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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 2015-80, Scottish Institute for Research in Economics (SIRE).
    3. 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.
    4. 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.
    5. 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.
    6. Dooruj Rambaccussing, 2015. "Modelling Housing Prices using a Present Value State Space Model," Dundee Discussion Papers in Economics 285, Economic Studies, University of Dundee.
    7. Polimenis, Vassilis & Neokosmidis, Ioannis M., 2016. "The modified dividend–price ratio," International Review of Financial Analysis, Elsevier, vol. 45(C), pages 31-38.
    8. repec:eee:eecrev:v:100:y:2017:i:c:p:293-317 is not listed on IDEAS
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. Lof, Matthijs, 2013. "Essays on Expectations and the Econometrics of Asset Pricing," MPRA Paper 59064, University Library of Munich, Germany.
    14. 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.
    15. 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).
    16. Gelain, Paolo & Lansing, Kevin J., 2014. "House prices, expectations, and time-varying fundamentals," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 3-25.
    17. Tom Engsted, 2016. "Fama On Bubbles," Journal of Economic Surveys, Wiley Blackwell, vol. 30(2), pages 370-376, April.
    18. 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.
    19. 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.
    20. 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).
    21. repec:lan:wpaper:52032583 is not listed on IDEAS
    22. Tom Engsted & Thomas Q. Pedersen, 2012. "Predicting returns and rent growth in the housing market using the rent-to-price ratio: Evidence from the OECD countries," CREATES Research Papers 2012-58, Department of Economics and Business Economics, Aarhus University.
    23. 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.

    More about this item

    Keywords

    Stock return; Taylor expansion; bubble; simulation; predictability;

    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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