Skip to main content
SpringerLink
Log in

Profit-driven and demand-driven investment growth and fluctuations in different accumulation regimes

  • Regular Article
  • Published:
Journal of Evolutionary Economics Aims and scope Submit manuscript

Abstract

The main task of this work is to develop a model able to encompass, at the same time, Keynesian, demand-driven, and Marxian, profit-driven, determinants of fluctuations. Our starting point is the Goodwin model (1967), rephrased in discrete time and extended by means of a full coupled dynamics structure. The model adds the combined interaction of a demand effect, which resembles a rudimentary first approximation to an accelerator, and of a hysteresis effect in wage formation in turn affecting investments. Our model yields “business cycle” movements either by means of persistent oscillations, or chaotic motions. These two different dynamical paths accounting for the behaviour of the system are influenced by its (predominantly) profit-led or demand-led structures.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. 1 For an exhaustive discussion of dynamical systems in economics together with the formal differences between conservative and dissipative systems see Medio (1992) and Lorenz (1993).

  2. 2 Conversely, a dynamical system is structurally stable if for every sufficiently small perturbation of the vector field the perturbed system is topologically equivalent to the original system.

  3. 3 In order to capture discrete economic delays interesting contributions have proposed a continuous-time framework with delays: see Manfredi and Fanti (1999), Tebaldi and Colacchio (2007) and Yoshida and Asada (2007)

  4. 4 In fact, the labour market equation of the “Growth Cycle”, being expressed in real terms, is not exactly a Phillips curve which is a negative relation between changes in money wages and the unemployment rate. It lies in between the Phillips curve and the so called Wage curve, i.e. a relation between the levels of real wages and the unemployment rate (see Blanchflower and Oswald (1994)).

  5. 5 The parameter values are quite standard and close to empirics (see also Silverberg (1984) for a similar parametrization).

  6. 6 As compared to the original Goodwin model, we have introduced two slight modifications: a depreciation factor and an “expectation augmented” Phillips curve (where expectations are adaptive, i.e. the expected wage level equals the past experienced one). Nonetheless, the former brings a dampening factor (in fact the explosive behaviour is still present, and it would be even much more evident with a zero depreciation rate). The latter change does not alter the qualitative behaviour of the quasi-Phillips curve discussed in Goodwin (1967), and it takes fully on board lags in wage setting.

    Fig. 1
    figure 1

    Goodwin discrete time model. Parameters values: \(A=0.5, \alpha =0.02, \beta =0.01, \delta =0.02, \lambda =0.03, \bar {v}=0.95\)

    Full size image

  7. 7 In Kaldor and Mirrlees (1962) the investment function expressed in continuous time is I/Y=v(Y−W). The significant advantage of our formulation is that we explicitly separate the income distribution/Goodwinian component from the demand/Keynesian one.

  8. 8 Concerning the parameter choices in the Goodwin plus Keynes model, lacking direct empirical proxies for our parameters in the following we will choose values which are qualitatively illustrative of the different regimes.

  9. 9 Three of them have no economic meaning having at least a zero coordinate. However, they may play a role in the definition of the basins of attraction of the system (see Bischi et al. (1998)).

  10. 10 For a detailed exposition on the conditions under which local bifurcations emerge see e.g. Whitley (1983) and Lorenz (1993).

  11. 11 In particular, the emergence of a flip bifurcation implies the birth of a two period cycle around the (unstable) fixed point. Conversely, when the fixed point undergoes a Neimark-Sacker bifurcation one observes the birth of an invariant closed curve Γ around the stationary solution. In this case a trajectory that starts on Γ lies on Γ for any (forward) iteration and generates periodic or quasi-periodic time series of the variables of the system. Since one of the aims of the present paper is to show the possibility of the emergence of observable endogenous fluctuations, we concentrate on the cases in which flip and Neimark-Sacker bifurcations are supercritical, that is when they generate attractors.

  12. 12 The other parameter values are b=−0.92,c=−0.37,d=0.96,e=0.8.

    Fig. 2
    figure 2

    Two parameters a and f bifurcation diagram. Different colours stand for different dynamics. The direction of the arrow flags the transition from a “Victorian” to a “Keynesian” phase, possibly going trough a “Goodwinian” one. Legend. Red: steady state locally symptofically stable; white: quasi periodic or high-period cycles or chaotic motions; blue: 2-period cycles; yellow: 4-period cycles; black: unfeasible trajectories

    Full size image

  13. 13 The parameter setting we explore to capture the Goodwinian set-up is a=−0.3,b=−0.92,c=0,d=0.96,e=0.8

  14. 14 Lyapunov exponents are obtained in Matlab by dividing the parameter interval into 1000 equidistant values. We took an initial condition in the basin of attraction and, using the procedure described by Alligood et al. (1996) (page 199), in order to eliminate the transient we iterated each point 10,000 times, before averaging over the subsequent 10,000 iterations (equivalent results have been obtained using the software IDMC by Marji Lines and Alfredo Medio (https://code.google.com/p/idmc/)).

