IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v41y2014icp281-288.html
   My bibliography  Save this article

Steady state distributions for models of locally explosive regimes: Existence and econometric implications

Author

Listed:
  • Knight, John
  • Satchell, Stephen
  • Srivastava, Nandini

Abstract

The purpose of this paper is to examine the properties of locally explosive regimes in the light of steady state results for threshold auto-regressive (TAR) models recently derived by Knight and Satchell (2011) [Journal of Time Series Econometrics, 3]. We study the conditions under which a steady state distribution of deviations of asset prices from fair value can be obtained using our simple model based on our particular definition of a bubble, noting that it is applicable to locally explosive regimes. After deriving general results, the analysis is further extended by considering the steady state distribution in three cases of a normally distributed error process, a non normally (exponentially) distributed steady-state process and a switching random walk with a fairly general iid error process. Then, the issues related to unit root testing for the presence of bubbles using standard econometric procedures are examined. Our results shed light on the ubiquitous finding of no bubbles in the econometric literature.

Suggested Citation

  • Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.
    • Handle: RePEc:eee:ecmode:v:41:y:2014:i:c:p:281-288
    DOI: 10.1016/j.econmod.2014.03.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999314001114
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2014.03.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Flavin, Marjorie A, 1983. "Excess Volatility in the Financial Markets: A Reassessment of the Empirical Evidence," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 929-956, December.
    2. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    3. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
    4. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    5. Azariadis, Costas & Smith, Bruce, 1998. "Financial Intermediation and Regime Switching in Business Cycles," American Economic Review, American Economic Association, vol. 88(3), pages 516-536, June.
    6. Simon van Norden & Huntley Schaller, 2002. "Fads or bubbles?," Empirical Economics, Springer, vol. 27(2), pages 335-362.
    7. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    8. 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.
    9. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
    10. Jordi Galí, 2011. "Monetary policy and rational asset price bubbles," Economics Working Papers 1293, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2013.
    11. William Branch & George Evans, 2011. "Monetary policy and heterogeneous expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 365-393, June.
    12. Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-530, June.
    13. Hooker, Mark A., 2000. "Misspecification versus bubbles in hyperinflation data: Monte Carlo and interwar European evidence," Journal of International Money and Finance, Elsevier, vol. 19(4), pages 583-600, August.
    14. John R. Conlon, 2004. "Simple Finite Horizon Bubbles Robust to Higher Order Knowledge," Econometrica, Econometric Society, vol. 72(3), pages 927-936, May.
    15. Harrison Hong & José Scheinkman & Wei Xiong, 2006. "Asset Float and Speculative Bubbles," Journal of Finance, American Finance Association, vol. 61(3), pages 1073-1117, June.
    16. Brunnermeier, Markus K. & Oehmke, Martin, 2013. "Bubbles, Financial Crises, and Systemic Risk," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1221-1288, Elsevier.
    17. Behzad T. Diba & Herschel I. Grossman, 1984. "Rational Bubbles in the Price of Gold," NBER Working Papers 1300, National Bureau of Economic Research, Inc.
    18. Ben S. Bernanke & Mark Gertler, 1999. "Monetary policy and asset price volatility," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 77-128.
    19. Allen F. & Morris S. & Postlewaite A., 1993. "Finite Bubbles with Short Sale Constraints and Asymmetric Information," Journal of Economic Theory, Elsevier, vol. 61(2), pages 206-229, December.
    20. Camerer, Colin, 1989. "Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
    21. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    22. Batini, Nicoletta & Nelson, Edward, 2001. "Optimal horizons for inflation targeting," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 891-910, June.
    23. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    24. KevinJ. Lansing, 2010. "Rational and Near-Rational Bubbles Without Drift," Economic Journal, Royal Economic Society, vol. 120(549), pages 1149-1174, December.
    25. repec:bla:jfinan:v:59:y:2004:i:5:p:2013-2040 is not listed on IDEAS
    26. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
    27. Sophie Moinas & Sebastien Pouget, 2013. "The Bubble Game: An Experimental Study of Speculation," Econometrica, Econometric Society, vol. 81(4), pages 1507-1539, July.
    28. Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, vol. 29(4), pages 808-837, August.
    29. Bohl, Martin T., 2003. "Periodically collapsing bubbles in the US stock market?," International Review of Economics & Finance, Elsevier, vol. 12(3), pages 385-397.
    30. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 725-737.
    31. Summers, Lawrence H, 1986. "Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
    32. Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
    33. Gregory, Allan W & Hansen, Bruce E, 1996. "Tests for Cointegration in Models with Regime and Trend Shifts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 555-560, August.
    34. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-154, March-Apr.
    35. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    36. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    37. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    38. Froot, Kenneth A & Obstfeld, Maurice, 1991. "Intrinsic Bubbles: The Case of Stock Prices," American Economic Review, American Economic Association, vol. 81(5), pages 1189-1214, December.
    39. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    40. repec:pri:metric:wp047_2012_brunnermeier_ssrn-id2103814.pdf is not listed on IDEAS
    41. Piergiorgio Alessandri, 2006. "Bubbles and fads in the stock market: another look at the experience of the US," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 11(3), pages 195-203.
    42. Hamilton, James D. & Whiteman, Charles H., 1985. "The observable implications of self-fulfilling expectations," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 353-373, November.
    43. Roche, Maurice J., 2001. "The rise in house prices in Dublin: bubble, fad or just fundamentals," Economic Modelling, Elsevier, vol. 18(2), pages 281-295, April.
    44. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    45. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-574, May.
    46. Franklin Allen & Gary Gorton, 1993. "Churning Bubbles," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 813-836.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Muhammad Farid Ahmed & Stephen Satchell, 2019. "Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity," JRFM, MDPI, vol. 12(3), pages 1-18, July.
    2. Ahmed Muhammad Farid & Satchell Stephen, 2018. "What Proportion of Time is a Particular Market Inefficient? … A Method for Analysing the Frequency of Market Efficiency when Equity Prices Follow Threshold Autoregressions," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-22, July.
    3. Chen, Shyh-Wei & Hsu, Chi-Sheng & Xie, Zixong, 2016. "Are there periodically collapsing bubbles in the stock markets? New international evidence," Economic Modelling, Elsevier, vol. 52(PB), pages 442-451.
    4. Galyna Grynkiv & Lars Stentoft, 2018. "Stationary Threshold Vector Autoregressive Models," JRFM, MDPI, vol. 11(3), pages 1-23, August.

