IDEAS home Printed from https://ideas.repec.org/p/fip/fedfwp/2018-11.html
   My bibliography  Save this paper

Taylor Rule Estimation by OLS

Author

Listed:
  • Carlos Carvalho
  • Fernanda Nechio
  • Tiago Tristao

Abstract

Ordinary Least Squares (OLS) estimation of monetary policy rules produces potentially inconsistent estimates of policy parameters. The reason is that central banks react to variables, such as inflation and the output gap, that are endogenous to monetary policy shocks. Endogeneity implies a correlation between regressors and the error term – hence, an asymptotic bias. In principle, Instrumental Variables (IV) estimation can solve this endogeneity problem. In practice, however, IV estimation poses challenges, as the validity of potential instruments depends on various unobserved features of the economic environment. We argue in favor of OLS estimation of monetary policy rules. To that end, we show analytically in the three-equation New Keynesian model that the asymptotic OLS bias is proportional to the fraction of the variance of regressors due to monetary policy shocks. Using Monte Carlo simulations, we then show that this relationship also holds in a quantitative model of the U.S. economy. Since monetary policy shocks explain only a small fraction of the variance of regressors typically included in monetary policy rules, the endogeneity bias tends to be small. For realistic sample sizes, OLS outperforms IV. Finally, we estimate a standard Taylor rule on different subsamples of U.S. data and find that OLS and IV estimates are quite similar.

Suggested Citation

  • Carlos Carvalho & Fernanda Nechio & Tiago Tristao, 2021. "Taylor Rule Estimation by OLS," Working Paper Series 2018-11, Federal Reserve Bank of San Francisco.
    • Handle: RePEc:fip:fedfwp:2018-11
    DOI: 10.24148/wp2018-11
    Note: The first version of this paper was September 6, 2018.
    as

