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Unobservable no more: estimating the natural rate of interest under flat IS and Phillips curves

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Abstract

We show that the Laubach and Williams (2003) model and its variants in Holston, Laubach and Williams (2017, 2023) cannot estimate the natural rate with finite precision when either the IS curve or the Phillips curve are flat. To solve this unobservability, we propose a simple augmented model with a mean-reverting interest rate gap that considerably narrows the natural rate’s confidence bands in those empirically relevant situations. We also assess the ability of the corporate risk premium and the share of working age population to explain movements in the natural rate, but they generate filtered estimates that fluctuate too much.

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  • Gabriele Fiorentini & Alessandro Galesi & Rodrigo Peña & Gabriel Pérez Quirós & Enrique Sentana, 2026. "Unobservable no more: estimating the natural rate of interest under flat IS and Phillips curves," Working Papers wp2026_2603, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2026_2603
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    1. Mesonnier, Jean-Stephane & Renne, Jean-Paul, 2007. "A time-varying "natural" rate of interest for the euro area," European Economic Review, Elsevier, vol. 51(7), pages 1768-1784, October.
    2. Hamilton, James D., 1986. "A standard error for the estimated state vector of a state-space model," Journal of Econometrics, Elsevier, vol. 33(3), pages 387-397, December.
    3. Lukasz Rachel & Thomas D. Smith, 2017. "Are Low Real Interest Rates Here to Stay?," International Journal of Central Banking, International Journal of Central Banking, vol. 13(3), pages 1-42, September.
    4. Kurt F. Lewis & Francisco Vazquez‐Grande, 2019. "Measuring the natural rate of interest: A note on transitory shocks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 425-436, April.
    5. Julien Garnier & Bjørn-Roger Wilhelmsen, 2009. "The natural rate of interest and the output gap in the euro area: a joint estimation," Empirical Economics, Springer, vol. 36(2), pages 297-319, May.
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    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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