Skip to main content
SpringerLink
Log in

Nonlinear monetary policy rules in a pure exchange overlapping generations model

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

Abstract

The dynamics of a pure exchange overlapping generations model with endogenous money growth rule is investigated. We consider a nonlinear monetary policy rule which, in each period, bounds the money growth rate so that money is determined by the deviation of the inflation rate from its target. More precisely, we introduce such a mechanism through a sigmoidal money adjustment mechanism characterized by the presence of two asymptotes that bound the money variation, and thus the dynamics. It is shown that, depending on the timing of the monetary policy and the degree of reaction of the Central Bank, the target equilibrium may be destabilized via different types of bifurcations. Multistability and coexistence of attractors may also occur and the study of the basins of attraction allows us to analyze the global dynamic properties of the economy under scrutiny. We find that active monetary policy rules may be relevant for their stabilizing properties, but they also may open the door to equilibrium cycles of any periodicity and even chaos.

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
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. 1Clarida and Gertler (1997) report empirical evidence about the strategy of leaning against the wind pursued by the Bundesbank during the eighties and nineties in the sense that it tightens monetary policy if inflation (and output) are rising.

  2. We recall that this specification of a sigmoid-shaped function can be also found in other (macro-) economic contexts such as Allen (1967), Goeree et al. (1998) and Naimzada and Pireddu (2015).

  3. See Bullard (1994) and Schönhofer (1999).

  4. Qualitatively represented in Fig. 4 with dashed curves.

  5. Since we consider the case in which the monetary equilibria are smaller than π a, the transcritical bifurcation of the autarkic steady state does not occur in our framework.

  6. 6See Medio and Lines (2001)

  7. It is indeed possible to prove a statement similar to Proposition 5 with analogous technique.

  8. We do not consider such an eventuality because it does not belong to the Samuelson case.

  9. In general, function g is invertible if \(\delta >\frac {2}{\pi ^{*}-\pi ^{a}}\) but, for the purpose of discussion, we distinguish the cases δ > 0 and δ < 0.

  10. From a speech given at College Foundation, October 27, 1998.

References

  • Agliari A (2006) Homoclinic connections and subcritical Neimark bifurcation in a duopoly model with adaptively adjusted productions. Chaos Soliton Fract 29:739–755

    Article  Google Scholar 

  • Allen RGD (1967) Macro-economic theory: a mathematical treatment. St. Martin’s Press, New York; Macmillan, London

  • Andersson M, Hoffman B (2009) Gauging the effectiveness of quantitative forward guidance: evidence from the inflation targeters. ECB Working Paper No. 1098

  • Arthur WB (1994) Increasing returns and path dependence in the economy. University of Michigan Press

  • Benhabib J, Schmitt-Grohé S, Uribe M (2001a) Monetary policy and multiple equilibria. Am Econ Rev 91:167–186

  • Benhabib J, Schmitt-Grohé S, Uribe M (2001b) The perils of Taylor rules. J Econ Theory 96:40–69

  • Benhabib J, Schmitt-Grohé S, Uribe M (2002) Chaotic interest-rate rules. Am Econ Rev 92:72–78

    Article  Google Scholar 

  • Bernanke B S, Woodford M (1997) Inflation forecasts and monetary policy. J Money Credit Bank 29:653–684

    Article  Google Scholar 

  • Bischi G I, Marimon R (2001) Global stability of inflation target policies with adaptive agents. Macroecon Dyn 5:148–179

    Article  Google Scholar 

  • Bullard J (1994) Learning equilibria. J Econ Theory 64:468–485

    Article  Google Scholar 

  • Bullard J (2012) Inflation targeting in the USA. Speech at the Union League Club of Chicago, February 6, 2012

  • Carlstrom CT, Fuerst TS (2000) Forward-looking versus backward-looking taylor rules (no. 0009). Federal Reserve Bank of Cleveland

  • Castro V (2011) Can central banks’ monetary policy be described by a linear (augmented) Taylor rule or by a nonlinear rule? J Financ Stability 7:228–246

    Article  Google Scholar 

  • Chen H J, Li M C (2009) Habit formation and chaotic dynamics in an n-dimensional cash-in-advance economy. Nonlinear Dynam 58:49–62

    Article  Google Scholar 

  • Clarida RH, Gertler M (1997) How the bundesbank conducts monetary policy. In: Reducing inflation: motivation and strategy. University of Chicago Press, pp 363–412

  • Clarida R, Galí J, Gertler M (1999) The science of monetary policy: a new keynesian perspective. J Econ Lit 37:1661–1707

    Article  Google Scholar 

  • Creel J, Hubert P (2015) Has inflation targeting changed the conduct of monetary policy? Macroecon Dyn 19:1–21

    Article  Google Scholar 

  • Debreu G (1974) Excess-demand functions. J Math Econ 1:15–21

    Article  Google Scholar 

  • Dolado J, Pedrero R M D, Ruge-Murcia F J (2004) Nonlinear monetary policy rules: some new evidence for the US. Stud Nonlinear Dyn E 8:2

    Google Scholar 

  • Dolado J, Mara-Dolores R, Naveira M (2005) Are monetary-policy reaction functions asymmetric? The role of nonlinearity in the Phillips curve. Eur Econ Rev 49:485–503

    Article  Google Scholar 

  • Du J G, Huang T, Sheng Z (2009) Analysis of decision-making in economic chaos control. Nonlinear Anal-Real 10:2493–2501

    Article  Google Scholar 

  • Fanti L, Gori L, Sodini M (2013) Complex dynamics in an OLG model of neoclassical growth with endogenous retirement age and public pensions. Nonlinear Anal-Real 14:829–841