    Download full text from publisher

    File URL: https://www.frbsf.org/economic-research/files/wp2018-11.pdf
    File Function: Full text - article PDF
    Download Restriction: no
    File URL: https://libkey.io/10.24148/wp2018-11?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Christina D. Romer & David H. Romer, 2004. "A New Measure of Monetary Shocks: Derivation and Implications," American Economic Review, American Economic Association, vol. 94(4), pages 1055-1084, September.
    2. Silvana Tenreyro & Gregory Thwaites, 2016. "Pushing on a String: US Monetary Policy Is Less Powerful in Recessions," American Economic Journal: Macroeconomics, American Economic Association, vol. 8(4), pages 43-74, October.
    3. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
    4. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(1), pages 147-180.
    5. John H. Cochrane, 2011. "Determinacy and Identification with Taylor Rules," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 565-615.
    6. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    7. Olivier Coibion & Yuriy Gorodnichenko, 2011. "Monetary Policy, Trend Inflation, and the Great Moderation: An Alternative Interpretation," American Economic Review, American Economic Association, vol. 101(1), pages 341-370, February.
    8. John B. Taylor, 1999. "A Historical Analysis of Monetary Policy Rules," NBER Chapters, in: Monetary Policy Rules, pages 319-348, National Bureau of Economic Research, Inc.
    9. Eichenbaum, Martin, 1992. "'Interpreting the macroeconomic time series facts: The effects of monetary policy' : by Christopher Sims," European Economic Review, Elsevier, vol. 36(5), pages 1001-1011, June.
    10. Olivier Coibion & Yuriy Gorodnichenko, 2012. "Why Are Target Interest Rate Changes So Persistent?," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(4), pages 126-162, October.
    11. Sims, Christopher A., 1992. "Interpreting the macroeconomic time series facts : The effects of monetary policy," European Economic Review, Elsevier, vol. 36(5), pages 975-1000, June.
    12. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    13. Eric M. Leeper & Christopher A. Sims & Tao Zha, 1996. "What Does Monetary Policy Do?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 27(2), pages 1-78.
    14. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    15. Orphanides, Athanasios, 2004. "Monetary Policy Rules, Macroeconomic Stability, and Inflation: A View from the Trenches," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(2), pages 151-175, April.
    16. Rudebusch, Glenn D., 2002. "Term structure evidence on interest rate smoothing and monetary policy inertia," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1161-1187, September.
    17. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    18. Jean Boivin & Marc P. Giannoni, 2006. "Has Monetary Policy Become More Effective?," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 445-462, August.
    19. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    20. Baumeister, Christiane & Liu, Philip & Mumtaz, Haroon, 2013. "Changes in the effects of monetary policy on disaggregate price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 543-560.
    21. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1.
    22. Mavroeidis, Sophocles, 2005. "Identification Issues in Forward-Looking Models Estimated by GMM, with an Application to the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 421-448, June.
    23. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    24. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    25. Efrem Castelnuovo & Paolo Surico, 2010. "Monetary Policy, Inflation Expectations and The Price Puzzle," Economic Journal, Royal Economic Society, vol. 120(549), pages 1262-1283, December.
    26. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    27. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hasan Engin Duran & Pawe³ Gajewski, 2023. "State-level Taylor rule and monetary policy stress," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 18(1), pages 89-120, March.
    2. Gokan, Yoichi & Turnovsky, Stephen J., 2023. "Taylor rules: Consequences for wealth and income inequality," Journal of Macroeconomics, Elsevier, vol. 77(C).
    3. Hack, Lukas & Istrefi, Klodiana & Meier, Matthias, 2023. "Identification of Systematic Monetary Policy," CEPR Discussion Papers 17999, C.E.P.R. Discussion Papers.
    4. Foroni, Claudia & Furlanetto, Francesco, 2022. "Explaining Deviations from Okun's Law," CEPR Discussion Papers 17369, C.E.P.R. Discussion Papers.
    5. Knut Are Aastveit & Jamie Cross & Francesco Furlanetto & Herman K. Van Dijk, 2024. "Taylor Rules with Endogenous Regimes," Tinbergen Institute Discussion Papers 24-030/III, Tinbergen Institute.
    6. Alovokpinhou, Sedjro Aaron & Malikane, Christopher, 2024. "The effect of output and the real exchange rate on equity price dynamics," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).
    7. Economou, Fotini & Panagopoulos, Yannis, 2023. "Assessing the credit creation process under the Basel III framework: Some evidence from the Eurozone," Finance Research Letters, Elsevier, vol. 51(C).
    8. Thang Ngoc Doan & Dong Phu Do & Dat Van Luong, 2023. "Monetary stance and favorableness of the monetary policy in the media: the case of Vietnam," Journal of Asian Business and Economic Studies, Emerald Group Publishing Limited, vol. 31(2), pages 111-123, August.
    9. Filardo, Andrew & Hubert, Paul & Rungcharoenkitkul, Phurichai, 2022. "Monetary policy reaction function and the financial cycle," Journal of Banking & Finance, Elsevier, vol. 142(C).
    10. Pang, Ke & Shiamptanis, Christos, 2024. "Is the Bank of Canada concerned about inflation or the state of the economy?," Journal of International Money and Finance, Elsevier, vol. 140(C).
    11. Yoosoon Chang & Steven N. Durlauf & Bo Hu & Joon Y. Park, 2024. "Accounting for Individual-Specific Heterogeneity in Intergenerational Income Mobility," Working Papers No 03/2024, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    12. Ferri, Piero & Cristini, Annalisa & Tramontana, Fabio, 2023. "Meta-models of the Phillips curve and income distribution," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 215-232.
    13. Marwil J. Dávila-Fernández & Germana Giombini & Edgar J. Sánchez-Carrera, 2023. "Climateflation and monetary policy in an environmental OLG growth model," Department of Economics University of Siena 905, Department of Economics, University of Siena.