References

  • Alligood K, Sauer T, Yorke J (1996) Chaos: An Introduction to Dynamical Systems. Springer-Verlag, New York

    Google Scholar 

  • Arthur B, Durlanf S, Lane D (1997) (eds) The economy as an evolving complex system II. Addison. Wesley, Reading, Ma

  • Bhaduri A, Marglin S (1990) Unemployment and the real wage: the economic basis for contesting political ideologies. Camb J Econ 14:375–393

    Google Scholar 

  • Bischi G, Stefanini L, Gardini L (1998) Synchronization, intermittency and critical curves in duopoly games. Math Comput Simul 44:559–585

    Article  Google Scholar 

  • Blanchflower D, Oswald A (1994) The Wage Curve. MIT Press, Cambridge

    Google Scholar 

  • Boyer R (1988a) Formalizing growth regime. In: Dosi G, Freeman C, Nelson R, Silverberg G, Soete L (eds) Technical change and Economic Theory. Pinter Publisher, London

    Google Scholar 

  • Boyer R (1988b) Technical change and theory of regulation. In: Dosi G, Freeman C, Nelson R, Silverberg G, Soete L (eds) Technical change and Economic Theory. Pinter Publisher, London

    Google Scholar 

  • Canry N (2005) Wage-led regime, profit-led regime and cycles: a model. Econ Appl LVIII:143–163

    Google Scholar 

  • Desai M (1974) Growth cycles and inflation in a model of the class struggle. Journal of Economic Theory 6:527–545

    Article  Google Scholar 

  • Domar ED (1946) Capital expansion, rate of growth and employment. Econometrica 14:137–147

    Article  Google Scholar 

  • Dosi G, Freeman C, Nelson R, Silverberg G, Soete L (eds) (1988) Technical change and Economic Theory. Pinter Publisher, London

    Google Scholar 

  • Flaschel P (1984) Some stability properties of goodwin’s growth cycle. a critical elaboration. Zeitschrift für Nationalökonomie 44:63–69

    Article  Google Scholar 

  • Frisch R (1933) Propagation problems and impulse problems in dynamic economics. In: Economic Essays in Honor of Gustav Cassel. Allen and Unwin, London, pp 1–35

  • Goodwin R (1951) The nonlinear accelerator and the persistence of business cycles. Econometrica 19:1–17

    Article  Google Scholar 

  • Goodwin R (1967) A growth cycle. In: Feinstein CH (ed) Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge, pp 54–58

    Google Scholar 

  • Goodwin R (1989) Chaotic Economic Dynamics. Oxford University Press, Oxford

    Google Scholar 

  • Harrod RF (1939) An essay in dynamic theory. Econ J 49:14–33

    Article  Google Scholar 

  • Kaldor N (1940) A model of the trade cycle. Econ J 50:78–92

    Article  Google Scholar 

  • Kaldor N, Mirrlees J (1962) A new model of economic growth. Rev Econ Stud 29:174–192

    Article  Google Scholar 

  • Kalecki M (1935) A macrodynamic theory of business cycles. Econometrica 3:327–344

    Article  Google Scholar 

  • Kalecki M (1949) A new approach to the problem of business cycles. Review of economic studies 6:57–64

  • Kirman A (2011) Complex economics. Individual and collective rationality. Routledge, London

  • Kuh E (1967) A productivity theory of wage levels: an alternative to the phillips curve. Rev Econ Stud 34:333–360

    Article  Google Scholar 

  • Lordon F (1995) Cycles et chaos dans un modèle hétérodoxe de croissance endogène. Revue économique 46:1405–1432

    Google Scholar 

  • Lorenz HW (1993) Nonlinear Dynamical Economics and Chaotic Motion. Springer, Berlin Heidelberg

    Book  Google Scholar 

  • Louca F (2001) Infriguing pendula: founding metaphors in the analysis of economic fluctuations. Cambridge journal of economics 25:25–45

    Article  Google Scholar 

  • Manfredi P, Fanti L (1999) Cycles in continuous-time economic models (with applications to Goodwin’s and Solow’s models). Discussion Paper 2003/9, Dipartimento di Economia e Management (DEM), University of Pisa

  • Medio A (1979) Teoria nonlineare del ciclo economico. Il Mulino, Bologna

    Google Scholar 

  • Medio A (1992) Chaotic Dynamics: Theory and Applications to Economics. Cambridge University Press, Cambridge

    Google Scholar 

  • Napoletano M, Dosi G, Fagiolo G, Roventini A (2012) Wage formation, investment behavior and growth regimes: An agent-based analysis. Revue de l’OFCE 124:235–261