    Article  Google Scholar 

  • Gardini L, Hommes C H, Tramontana F, De Vilder R (2009) Forward and backward dynamics in implicitly defined overlapping generations models. J Econ Behav Organ 71:110–129

    Article  Google Scholar 

  • Goeree JK, Hommes C, Weddepohl C (1998) Stability and complex dynamics in a discrete tâtonnement model. J Econ Behav Org 33:395–410

    Article  Google Scholar 

  • Grandmont J M (1985) On endogenous competitive business cycles. Econometrica 53:995–1045

    Article  Google Scholar 

  • Holyst J A, Hagel T, Haag G, Weidlich W (1996) How to control a chaotic economy? J Evol Econ 6:31–42

    Article  Google Scholar 

  • Hommes CH (2013) Behavioral rationality and heterogeneous expectations in complex economic systems. Cambridge University Press

  • Ingram W T (2002) Invariant sets and inverse limits. Topol Appl 126:393–408

    Article  Google Scholar 

  • Kopel M (1997) Improving the performance of an economic system: controlling chaos. J Evol Econ 7:269–289

    Article  Google Scholar 

  • Mantel R (1974) On the characterization of aggregate excess-demand. J Econ Theory 7:348–353

    Article  Google Scholar 

  • Martin C, Milas C (2004) Modelling monetary policy: inflation targeting in practice. Economica 71:209–221

    Article  Google Scholar 

  • Medio A, Lines M (2001) Nonlinear dynamics: a primer. Cambridge University Press

  • Medio A, Raines B (2007) Backward dynamics in economics. The inverse limit approach. J Econ Dyn Control 31:1633–1671

    Article  Google Scholar 

  • Mira C, Gardini L, Barugola A, Cathala JC (1996) Chaotic dynamics in two-dimensional noninvertible maps. World Scientific, Singapore

  • Naimzada A, Tramontana F (2009) Controlling chaos through local knowledge. Chaos, Solitons Fractals 42:2439–2449

    Article  Google Scholar 

  • Naimzada A, Pireddu M (2015) Introducing a price variation limiter mechanism into a behavioral financial market model. Chaos 25:083112

    Article  Google Scholar 

  • Naimzada A, Sacco P, Sodini M (2013) Wealth-sensitive positional competition as a source of dynamic complexity in OLG models. Nonlinear Anal-Real 14:1–13

    Article  Google Scholar 

  • Schönhofer M (1999) Chaotic learning equilibria. J Econ Theory 89:1–20

    Article  Google Scholar 

  • Sheng Z, Du J, Mei Q, Huang T (2013) New analyses of duopoly game with output lower limiters. Abstr Appl Anal 406743:2013

    Google Scholar 

  • Shinbrot T, Ott E, Grebogi C, Yorke J A (1990) Using chaos to direct trajectories to targets. Phys Rev Lett 65(26):3215

    Article  Google Scholar 

  • Sonnenschein H (1973) Do Walras’ identity and continuity characterize the class of community excess demand functions? J Econ Theory 6:345–354

    Article  Google Scholar 

  • Surico P (2007) The Fed’s monetary policy rule and US inflation: the case of asymmetric preferences. J Econ Dyn Control 31:305–324

    Article  Google Scholar 

  • Taylor JB (2007) Monetary policy rules. University of Chicago Press

  • Taylor M P, Davradakis E (2006) Interest rate setting and inflation targeting: evidence of a nonlinear Taylor rule for the United Kingdom. Stud Nonlinear Dyn E 10

  • Tillmann P (2011) Parameter uncertainty and nonlinear monetary policy rules. Macroecon Dyn 15:184–200

    Article  Google Scholar 

  • Tuinstra J (2003) Beliefs equilibria in an overlapping generations model. J E Behav Organ 50:145–164

    Article  Google Scholar 

  • Von Hagen J (1999) Money growth targeting by the Bundesbank. J Monetary Econ 43:681–701

    Article  Google Scholar 

  • Yao H X, Wu C Y, Jiang D P, Ding J (2008) Chaos control in an investment model with straight-line stabilization method. Nonlinear Anal-Real 9:651–662

    Article  Google Scholar 

  • Walsh C E (2009) Inflation targeting: what have we learned? Int Financ 12:195–233

    Article  Google Scholar 

  • Wieland C, Westerhoff F (2005) Exchange rate dynamics, Central Bank intervention and chaos control methods. J Econ Behav Org 58:117–132

    Article  Google Scholar 

Download references

Acknowledgements

Authors thank two anonymous referees for valuable comments and remarks. Authors also thank all the participants to the 9th International Conference on Nonlinear Economic Dynamics (NED2015) held at Chuo University, Tokyo, Japan, on June 25–27 2015 for useful suggestions. The usual caveats apply.

The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Economics and Social Sciences, Catholic University, Via Emilia Parmense 84, 29100, Piacenza, Italy

    Anna Agliari & Nicolò Pecora

  2. Department of Economics, Quantitative Methods and Management, University of Milano - Bicocca, Piazza Ateneo Nuovo 1, 20126, Milano, Italy

    Ahmad Naimzada

Authors
  1. Anna Agliari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmad Naimzada
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicolò Pecora
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicolò Pecora.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agliari, A., Naimzada, A. & Pecora, N. Nonlinear monetary policy rules in a pure exchange overlapping generations model. J Evol Econ 27, 1181–1203 (2017). https://doi.org/10.1007/s00191-017-0522-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00191-017-0522-8

Keywords

JEL Classification

Search

Navigation