Victor Bystrov

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The results of the study presented in this paper demonstrate that a structural model of the natural interest rate, which is consistent with the standard assumptions of the natural rate theory, admits an interpretable, observationally equivalent representation in which a redefined, ’unnatural’ equilibrium rate is different from the natural rate in the original model. The alternative representation was obtained by an invertible transformation implemented in the minimal state-space form of the natural-rate model. The identification theory for state-space models is used in the paper to prove the observational equivalence of these two representations. In the alternative representation, the equilibrium interest rate fails to meet the assumption of the natural rate theory, because it depends on past demand shocks. The alternative model, being observationally equivalent, has different implications for the conduct of monetary policy. The problem of observational equivalence arises in relation to natural-rate models because of the inherent unobservability of the natural interest rate; a potential solution to this problem could be the augmentation of the information set which is used to identify and estimate the natural rate.


natural rate of interest, state-space model, observational equivalence


C32, C51, E43


Beyer, R. C. M., Wieland V. (2017), Instability, imprecision and inconsistent use of the equilibrium real interest rate estimates, CEPR Discussion Papers, DP11927.

Constancio, V. (2016), The challenge of low real interest rates for monetary policy, Lecture at the Macroeconomic Symposium at Utrecht School of Economics,

Durbin J., Koopman S. J., (2012), Time Series Analysis by State-Space Methods: Second Edition, Oxford University Press, Oxford.

Fiorentini, G., Galesi, A., Pérez-Quirós, G., Sentana E. (2018), The rise and fall of the natural interest rate, Banco de Espana Working Papers, 1822.

Fries, S., Mésonnier, J.-S., Mouabbi, S., Renne, J.-P. (2018), National natural rates of interest and the single monetary policy in the euro area, Journal of Applied Econometrics, 33(6), 763–769.

Garnier, J., Wilhelmsen, B.-R. (2009), The natural rate of interest and the output gap in the Euro Area: a joint estimation, Empirical Economics, 36, 297–319.

Grossman, V., Martínez-García, E., Wynne, M., Zhang, R. (2019), Ties that bind: estimating the natural rate of interest for small open economies, Globalization and Monetary Policy Institute Working Papers, 359.

Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press, Princeton NJ.

Hamilton, J. D, Harris, E. S., Hatzius, J., West, K. D. (2016), The equilibrium real funds rate: past, present and future, IMF Economic Review, 64(4), 660–707.

Hendry, D. F. (1995), Dynamic Econometrics, Oxford University Press, Oxford.

Holston, K., Laubach, T., Williams, J. C. (2017), Measuring the natural rate of interest: international trends and determinants, Journal of International Economics, 108(S1), 59–75.

Kiley, M. T. (2019), The global equilibrium real interest rate: concepts, estimates, and challenges, Finance and Economics Discussion Series, 2019-076, Board of Governors of the Federal Reserve System, Washington.

Laubach, T., Williams, J. C. (2003), Measuring the natural rate of interest, Review of Economics and Statistics, 85(4), 1063–1070.

Laubach, T., Williams, J. C. (2016.), Measuring the natural rate of interest redux, Business Economics, 51(2), 57–67.

Lewis, K. F., Vazquez-Grande, F. (2017), Measuring the natural rate of interest: alternative specifications, Finance and Economic Discussion Series, 2017–059, Board of Governors of the Federal Reserve System, Washington.

Mésonnier, J.-S., Renne, J.-P. (2007), A time-varying ’natural’ rate of interest for the euro area, European Economic Review, 51, 1768–1784.

Preston, A. J. (1978), Concepts of structure and model identifiability for econometric systems, [in] Bergstrom, A. R., Catt, A. J. L., Peston, M. H., Silverstone, B. D. J. (eds.), Stability and Inflation: A Volume of Essays to Honour the Memory of A.W.H. Phillips, 275–97, Wiley, New York.

Rothenberg, T. J. (1971), Identification in Parametric Models, Econometrica, 39(3), 577–591.

Sargent, T. J. (1976), The observational equivalence of natural and unnatural rate theories of macroeconomics, Journal of Political Economy, 84(3), 631–640.

Stock, J. H. (1994), Unit roots, structural breaks and trends, [in] R.F. Engle, R. F., McFadden, D. L. (eds.), Handbook of Econometrics, 4, Elsevier Science B.V., 2739–2841.

Stock, J. H., Watson, M. W. (1998), Median unbiased estimation of coefficient variance in a timevarying parameter model, Journal of American Statistical Association, 93(441), 349–357.

Taylor, J. B., Wieland, V. (2016), Finding the equilibrium real interest rate in a fog of policy deviations, Business Economics, 51(3), 147–154.

Wall, K. D. (1987), Identification theory for varying coefficient regression models, Journal of Time Series Analysis, 8(3), 359–371.

Wicksell, K. (1898), Interest and Prices, Sentry Press, New York.

Williams, J. C. (2003), The natural rate of interest, FRBSF Economic Letters, 2003–32.

Wynne, M. A., Zhang, R. (2018a), Estimating the natural rate of interest in an open economy, Empirical Economics 55(3), 1291–1318.

Wynne, M. A. and Zhang, R. (2018b), Measuring the world natural rate of interest, Economic Inquiry 56(1), 530–544.

Yellen, J. (2015), Normalizing Monetary Policy: Prospects and Perspectives, Speech at the ’New Normal Monetary Policy’, Conference,

Youla, D. C. (1966), The synthesis of linear dynamical systems from prescribed weighting patterns, SIAM Journal of Applied Mathematics, 14(3), 527–549.

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