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A Simple Method for Estimating Multiple Natural Rates Simultaneously: Estimation of Japan's Potential Output and Natural Foreign Exchange Rate

Author

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  • Koichiro Kamada

    (Faculty of Business and Commerce, Keio University)

Abstract

We propose a simple method for estimating multiple natural rates in a system of simultaneous equations. Our estimators of natural rates are closely related to the HP filter and accessible by many practitioners. As an application, Japan’s potential output and natural foreign exchange rate are estimated. It is shown that Japan’s potential output has been growing, but the natural foreign exchange rate has experienced stepwise downward shifts since the beginning of the 21st century. While Japan suffered the long-lasting stagnation, emerging markets, particularly China, achieved tremendous economic growth. The declines in the natural foreign exchange rate indicate Japan’s lost competitiveness in the world economy clearly.

Suggested Citation

  • Koichiro Kamada, 2026. "A Simple Method for Estimating Multiple Natural Rates Simultaneously: Estimation of Japan's Potential Output and Natural Foreign Exchange Rate," Keio-IES Discussion Paper Series DP2026-005, Institute for Economics Studies, Keio University.
    • Handle: RePEc:keo:dpaper:dp2026-005
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    References listed on IDEAS

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    1. Laurence Ball & N. Gregory Mankiw, 2002. "The NAIRU in Theory and Practice," Journal of Economic Perspectives, American Economic Association, vol. 16(4), pages 115-136, Fall.
    2. Kuttner, Kenneth N, 1994. "Estimating Potential Output as a Latent Variable," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 361-368, July.
    3. Roberts, John M, 1995. "New Keynesian Economics and the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 975-984, November.
    4. Hirose, Yasuo & Kamada, Koichiro, 2003. "A New Technique for Simultaneous Estimation of Potential Output and the Phillips Curve," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 21(2), pages 93-112, August.
    5. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • F14 - International Economics - - Trade - - - Empirical Studies of Trade
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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