Journal of Evolutionary Economics

, Volume 27, Issue 5, pp 1181–1203 | Cite as

Nonlinear monetary policy rules in a pure exchange overlapping generations model

Regular Article
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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.

Keywords

OLG model Nonlinear dynamics Monetary policy Stability Global bifurcations 

JEL Classification

E32 E52 C62 

Notes

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.

References

  1. Agliari A (2006) Homoclinic connections and subcritical Neimark bifurcation in a duopoly model with adaptively adjusted productions. Chaos Soliton Fract 29:739–755CrossRefGoogle Scholar
  2. Allen RGD (1967) Macro-economic theory: a mathematical treatment. St. Martin’s Press, New York; Macmillan, LondonGoogle Scholar
  3. Andersson M, Hoffman B (2009) Gauging the effectiveness of quantitative forward guidance: evidence from the inflation targeters. ECB Working Paper No. 1098Google Scholar
  4. Arthur WB (1994) Increasing returns and path dependence in the economy. University of Michigan PressGoogle Scholar
  5. Benhabib J, Schmitt-Grohé S, Uribe M (2001a) Monetary policy and multiple equilibria. Am Econ Rev 91:167–186Google Scholar
  6. Benhabib J, Schmitt-Grohé S, Uribe M (2001b) The perils of Taylor rules. J Econ Theory 96:40–69Google Scholar
  7. Benhabib J, Schmitt-Grohé S, Uribe M (2002) Chaotic interest-rate rules. Am Econ Rev 92:72–78CrossRefGoogle Scholar
  8. Bernanke B S, Woodford M (1997) Inflation forecasts and monetary policy. J Money Credit Bank 29:653–684CrossRefGoogle Scholar
  9. Bischi G I, Marimon R (2001) Global stability of inflation target policies with adaptive agents. Macroecon Dyn 5:148–179CrossRefGoogle Scholar
  10. Bullard J (1994) Learning equilibria. J Econ Theory 64:468–485CrossRefGoogle Scholar
  11. Bullard J (2012) Inflation targeting in the USA. Speech at the Union League Club of Chicago, February 6, 2012Google Scholar
  12. Carlstrom CT, Fuerst TS (2000) Forward-looking versus backward-looking taylor rules (no. 0009). Federal Reserve Bank of ClevelandGoogle Scholar
  13. Castro V (2011) Can central banks’ monetary policy be described by a linear (augmented) Taylor rule or by a nonlinear rule? J Financ Stability 7:228–246CrossRefGoogle Scholar
  14. Chen H J, Li M C (2009) Habit formation and chaotic dynamics in an n-dimensional cash-in-advance economy. Nonlinear Dynam 58:49–62CrossRefGoogle Scholar
  15. Clarida RH, Gertler M (1997) How the bundesbank conducts monetary policy. In: Reducing inflation: motivation and strategy. University of Chicago Press, pp 363–412Google Scholar
  16. Clarida R, Galí J, Gertler M (1999) The science of monetary policy: a new keynesian perspective. J Econ Lit 37:1661–1707CrossRefGoogle Scholar
  17. Creel J, Hubert P (2015) Has inflation targeting changed the conduct of monetary policy? Macroecon Dyn 19:1–21CrossRefGoogle Scholar
  18. Debreu G (1974) Excess-demand functions. J Math Econ 1:15–21CrossRefGoogle Scholar
  19. 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 8:2Google Scholar
  20. 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 49:485–503CrossRefGoogle Scholar
  21. Du J G, Huang T, Sheng Z (2009) Analysis of decision-making in economic chaos control. Nonlinear Anal-Real 10:2493–2501CrossRefGoogle Scholar
  22. 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 14:829–841CrossRefGoogle Scholar
  23. 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 71:110–129CrossRefGoogle Scholar
  24. Goeree JK, Hommes C, Weddepohl C (1998) Stability and complex dynamics in a discrete tâtonnement model. J Econ Behav Org 33:395–410CrossRefGoogle Scholar
