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Optimal Control and Filtering in Linear Forward-looking Economies: A Toolkit

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  • Lippi, Francesco
  • Gerali, Andrea

Abstract

We provide algorithms to solve a linear-quadratic optimal control problem with commitment. By extending to the case of imperfect information a procedure outlined in Ljungqvist and Sargent (2002), we make the results of Svensson and Woodford (2000) easy to implement. We provide a Mat-lab package that solves this class of models and analyses their properties using simulations, impulse response functions and other techniques, with both commitment and discretion. A monetary policy application, based on the ?new-Keynesian? model of Clarida, Galí and Gertler (1999), is used to illustrate how the toolkit can be used.

Suggested Citation

  • Lippi, Francesco & Gerali, Andrea, 2003. "Optimal Control and Filtering in Linear Forward-looking Economies: A Toolkit," CEPR Discussion Papers 3706, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:3706
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    References listed on IDEAS

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    1. Orphanides, Athanasios, 2003. "The quest for prosperity without inflation," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 633-663, April.
    2. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    3. Athanasios Orphanides, 2001. "Monetary Policy Rules Based on Real-Time Data," American Economic Review, American Economic Association, vol. 91(4), pages 964-985, September.
    4. Svensson, Lars E. O. & Woodford, Michael, 2003. "Indicator variables for optimal policy," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 691-720, April.
    5. Michael Woodford, 1999. "Optimal Monetary Policy Inertia," Manchester School, University of Manchester, vol. 67(s1), pages 1-35.
    6. Michael Woodford, 1999. "Optimal monetary policy inertia," Proceedings, Federal Reserve Bank of San Francisco.
    7. Lars E. O. Svensson & Michael Woodford, 2003. "Optimal Policy with Partial Information in a Forward-Looking Model: Certainty-Equivalence Redux," NBER Working Papers 9430, National Bureau of Economic Research, Inc.
    8. Ehrmann, Michael & Smets, Frank, 2003. "Uncertain potential output: implications for monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1611-1638, July.
    9. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    10. Currie, David & Levine, Paul, 1986. "Time inconsistency and optimal policies in deterministic and stochastic worlds," Journal of Economic Dynamics and Control, Elsevier, vol. 10(1-2), pages 191-199, June.
    11. Backus, David & Driffill, John, 1986. "The Consistency of Optimal Policy in Stochastic Rational Expectations Models," CEPR Discussion Papers 124, C.E.P.R. Discussion Papers.
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    Citations

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    Cited by:

    1. Carl E. Walsh, 2003. "Implications of a changing economic structure for the strategy of monetary policy," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 297-348.
    2. Eugenio Gaiotti & Alessandro Secchi, 2004. "Is there a cost channel of monetary policy transmission? An investigation into the pricing behaviour of 2,000 firms," Temi di discussione (Economic working papers) 525, Bank of Italy, Economic Research and International Relations Area.
    3. Andrés González Gómez & Lavan Mahadeva & Diego Rodríguez & Luis Eduardo Rojas, 2009. "Monetary Policy Forecasting in a DSGE Model with Data that is Uncertain, Unbalanced and About the Future," Borradores de Economia 559, Banco de la Republica de Colombia.
    4. Eugenio Gaiotti, 2004. "Pitfalls of monetary policy under incomplete information: imprecise indicators and real indeterminacy," Temi di discussione (Economic working papers) 488, Bank of Italy, Economic Research and International Relations Area.
    5. Cukierman, Alex & Lippi, Francesco, 2005. "Endogenous monetary policy with unobserved potential output," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1951-1983, November.
    6. Lavan Mahadeva & Alex Muscatelli, 2005. "National Accounts Revisions and Output Gap Estimates in a Model of Monetary Policy with Data Uncertainty," Discussion Papers 14, Monetary Policy Committee Unit, Bank of England.
    7. Juha Kilponen, 2004. "Robust expectations and uncertain models – A robust control approach with application to the New Keynesian economy," GE, Growth, Math methods 0404004, University Library of Munich, Germany.
    8. Francesco Lippi, 2003. "Monetary policy with unobservedpotential output," BIS Papers chapters, in: Bank for International Settlements (ed.), Monetary policy in a changing environment, volume 19, pages 258-275, Bank for International Settlements.
    9. repec:zbw:bofrdp:2007_033 is not listed on IDEAS
    10. Lippi, Francesco & Neri, Stefano, 2003. "Information Variables for Monetary Policy in a Small Structural Model of the Euro Area," CEPR Discussion Papers 4125, C.E.P.R. Discussion Papers.
    11. Martha R. López & Juan David Prada, 2010. "Optimal monetary policy and asset prices: the case of Colombia," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, vol. 28(61), pages 167-197, August.
    12. Neri, Stefano & Ropele, Tiziano, 2019. "Disinflationary shocks and inflation target uncertainty," Economics Letters, Elsevier, vol. 181(C), pages 77-80.
    13. Simona Delle Chiaie, 2007. "Monetary Policy and Potential Output Uncertainty: A Quantitative Assessment," CEIS Research Paper 94, Tor Vergata University, CEIS.
    14. Lam Jean-Paul, 2010. "The Importance of Commitment in the New Keynesian Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 10(1), pages 1-23, November.
    15. Kilponen, Juha & Milne, Alistair, 2007. "The lending channel under optimal choice of monetary policy," Bank of Finland Research Discussion Papers 33/2007, Bank of Finland.
    16. Pawel Kowal, 2005. "Solving Models with Imperfect and Asymmetric Information," Macroeconomics 0505025, University Library of Munich, Germany.
    17. Lippi, Francesco & Neri, Stefano, 2007. "Information variables for monetary policy in an estimated structural model of the euro area," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1256-1270, May.
    18. Alessandro Piergallini, 2006. "Real Balance Effects and Monetary Policy," Economic Inquiry, Western Economic Association International, vol. 44(3), pages 497-511, July.
    19. Richard Mash, 2003. "A Note on Simple MSV Solution Methods for Rational Expectations Models of Monetary Policy," Economics Series Working Papers 173, University of Oxford, Department of Economics.
    20. Kilponen, Juha & Milne, Alistair, 2007. "The lending channel under optimal choice of monetary policy," Research Discussion Papers 33/2007, Bank of Finland.
    21. Piergallini, Alessandro, 2004. "Real Balance Effects, Determinacy and Optimal Monetary Policy," MPRA Paper 59832, University Library of Munich, Germany.

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    More about this item

    Keywords

    Optimal control; Filtering; Commitment;
    All these keywords.

    JEL classification:

    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

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