IDEAS home Printed from https://ideas.repec.org/a/psc/journl/v12y2020i4p413-429.html

Identification and Estimation of Initial Conditions in Non-Minimal State-Space Models

Author

Listed:
  • Victor Bystrov

    (University of Lodz)

Abstract

In this paper the identification problem is considered for initial conditions in a non-minimal state-space model that includes interpretable state variables generated by non-stationary stochastic processes. In order to solve the identification problem, structural restrictions are imposed on initial conditions in a state-space model with redundant state variables. The corresponding restricted maximum likelihood estimator of initial conditions is derived. The restricted estimator of initial conditions can be used in order to compute uniquely identified realizations of interpretable latent variables. The identification problem is illustrated analytically using a simple structural economic model.

Suggested Citation

  • Victor Bystrov, 2020. "Identification and Estimation of Initial Conditions in Non-Minimal State-Space Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(4), pages 413-429, December.
    • Handle: RePEc:psc:journl:v:12:y:2020:i:4:p:413-429
    as

    Download full text from publisher

    File URL: http://cejeme.org/publishedarticles/2020-52-26-637420207602331425-3747.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nathan S. Balke & Mark E. Wohar, 2002. "Low-Frequency Movements in Stock Prices: A State-Space Decomposition," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 649-667, November.
    2. repec:rim:rimwps:18-29 is not listed on IDEAS
    3. 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.
    4. Thomas Laubach, 2001. "Measuring The NAIRU: Evidence From Seven Economies," The Review of Economics and Statistics, MIT Press, vol. 83(2), pages 218-231, May.
    5. Robert J. Gordon, 1997. "The Time-Varying NAIRU and Its Implications for Economic Policy," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 11-32, Winter.
    6. Marc K. Francke & Siem Jan Koopman & Aart F. De Vos, 2010. "Likelihood functions for state space models with diffuse initial conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 407-414, November.
    7. Holston, Kathryn & Laubach, Thomas & Williams, John C., 2017. "Measuring the natural rate of interest: International trends and determinants," Journal of International Economics, Elsevier, vol. 108(S1), pages 59-75.
    8. Ellen R. McGrattan, 2010. "Measurement with minimal theory," Quarterly Review, Federal Reserve Bank of Minneapolis, issue July, pages 2-13.
    9. Kent D. Wall, 1987. "Identification Theory For Varying Coefficient Regression Models1," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 359-371, May.
    10. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    11. 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.
    12. Robert J. Gordon, 2013. "The Phillips Curve is Alive and Well: Inflation and the NAIRU During the Slow Recovery," NBER Working Papers 19390, National Bureau of Economic Research, Inc.
    13. Burmeister, Edwin & Wall, Kent D & Hamilton, James D, 1986. "Estimation of Unobserved Expected Monthly Inflation Using Kalman Filtering," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(2), pages 147-160, April.
    14. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    15. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    16. Douglas O. Staiger & James H. Stock & Mark W. Watson, 1997. "How Precise Are Estimates of the Natural Rate of Unemployment?," NBER Chapters, in: Reducing Inflation: Motivation and Strategy, pages 195-246, National Bureau of Economic Research, Inc.
    17. Thomas Laubach & John C. Williams, 2015. "Measuring the natural rate of interest redux," Working Paper Series 2015-16, Federal Reserve Bank of San Francisco.
    18. Kent D. Wall & David S. Stoffer, 2002. "A State space approach to bootstrapping conditional forecasts in arma models," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 733-751, November.
    Full references (including those not matched with items on IDEAS)

