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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.
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    14. Knut Are Aastveit & Jamie L. Cross & Francesco Furlanetto & Herman K. Van Dijk, 2024. "Taylor Rules with Endogenous Regimes," Working Papers No 04/2024, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
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    21. Divino, Jose Angelo & Haraguchi, Carlos, 2024. "(Mis)Alignment between observed and expected monetary policy: The case of Brazil," International Economics, Elsevier, vol. 178(C).
    22. 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.
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    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

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