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The log-linear return approximation, bubbles, and predictability

Author

Listed:
  • Tom Engsted

    () (School of Economics and Management, Aarhus University and CREATES)

  • Thomas Q. Pedersen

    () (School of Economics and Management, Aarhus University and CREATES)

  • Carsten Tanggaard

    () (School of Economics and Management, Aarhus University and CREATES)

Abstract

We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividendprice ratio. Next, we simulate various rational bubbles which have explosive conditional expectation, and we investigate the magnitude of the approximation error in those cases. We find that surprisingly the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we find evidence that bubbles generate large approximation errors. Finally, we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented.

Suggested Citation

  • Tom Engsted & Thomas Q. Pedersen & Carsten Tanggaard, 2010. "The log-linear return approximation, bubbles, and predictability," CREATES Research Papers 2010-37, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-37
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    Citations

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    Cited by:

    1. Matthijs Lof, 2015. "Rational Speculators, Contrarians, and Excess Volatility," Management Science, INFORMS, vol. 61(8), pages 1889-1901, August.
    2. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," SIRE Discussion Papers 2015-32, Scottish Institute for Research in Economics (SIRE).
    3. Engsted, Tom & Pedersen, Thomas Q., 2014. "Housing market volatility in the OECD area: Evidence from VAR based return decompositions," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 91-103.
    4. Polimenis, Vassilis & Neokosmidis, Ioannis M., 2016. "The modified dividend–price ratio," International Review of Financial Analysis, Elsevier, vol. 45(C), pages 31-38.
    5. Dave, Chetan & Malik, Samreen, 2017. "A tale of fat tails," European Economic Review, Elsevier, vol. 100(C), pages 293-317.
    6. Efthymios Pavlidis & Alisa Yusupova & Ivan Paya & David Peel & Enrique Martinez-Garcia & Adrienne Mack & Valerie Crossman, 2014. "Episodes of exuberance in housing markets," Working Papers 64908732, Lancaster University Management School, Economics Department.
    7. Bollerslev, Tim & Xu, Lai & Zhou, Hao, 2015. "Stock return and cash flow predictability: The role of volatility risk," Journal of Econometrics, Elsevier, vol. 187(2), pages 458-471.
    8. Lof, Matthijs, 2013. "Essays on Expectations and the Econometrics of Asset Pricing," MPRA Paper 59064, University Library of Munich, Germany.
    9. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-32, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. Cenedese, Gino & Mallucci, Enrico, 2016. "What moves international stock and bond markets?," Journal of International Money and Finance, Elsevier, vol. 60(C), pages 94-113.
    11. Itamar Caspi, 2015. "Testing for a Housing Bubble at the National and Regional Level: The Case of Israel," Bank of Israel Working Papers 2015.05, Bank of Israel.
    12. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-80, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Gelain, Paolo & Lansing, Kevin J., 2014. "House prices, expectations, and time-varying fundamentals," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 3-25.
    14. Maio, Paulo & Xu, Danielle, 2020. "Cash-flow or return predictability at long horizons? The case of earnings yield," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 172-192.
    15. Vassilis Polimenis & Ioannis Neokosmidis, 2019. "Non-stationary dividend-price ratios," Journal of Asset Management, Palgrave Macmillan, vol. 20(7), pages 552-567, December.
    16. repec:lan:wpaper:52032583 is not listed on IDEAS
    17. Engsted, Tom & Pedersen, Thomas Q., 2015. "Predicting returns and rent growth in the housing market using the rent-price ratio: Evidence from the OECD countries," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 257-275.
    18. Tilak Abeysinghe & Jiaying Gu, 2016. "Estimating fundamental and affordable housing price trends: a study based on Singapore," Applied Economics, Taylor & Francis Journals, vol. 48(49), pages 4783-4798, October.
    19. Peter C.B. Phillips & Ye Chen, "undated". "Restricted Likelihood Ratio Tests in Predictive Regression," Cowles Foundation Discussion Papers 1968, Cowles Foundation for Research in Economics, Yale University.
    20. Tom Engsted & Thomas Q. Pedersen, 2016. "The predictive power of dividend yields for future infl?ation: Money illusion or rational causes?," CREATES Research Papers 2016-11, Department of Economics and Business Economics, Aarhus University.
    21. Engsted, Tom & Hviid, Simon J. & Pedersen, Thomas Q., 2016. "Explosive bubbles in house prices? Evidence from the OECD countries," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 40(C), pages 14-25.
    22. Tom Engsted, 2016. "Fama On Bubbles," Journal of Economic Surveys, Wiley Blackwell, vol. 30(2), pages 370-376, April.
    23. 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.
    24. Tom Engsted & Thomas Q. Pedersen, 2018. "Disappearing money illusion," CREATES Research Papers 2018-24, Department of Economics and Business Economics, Aarhus University.
    25. Itamar Caspi, 2016. "Testing for a housing bubble at the national and regional level: the case of Israel," Empirical Economics, Springer, vol. 51(2), pages 483-516, September.

    More about this item

    Keywords

    Stock return; Taylor expansion; bubble; simulation; predictability;
    All these 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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