    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. John Knight & Stephen Satchell & Nandini Srivastava, 2012. "Steady-State Distributions for Models of Bubbles: their Existence and Econometric Implications," Birkbeck Working Papers in Economics and Finance 1208, Birkbeck, Department of Economics, Mathematics & Statistics.
    2. Tolhurst, Tor N., 2018. "A Model-Free Bubble Detection Method: Application to the World Market for Superstar Wines," 2018 Annual Meeting, August 5-7, Washington, D.C. 274387, Agricultural and Applied Economics Association.
    3. Drobyshevsky Sergey & Narkevich Sergey & E. Pikulina & D. Polevoy, 2009. "Analysis Of a Possible Bubble On the Russian Real Estate Market," Research Paper Series, Gaidar Institute for Economic Policy, issue 128.
    4. repec:zbw:bofism:2012_047 is not listed on IDEAS
    5. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs, Bank of Finland, number 2012_047.
    6. Refet S. Gürkaynak, 2008. "Econometric Tests Of Asset Price Bubbles: Taking Stock," Journal of Economic Surveys, Wiley Blackwell, vol. 22(1), pages 166-186, February.
    7. Taipalus, Katja, 2006. "Bubbles in the Finnish and US equities markets," Scientific Monographs, Bank of Finland, number 35/2006.
    8. Anderson, Keith & Brooks, Chris & Katsaris, Apostolos, 2010. "Speculative bubbles in the S&P 500: Was the tech bubble confined to the tech sector?," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 345-361, June.
    9. Yuchao Fan, 2022. "Dissecting the dot-com bubble in the 1990s NASDAQ," Papers 2206.14130, arXiv.org, revised Jul 2022.
    10. repec:zbw:bofism:2006_035 is not listed on IDEAS
    11. Michaelides, Panayotis G. & Tsionas, Efthymios G. & Konstantakis, Konstantinos N., 2016. "Non-linearities in financial bubbles: Theory and Bayesian evidence from S&P500," Journal of Financial Stability, Elsevier, vol. 24(C), pages 61-70.
    12. Tsvetanov, Daniel & Coakley, Jerry & Kellard, Neil, 2016. "Bubbling over! The behaviour of oil futures along the yield curve," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 516-533.
    13. Frank J. Fabozzi & Iason Kynigakis & Ekaterini Panopoulou & Radu S. Tunaru, 2020. "Detecting Bubbles in the US and UK Real Estate Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 60(4), pages 469-513, May.
    14. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2012_047, March.
    15. Paulo M.M. Rodrigues & Rita Fradique Lourenço, 2015. "House prices: bubbles, exuberance or something else? Evidence from euro area countries," Working Papers w201517, Banco de Portugal, Economics and Research Department.
    16. Efthymios Pavlidis & Alisa Yusupova & Ivan Paya & David Peel & Enrique Martínez-García & Adrienne Mack & Valerie Grossman, 2016. "Episodes of Exuberance in Housing Markets: In Search of the Smoking Gun," The Journal of Real Estate Finance and Economics, Springer, vol. 53(4), pages 419-449, November.
    17. Wei Long & Dingding Li & Qi Li, 2016. "Testing explosive behavior in the gold market," Empirical Economics, Springer, vol. 51(3), pages 1151-1164, November.
    18. Brunnermeier, Markus K. & Oehmke, Martin, 2013. "Bubbles, Financial Crises, and Systemic Risk," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1221-1288, Elsevier.
    19. 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.
    20. Su, Chi-Wei & Li, Zheng-Zheng & Chang, Hsu-Ling & Lobonţ, Oana-Ramona, 2017. "When Will Occur the Crude Oil Bubbles?," Energy Policy, Elsevier, vol. 102(C), pages 1-6.
    21. Zhao, Yanping & Chang, Hsu-Ling & Su, Chi-Wei & Nian, Rui, 2015. "Gold bubbles: When are they most likely to occur?," Japan and the World Economy, Elsevier, vol. 34, pages 17-23.
    22. Vogel, Harold L. & Werner, Richard A., 2015. "An analytical review of volatility metrics for bubbles and crashes," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 15-28.

    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:eee:ecmode:v:41:y:2014:i:c:p:281-288. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    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.