    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. Victor Bystrov, 2018. "Measuring the Natural Rates of Interest in Germany and Italy," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 10(4), pages 333-353, December.
    2. Marie-Elisabeth de la Serve & Matthieu Lemoine, 2011. "Measuring the NAIRU: a complementary approach," Working papers 342, Banque de France.
    3. Brand, Claus & Goy, Gavin W & Lemke, Wolfgang, 2020. "Natural rate chimera and bond pricing reality," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224546, Verein für Socialpolitik / German Economic Association.
    4. Arabinda Basistha & Richard Startz, 2004. "Measuring the NAIRU with Reduced Uncertainty: A Multiple Indicator-Common Component Approach," Working Papers UWEC-2004-22, University of Washington, Department of Economics.
    5. Rodríguez, Gabriel, 2010. "Using A Forward-Looking Phillips Curve to Estimate the Output Gap in Peru," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 6(01-2), pages 1-13, April.
    6. Basistha, Arabinda & Nelson, Charles R., 2007. "New measures of the output gap based on the forward-looking new Keynesian Phillips curve," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 498-511, March.
    7. Ladislav Wintr & Paolo Guarda & Abdelaziz Rouabah, 2005. "Estimating the natural interest rate for the euro area and Luxembourg," BCL working papers 15, Central Bank of Luxembourg.
    8. Del Negro, Marco & Giannone, Domenico & Giannoni, Marc P. & Tambalotti, Andrea, 2019. "Global trends in interest rates," Journal of International Economics, Elsevier, vol. 118(C), pages 248-262.
    9. Claus Brand & Gavin Goy & Wolfgang Lemke, 2026. "Estimating the Natural Rate of Interest in a Macro-Finance Yield Curve Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 44(3), pages 797-809, July.
    10. Buncic, Daniel, 2020. "Econometric issues with Laubach and Williams’ estimates of the natural rate of interest," Working Paper Series 397, Sveriges Riksbank (Central Bank of Sweden).
    11. repec:spo:wpmain:info:hdl:2441/1904 is not listed on IDEAS
    12. Cui, Wei & Härdle, Wolfgang Karl & Wang, Weining, 2015. "Estimation of NAIRU with inflation expectation data," SFB 649 Discussion Papers 2015-010, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Maximilian Grimm & Òscar Jordà & Moritz Schularick & Alan M. Taylor, 2023. "Loose Monetary Policy and Financial Instability," NBER Working Papers 30958, National Bureau of Economic Research, Inc.
    14. Rebecca L Driver & Jennifer V Greenslade & Richard G Pierse, 2003. "The role of expectations in estimates of the NAIRU in the United States and the United Kingdom," Bank of England Staff Working Paper series 180, Bank of England.
    15. Arabinda Basistha, 2009. "Hours per capita and productivity: evidence from correlated unobserved components models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 187-206.
    16. Ray C. Fair, 2005. "Natural Concepts in Macroeconomics," Cowles Foundation Discussion Papers 1525, Cowles Foundation for Research in Economics, Yale University.
    17. Anthony J Evans, 2020. "The natural rate of interest: An estimate for the United Kingdom," Economic Affairs, Wiley Blackwell, vol. 40(1), pages 24-35, February.
    18. Castillo, Luis & Florián, David, 2019. "Measuring the output gap, potential output growth and natural interest rate from a semi-structural dynamic model for Peru," Working Papers 2019-012, Banco Central de Reserva del Perú.
    19. Omar Kaykhusraw, 2025. "Longer‐run equilibrium interest rates: evidence from the United Kingdom," Economica, London School of Economics and Political Science, vol. 92(366), pages 457-482, April.
    20. Eric Heyer & Frédéric Reynès & Henri Sterdyniak, 2004. "Observable and unobservable variables in the theory of the equilibrium rate of unemployment, a comparison between France and the United States," Sciences Po Economics Publications (main) hal-01027420, HAL.
    21. Heyer, Eric & Reynes, Frederic & Sterdyniak, Henri, 2007. "Structural and reduced approaches of the equilibrium rate of unemployment, a comparison between France and the United States," Economic Modelling, Elsevier, vol. 24(1), pages 42-65, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:psc:journl:v:12:y:2020:i:4:p:413-429. 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: Damian Jelito (email available below). General contact details of provider: http://cejeme.org/ .

    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.