Monetary policy and PID control

  • Raymond J. Hawkins
  • Jeffrey K. Speakes
  • Dan E. Hamilton
Regular Article


We show that many currently popular monetary policy rules fall structurally within a class of robust industrial control known as proportional-integral-differential, or PID, control. From this identification we propose a general class of PID-based monetary policy rules that include as limiting cases the original Taylor rule as well as lagged and forward-looking extensions of thereof. The effectiveness of parsimonious extensions of the Taylor rule are consistent with the well-known effectiveness and parsimony of PID control. We find that for the same reason encountered in other PID control applications—noisy data—most monetary policy rules fall in the proportional-integral subset of PID control known as PI control. We estimate both PID and PI monetary policy rules using the historical analysis approach of Taylor and compare the performance of our PI rule to other policy rules using a recently-developed macroeconomic-model comparison methodology. A key feature of PID control is its remarkable effectiveness for systems where the equations of motion are not known. Thus, PID-based rules both link monetary policy with a tradition of practical control in the absence of known dynamical equations and provide baseline rules for monetary policy in the face of macroeconomic model uncertainty.


Monetary-policy rules Model uncertainty Macroeconomic models PID control 



We thank Stuart Bennett for his illuminating insights on the history of PID control. We thank Volker Wieland, Sebastian Schmidt and Elena Afanasyeva for very helpful conversations concerning the MMB software. Finally, we thank Masanao Aoki for his pioneering and inspiring work bridging control theory and practice in engineering and economics.