    Google Scholar 

  • Nicolis G, Prigogine I (1997) Self organization in non-equilibrium systems: from dissipative structure to order through fluctuations. Wiley and Sons, New York

  • Pasinetti L (1960) Cyclical fluctuations and economic growth. Oxf Econ Pap 12:215–241

    Google Scholar 

  • Pohjola M (1981) Stable, cyclic and chaotic growth: The dynamics of a discrete-time version of goodwin’s growth cycle. Zeitschrift für Nationalökonomie 41:27–38

    Article  Google Scholar 

  • Puu T, Sushko I (2006) Business Cycle Dynamics: Models and Tools. Springer, Berlin Heidelberg

    Book  Google Scholar 

  • Rosser B (1999) On the complexities of complex economic dynamics. J Ec Perspectives 13:196–192

  • Samuelson P (1939a) Interactions between the multiplier analysis and the principle of acceleration. Rev Econ Stat 21:75–78

    Article  Google Scholar 

  • Samuelson P (1939b) A synthesis of the principle of acceleration and the multiplier. J Polit Econ 47:786–797

    Article  Google Scholar 

  • Schumpeter J (1934) The Theory of Economic Development: An inquiry into Profits, Capital, Credit, Interest and the Business Cycle. Harvard University Press, Cambridge

    Google Scholar 

  • Silverberg G (1984) Embodied technical progress in a dynamic economic model: the self-organization paradigm. In: Goodwin R, Krüger M, Vercelli A (eds) Nonlinear Models of Fluctuating Growth. Springer, Berlin Heidelberg, pp 192–208

    Chapter  Google Scholar 

  • Silverberg G, Lehnert D (1994) Growth fluctuations in an evolutionary model of creative destruction. In: Silverberg G, Soete L (eds) The Economics of Growth and Technical Change: Technologies, Nations, Agents. Edward Elgar Publishing Ltd., Aldershot, pp 74–108

    Google Scholar 

  • Sordi S (1999) Economic models and the relevance of “chaotic regions”: An application to goodwin’s growth cycle model. Ann Oper Res 89:3–19

    Article  Google Scholar 

  • Tebaldi C, Colacchio G (2007) Chaotic behavior in a modified goodwin’s growth cycle model. In: Proceedings of the 25th International Conference of the System Dynamics Society and 50th Anniversary Celebration. System Dynamics Society

  • Velupillai K (1979) Some stability properties of goodwin’s growth cycle model. Zeitschrift für Nationalökonomie 39:245–257

    Article  Google Scholar 

  • Whitley D (1983) Discrete dynamical systems in dimensions one and two. Bull Lond Math Soc 15:177–217

    Article  Google Scholar 

  • Wolfstetter E (1982) Fiscal policy and the classical growth cycle. Zeitschrift für Nationalökonomie 42:375–393

    Article  Google Scholar 

  • Yoshida H, Asada T (2007) Dynamic analysis of policy lag in a keynes–goodwin model: Stability, instability, cycles and chaos. J Econ Behav Orga 62:441–469

    Article  Google Scholar 

Download references

Acknowledgments

We are grateful for helpful comments to several participants at the 8th International Conference on Nonlinear Economic Dynamics (NED), Siena, July 2013; the Workshop on Deterministic and Stochastic Dynamics in Economics and Finance, Scuola Normale Superiore, Pisa, December 2013; the 5th International Conference of the International Schumpeter Society (ISS), Jena, July 2014; and to two anonymous referees. The authors gratefully acknowledge the financial support of the Institute for New Economic Thinking (INET) grant INO12-00039, “INET Taskforce in Macroeconomic Efficiency and Stability”.

Author information

Authors and Affiliations

  1. Scuola Superiore Sant’ Anna, P isa, Italy

    Giovanni Dosi & Maria Enrica Virgillito

  2. University of Pisa, Pisa, Italy

    Mauro Sodini

Authors
  1. Giovanni Dosi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mauro Sodini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria Enrica Virgillito
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni Dosi.

Appendix A

Appendix A

Fig. 7
figure 7

“Classic” investment dynamics with path-dependent wages and price making firms. Parameters values: a=−0.9,b=−1.4,c=−4,d=1.3,e=0.98

Full size image
Fig. 8
figure 8

Multiple attractors.Parameters values: a=−1.5,b=−1.4,c=−6.7,d=1.6,e=1.1

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dosi, G., Sodini, M. & Virgillito, M.E. Profit-driven and demand-driven investment growth and fluctuations in different accumulation regimes. J Evol Econ 25, 707–728 (2015). https://doi.org/10.1007/s00191-015-0406-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00191-015-0406-8

Keywords

JEL Classification

Search

Navigation