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Testing explosive bubbles with time-varying volatility: The case of Spanish public debt

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  • Esteve, Vicente
  • Prats, María A.

Abstract

In this paper the dynamics of the Spanish public debt-GDP ratio is analysed during the period 1850–2021. We use recent procedures to test for explosive bubbles in the presence under time-varying volatility (Harvey et al., 2016; Harvey et al., 2019, 2020; Kurozumi et al., 2022) in order to test the explosive behavior of Spanish public debt over this long period. We extend previous analysis of Esteve and Prats (2022) where assume constant unconditional volatility in the underlying error process.

Suggested Citation

  • Esteve, Vicente & Prats, María A., 2023. "Testing explosive bubbles with time-varying volatility: The case of Spanish public debt," Finance Research Letters, Elsevier, vol. 51(C).
    • Handle: RePEc:eee:finlet:v:51:y:2023:i:c:s1544612322005098
    DOI: 10.1016/j.frl.2022.103330
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    2. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1228-1276, October.
    3. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    4. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert & Taylor, A.M. Robert, 2016. "Tests for explosive financial bubbles in the presence of non-stationary volatility," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 548-574.
    5. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    6. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1079-1134, November.
    7. Phillips, Peter C.B. & Shi, Shu-Ping, 2018. "Financial Bubble Implosion And Reverse Regression," Econometric Theory, Cambridge University Press, vol. 34(4), pages 705-753, August.
    8. Vicente Esteve & María A. Prats, 2022. "Testing for multiple bubbles: historical episodes on the sustainability of public debt in Spain, 1850–2020," Applied Economic Analysis, Emerald Group Publishing Limited, vol. 31(91), pages 1-18, March.
    9. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    10. D’Erasmo, P. & Mendoza, E.G. & Zhang, J., 2016. "What is a Sustainable Public Debt?," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 2493-2597, Elsevier.
    11. Giuseppe Cavaliere & A. M. Robert Taylor, 2008. "Time‐Transformed Unit Root Tests for Models with Non‐Stationary Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 300-330, March.
    12. David E. Rapach & Jack K. Strauss & Mark E. Wohar, 2008. "Chapter 10 Forecasting Stock Return Volatility in the Presence of Structural Breaks," Frontiers of Economics and Globalization, in: Forecasting in the Presence of Structural Breaks and Model Uncertainty, pages 381-416, Emerald Group Publishing Limited.
    13. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1079-1134, November.
    14. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(1), pages 43-71, February.
    15. Peter C. B. Phillips & Shuping Shi, 2019. "Detecting Financial Collapse and Ballooning Sovereign Risk," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(6), pages 1336-1361, December.
    16. David I. Harvey & Stephen J. Leybourne & Yang Zu, 2019. "Testing explosive bubbles with time-varying volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1131-1151, November.
    17. Beqiraj, Elton & Fedeli, Silvia & Forte, Francesco, 2018. "Public debt sustainability: An empirical study on OECD countries," Journal of Macroeconomics, Elsevier, vol. 58(C), pages 238-248.
    18. Harvey, David I. & Leybourne, Stephen J. & Zu, Yang, 2020. "Sign-Based Unit Root Tests For Explosive Financial Bubbles In The Presence Of Deterministically Time-Varying Volatility," Econometric Theory, Cambridge University Press, vol. 36(1), pages 122-169, February.
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    1. Xuanling Yang & Dong Li & Ting Zhang, 2024. "A simple stochastic nonlinear AR model with application to bubble," Papers 2401.07038, arXiv.org.

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    More about this item

    Keywords

    Public debt; Rational bubble; Explosive autoregression; Time-varying volatility; Right-tailed unit root testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory
    • H62 - Public Economics - - National Budget, Deficit, and Debt - - - Deficit; Surplus
    • H63 - Public Economics - - National Budget, Deficit, and Debt - - - Debt; Debt Management; Sovereign Debt

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