  1. Adolfson M, Laséen S, Lindé J, Villani M (2007) Bayesian estimation of an open economy DSGE model with incomplete pass-through. J Int Econ 72:481–511CrossRefGoogle Scholar
  2. Altig DE, Christiano LJ, Eichenbaum M, Lindé J (2005) Firm-specific capital, nominal rigidities and the business cycle. CERP Discussion Papers 4858, Centre for Economic Policy ResearchGoogle Scholar
  3. Aoki M (1967) Optimization of stochastic systems: topics in discrete-time systems, mathematics in science and engineering, vol 32. Academic Press, New York, NYGoogle Scholar
  4. Aoki M (1996) New approaches to macroeconomic modeling: evolutionary stochastic dynamics, multiple equilibria, and externalities as field effects. Cambridge University Press, New York, NYCrossRefGoogle Scholar
  5. Aoki M (2000) Modeling aggregate fluctuations in economics: stochastic views of interacting agents. Cambridge University Press, New York, NYGoogle Scholar
  6. Aoki M, Yoshikawa H (2007) Reconstructing macroeconomics: a perspective from statistical physics and combinatorial stochastic processes. Japan-US Center UFJ Bank Monographs on International Financial Markets, Cambridge University Press, New York, NYGoogle Scholar
  7. Åström KJ, Murray RM (2008) Feedback systems: an introduction for scientists and engineers. Princeton University Press, Princeton, NJGoogle Scholar
  8. Batini N, Haldane A (1999) Forward-looking rules for monetary policy. In: Taylor (1999b), pp 157–192Google Scholar
  9. Bennett S (1993) A history of control engineering 1930–1955. Peter Peregrinus Ltd., StevenageCrossRefGoogle Scholar
  10. Carabenciov I, Ermolaev I, Freedman C, Juillard M, Kamenik O, Laxton D (2008) A small quarterly projection model of the US economy. IMF Working Paper 08/278, International Monetary FundGoogle Scholar
  11. Christensen I, Dib A (2008) The financial accelerator in an estimated New Keynesian model. Rev Econ Dyn 11:155–178CrossRefGoogle Scholar
  12. Christiano LJ, Eichenbaum M, Evans CL (2005) Nominal rigidities and the dynamic effects of a shock to monetary policy. J Polit Econ 113:1–45CrossRefGoogle Scholar
  13. Christoffel K, Kuester K (2008) Resuscitating the wage channel in models with unemployment fluctuations. J Monet Econ 55:865–887CrossRefGoogle Scholar
  14. Christoffel K, Kuester K, Linzert T (2009) The role of labor markets for euro area monetary policy. Eur Econ Rev 53:908–936CrossRefGoogle Scholar
  15. Clarida R, Galí J, Gertler M (1998) Monetary policy rules in practice: some international evidence. Eur Econ Rev 42:1033–1067CrossRefGoogle Scholar
  16. Clarida R, Galí J, Gertler M (1999) The science of monetary policy: a New Keynesian perspective. J Econ Lit 37:1661–1701CrossRefGoogle Scholar
  17. Coenen G, Wieland V (2005) A small estimated euro area model with rational expectations and nominal rigidities. Eur Econ Rev 49:1081–1104CrossRefGoogle Scholar
  18. Colander D (ed) (2006) Post Walrasian macroeconomics: beyond the dynamic stochastic general equilibrium model. Cambridge University Press, CambridgeGoogle Scholar
  19. de Castro MR, Gouvea SN, Minella A, dos Santos RC, Souza-Sobrinho NF (2011) SAMBA: stochastic analytical model with a Bayesian approach. Banco Central do Brasil Working Paper Series 239, Banco Central do BrasilGoogle Scholar
  20. De Graeve F (2008) The external finance premium and the macroeconomy: US post-WWII evidence. J Econ Dyn Control 32:3415–3440Google Scholar
  21. Fuhrer JC, Moore G (1995) Inflation persistence. Q J Econ 110:127–159CrossRefGoogle Scholar
  22. Funke M, Paetz M, Pytlarczyk E (2011) Stock market wealth effects in an estimated DSGE model for Hong Kong. Econ Model 28:316–334CrossRefGoogle Scholar
  23. Galí J, Monacelli T (2005) Monetary policy and exchange rate volatility in a small open economy. Rev Econ Stud 72:707–734CrossRefGoogle Scholar
  24. Gelain P (2010) The external finance premium in the euro area: a dynamic stochastic general equilibrium analysis. N Am J Econ Financ 21:49–71CrossRefGoogle Scholar
  25. Gerdesmeier D, Roffia B (2005) Empirical estimates of reaction functions for the euro area. Swiss J Econ Stat 140:37–66Google Scholar
  26. Iacoviello M (2005) Housing prices, borrowing constraints, and monetary policy in the business cycle. Am Econ Rev 95:739–764CrossRefGoogle Scholar
  27. Ireland PN (2004) Money’s role in the monetary business cycle. J Money Credit Bank 36:969–983CrossRefGoogle Scholar
  28. Ireland PN (2011) A New Keynesian perspective on the great recession. J Money Credit Bank 43:31–54Google Scholar
  29. Juillard M (1996) Dynare: a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm. CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAPGoogle Scholar
  30. Juillard M (2001) Dynare: a program for the simulation of rational expectation models. Computing in Economics and Finance 2001 213, Society for Computational EconomicsGoogle Scholar
  31. Laxton D, Pesenti P (2003) Monetary rules for small, open, emerging economies. J Monet Econ 50: 1109–1146Google Scholar
  32. Levin A, Wieland V, Williams JC (1999) Robustness of simple monetary policy rules under model uncertainty. In: Taylor (1999b), pp 263–318Google Scholar
  33. Levin A, Wieland V, Williams JC (2003) The performance of forecast-based monetary policy rules under model uncertainty. Am Econ Rev 93:622–645CrossRefGoogle Scholar
  34. Lubik TA, Schorfheide F (2007) Do central banks respond to exchange rate movements? A structural investigation. J Monet Econ 54:1069–1087CrossRefGoogle Scholar
  35. Maxwell JC (1867–1868) On governors. Proc R Soc 16:270–283Google Scholar
  36. McCallum B, Nelson E (1999) Performance of operational policy rules in an estimated semiclassical structural model. In: Taylor (1999b), pp 15–56Google Scholar
  37. Medina JP, Soto C (2007) The Chilean business cycles through the lens of a stochastic general equilibrium model. Working Paper Series of the Central Bank of Chile 457, Banco Central de ChileGoogle Scholar
  38. Orphanides A (2001) Monetary policy rules based on real-time data. Am Econ Rev 91:964–985CrossRefGoogle Scholar
  39. Orphanides A, Wieland V (1998) Price stability and monetary policy effectiveness when nominal interest rates are bounded at zero. Finance and Economics Discussion Series 98–35, Board of Governors of the Federal Reserve SystemGoogle Scholar
  40. Rabanal P (2007) Does inflation increase after a monetary policy tightening? Answers based on an estimated DSGE model. J Econ Dyn Control 31:906–937CrossRefGoogle Scholar
  41. Ratto M, Roeger W, in ’t Veld J (2009) QUEST III: an estimated open-economy DSGE model of the euro area with fiscal and monetary policy. Econ Model 26:222–233Google Scholar
  42. Rotemberg JJ, Woodford M (1997) An optimization-based economic framework for the evaluation of monetary policy. NBER Macroecon Annu 12:297–346CrossRefGoogle Scholar
  43. Smets F, Wouters R (2007) Shocks and frictions in US business cycles: a Bayesian DSGE approach. Am Econ Rev 97:586–606CrossRefGoogle Scholar
  44. Taylor JB (1993a) Discretion versus policy rules in practice. Carnegie-Rochester Conf Ser Public Policy 39:195–214CrossRefGoogle Scholar
  45. Taylor JB (1993b) Macroeconomic policy in a world economy: from econometric design to practical operation. W. W. Norton & Co, New YorkGoogle Scholar
  46. Taylor JB (1999a) A historical analysis of monetary policy. In: Taylor (1999b), pp 319–348Google Scholar
  47. Taylor JB (ed) (1999b) Monetary policy rules, NBER—business cycles series, vol 31. University of Chicago Press, Chicago, ILGoogle Scholar
  48. Taylor JB, Wieland V (2012) Surprising comparative properties of monetary models: results from a new model database. Rev Econ Stat 94(3):800–816CrossRefGoogle Scholar
  49. Taylor JB, Williams JC (2011) Simple and robust rules for monetary policy. In: Friedman BM, Woodford M (eds) Monetary economics, handbooks in economics, vol 3B. North-Holland, Amsterdam, pp 829–859Google Scholar
  50. Wicksell K (1898) Geldzins und Güterpreise. G. Fischer, Jena, reprint translation by R. F. Kahn as Interest and Prices published by R. & R. Clark, EdinburghGoogle Scholar
  51. Wicksell K (1907) The influence of the rate of interest on prices. Econ J 17(66):213–220CrossRefGoogle Scholar
  52. Wieland V, Cwik T, Müller GJ, Schmidt S, Wolters M (2011) A new comparative approach to macroeconomic modeling and policy analysis. Working paper, Goethe University of Frankfurt, Frankfurt am Main, Germany., September 2011 (revised edition)
  53. Woodford M (2003) Interest and prices: foundations of a theory of monetary policy. Princeton University Press, Princeton, NJGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Raymond J. Hawkins
    • 1
  • Jeffrey K. Speakes
    • 2
  • Dan E. Hamilton
    • 2
  1. 1.The College of Optical SciencesThe University of ArizonaTucsonUSA
  2. 2.School of ManagementCalifornia Lutheran UniversityThousand OaksUSA

Personalised recommendations