Eine Untersuchung über die den Tauschwert des Geldes bestimmenden Ursachen. Gustav Fischer, Jena, as quoted in Laidler, D. (1991), The golden age of the quantity theory. Princeton University Press.

    Google Scholar 

  • Yoshida, H., & Asada, T. (2007). Dynamic analysis of policy lag in a Keynes-Goodwin model: Stability, instability, cycles and chaos. Journal of Economic Behavior & Organization, 62(3), 441–469.

    Article  Google Scholar 

  • Yoshida, H. (2021). From local bifurcations to global dynamics: Hopf systems from the applied perspective. In G. Orlando, A. N. Pisarchik, & R. Stoop (Eds.), Nonlinearities in economics. Dynamic modeling and econometrics in economics and finance (vol. 29). Springer. https://doi.org/10.1007/978-3-030-70982-2_5

  • Zimatore, G., Fetoni, A. R., Paludetti, G., Cavagnaro, M., Podda, M. V., & Troiani, D. (2011). Post-processing analysis of transient-evoked otoacoustic emissions to detect 4 khz-notch hearing impairment–a pilot study. Medical Science Monitor: International Medical Journal of Experimental and Clinical Research, 17(6), MT41.

    Google Scholar 

  • Zimatore, G., Garilli, G., Poscolieri, M., Rafanelli, C., Terenzio Gizzi, F., & Lazzari, M. (2017). The remarkable coherence between two Italian far away recording stations points to a role of acoustic emissions from crustal rocks for earthquake analysis. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(4), 043101.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Giuseppe Orlando .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Orlando, G., Sportelli, M. (2023). A Survey on Business Cycles: History, Theory and Empirical Findings. In: Kumar, V., Kuzmin, E., Zhang, WB., Lavrikova, Y. (eds) Consequences of Social Transformation for Economic Theory. EASET 2022. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-031-27785-6_2

Download citation

Publish with us

Policies and ethics