    14. Divino, Jose Angelo & Haraguchi, Carlos, 2024. "(Mis)Alignment between observed and expected monetary policy: The case of Brazil," International Economics, Elsevier, vol. 178(C).
    15. Christina Anderl & Guglielmo Maria Caporale, 2024. "Time-varying parameters in monetary policy rules: a GMM approach," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 51(9), pages 148-176, January.
    16. Donato Masciandaro, 2023. "How Elastic and Predictable Money Should Be: Flexible Monetary Policy Rules from the Great Moderation to the New Normal Times (1993-2023)," BAFFI CAREFIN Working Papers 23196, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    17. Bordo, Michael & Istrefi, Klodiana, 2023. "Perceived FOMC: The making of hawks, doves and swingers," Journal of Monetary Economics, Elsevier, vol. 136(C), pages 125-143.
    18. Kwok Ping Tsang & Zichao Yang, 2023. "Agree to Disagree: Measuring Hidden Dissent in FOMC Meetings," Papers 2308.10131, arXiv.org, revised Nov 2024.
    19. Xiekui Zhang & Peiyao Liu & Hongfei Zhu, 2022. "The Impact of Industrial Intelligence on Energy Intensity: Evidence from China," Sustainability, MDPI, vol. 14(12), pages 1-16, June.
    20. Alex Hsu & Francisco Palomino & Liang Qian, 2023. "Gone with the Vol: A Decline in Asset Return Predictability During the Great Moderation," Management Science, INFORMS, vol. 69(5), pages 3025-3047, May.
    21. Makram El-Shagi & Kiril Tochkov, 2024. "Regional Effects of Monetary Policy in China," CFDS Discussion Paper Series 2024/1, Center for Financial Development and Stability at Henan University, Kaifeng, Henan, China.
    22. Hüpper, Florian & Kempa, Bernd, 2023. "Inflation targeting and inflation communication of the Federal Reserve: Words and deeds," Journal of Macroeconomics, Elsevier, vol. 75(C).
    23. Curi, Claudia & Murgia, Lucia Milena, 2023. "Forecast Targeting and Financial Stability: Evidence from the European Central Bank and Bank of England," Finance Research Letters, Elsevier, vol. 51(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ramey, V.A., 2016. "Macroeconomic Shocks and Their Propagation," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 71-162, Elsevier.
    2. Olivier Coibion, 2012. "Are the Effects of Monetary Policy Shocks Big or Small?," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 1-32, April.
    3. Julio Carrillo & Patrick Fève & Julien Matheron, 2007. "Monetary Policy Inertia or Persistent Shocks: A DSGE Analysis," International Journal of Central Banking, International Journal of Central Banking, vol. 3(2), pages 1-38, June.
    4. Hanson, Michael S., 2006. "Varying monetary policy regimes: A vector autoregressive investigation," Journal of Economics and Business, Elsevier, vol. 58(5-6), pages 407-427.
    5. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2013. "Identification-robust analysis of DSGE and structural macroeconomic models," Journal of Monetary Economics, Elsevier, vol. 60(3), pages 340-350.
    6. Marek Rusnak & Tomas Havranek & Roman Horvath, 2013. "How to Solve the Price Puzzle? A Meta-Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(1), pages 37-70, February.
    7. Pao‐Lin Tien & Tara M. Sinclair & Edward N. Gamber, 2021. "Do Fed Forecast Errors Matter?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(3), pages 686-712, June.
    8. James Cloyne & Patrick Hürtgen, 2016. "The Macroeconomic Effects of Monetary Policy: A New Measure for the United Kingdom," American Economic Journal: Macroeconomics, American Economic Association, vol. 8(4), pages 75-102, October.
    9. Carrillo, Julio A., 2012. "How well does sticky information explain the dynamics of inflation, output, and real wages?," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 830-850.
    10. Efrem Castelnuovo, 2012. "Testing the Structural Interpretation of the Price Puzzle with a Cost-Channel Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(3), pages 425-452, June.
    11. Yasuo Hirose & Takushi Kurozumi & Willem Van Zandweghe, 2020. "Monetary Policy and Macroeconomic Stability Revisited," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 255-274, July.
    12. Castelnuovo, Efrem & Pellegrino, Giovanni, 2018. "Uncertainty-dependent effects of monetary policy shocks: A new-Keynesian interpretation," Journal of Economic Dynamics and Control, Elsevier, vol. 93(C), pages 277-296.
    13. Champagne, Julien & Sekkel, Rodrigo, 2018. "Changes in monetary regimes and the identification of monetary policy shocks: Narrative evidence from Canada," Journal of Monetary Economics, Elsevier, vol. 99(C), pages 72-87.
    14. Cucciniello, Maria Chiara & Deleidi, Matteo & Levrero, Enrico Sergio, 2022. "The cost channel of monetary policy: The case of the United States in the period 1959–2018," Structural Change and Economic Dynamics, Elsevier, vol. 61(C), pages 409-433.
    15. Leonardo Melosi, 2017. "Signalling Effects of Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 853-884.
    16. repec:zbw:bofrdp:2009_020 is not listed on IDEAS
    17. Lakdawala, Aeimit, 2016. "Changes in Federal Reserve preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 124-143.
    18. Matthew Doyle & Jean-Paul Lam, 2010. "Is the New Keynesian Explanation of the Great Dis-Inflation Consistent with the Cross Country Data?," Working Papers 1010, University of Waterloo, Department of Economics, revised Oct 2010.
    19. Efrem Castelnuovo, 2012. "Testing the Structural Interpretation of the Price Puzzle with a Cost-Channel Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(3), pages 425-452, June.
    20. Jean Boivin & Marc P. Giannoni, 2006. "Has Monetary Policy Become More Effective?," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 445-462, August.
    21. Adnan Haider & Musleh ud Din & Ejaz Ghani, 2012. "Monetary Policy, Informality and Business Cycle Fluctuations in a Developing Economy Vulnerable to External Shocks," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 51(4), pages 609-681.

    More about this item

    Keywords

    Taylor Rule; Ordinary Least Squares (OLS); GMM; endogeneity; bias; weak instruments; New Keynesian models;
    All these keywords.

    JEL classification:

    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedfwp:2018-11. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Federal Reserve Bank of San Francisco Research Library (email available below). General contact details of provider: https://edirc.repec.org/data/frbsfus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.