  25. Grandmont J M (1985) On endogenous competitive business cycles. Econometrica 53:995–1045CrossRefGoogle Scholar
  26. Holyst J A, Hagel T, Haag G, Weidlich W (1996) How to control a chaotic economy? J Evol Econ 6:31–42CrossRefGoogle Scholar
  27. Hommes CH (2013) Behavioral rationality and heterogeneous expectations in complex economic systems. Cambridge University PressGoogle Scholar
  28. Ingram W T (2002) Invariant sets and inverse limits. Topol Appl 126:393–408CrossRefGoogle Scholar
  29. Kopel M (1997) Improving the performance of an economic system: controlling chaos. J Evol Econ 7:269–289CrossRefGoogle Scholar
  30. Mantel R (1974) On the characterization of aggregate excess-demand. J Econ Theory 7:348–353CrossRefGoogle Scholar
  31. Martin C, Milas C (2004) Modelling monetary policy: inflation targeting in practice. Economica 71:209–221CrossRefGoogle Scholar
  32. Medio A, Lines M (2001) Nonlinear dynamics: a primer. Cambridge University PressGoogle Scholar
  33. Medio A, Raines B (2007) Backward dynamics in economics. The inverse limit approach. J Econ Dyn Control 31:1633–1671CrossRefGoogle Scholar
  34. Mira C, Gardini L, Barugola A, Cathala JC (1996) Chaotic dynamics in two-dimensional noninvertible maps. World Scientific, SingaporeGoogle Scholar
  35. Naimzada A, Tramontana F (2009) Controlling chaos through local knowledge. Chaos, Solitons Fractals 42:2439–2449CrossRefGoogle Scholar
  36. Naimzada A, Pireddu M (2015) Introducing a price variation limiter mechanism into a behavioral financial market model. Chaos 25:083112CrossRefGoogle Scholar
  37. Naimzada A, Sacco P, Sodini M (2013) Wealth-sensitive positional competition as a source of dynamic complexity in OLG models. Nonlinear Anal-Real 14:1–13CrossRefGoogle Scholar
  38. Schönhofer M (1999) Chaotic learning equilibria. J Econ Theory 89:1–20CrossRefGoogle Scholar
  39. Sheng Z, Du J, Mei Q, Huang T (2013) New analyses of duopoly game with output lower limiters. Abstr Appl Anal 406743:2013Google Scholar
  40. Shinbrot T, Ott E, Grebogi C, Yorke J A (1990) Using chaos to direct trajectories to targets. Phys Rev Lett 65(26):3215CrossRefGoogle Scholar
  41. Sonnenschein H (1973) Do Walras’ identity and continuity characterize the class of community excess demand functions? J Econ Theory 6:345–354CrossRefGoogle Scholar
  42. Surico P (2007) The Fed’s monetary policy rule and US inflation: the case of asymmetric preferences. J Econ Dyn Control 31:305–324CrossRefGoogle Scholar
  43. Taylor JB (2007) Monetary policy rules. University of Chicago PressGoogle Scholar
  44. 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 10Google Scholar
  45. Tillmann P (2011) Parameter uncertainty and nonlinear monetary policy rules. Macroecon Dyn 15:184–200CrossRefGoogle Scholar
  46. Tuinstra J (2003) Beliefs equilibria in an overlapping generations model. J E Behav Organ 50:145–164CrossRefGoogle Scholar
  47. Von Hagen J (1999) Money growth targeting by the Bundesbank. J Monetary Econ 43:681–701CrossRefGoogle Scholar
  48. 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 9:651–662CrossRefGoogle Scholar
  49. Walsh C E (2009) Inflation targeting: what have we learned? Int Financ 12:195–233CrossRefGoogle Scholar
  50. Wieland C, Westerhoff F (2005) Exchange rate dynamics, Central Bank intervention and chaos control methods. J Econ Behav Org 58:117–132CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Economics and Social SciencesCatholic UniversityPiacenzaItaly
  2. 2.Department of Economics, Quantitative Methods and ManagementUniversity of Milano - BicoccaMilanoItaly

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