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Interpreting long-horizon estimates in predictive regressions

  • Erik Hjalmarsson

This paper analyzes the asymptotic properties of long-horizon estimators under both the null hypothesis and an alternative of predictability. Asymptotically, under the null of no predictability, the long-run estimator is an increasing deterministic function of the short-run estimate and the forecasting horizon. Under the alternative of predictability, the conditional distribution of the long-run estimator, given the short-run estimate, is no longer degenerate and the expected pattern of coefficient estimates across horizons differs from that under the null. Importantly, however, under the alternative, highly endogenous regressors, such as the dividend-price ratio, tend to deviate much less than exogenous regressors, such as the short interest rate, from the pattern expected under the null, making it more difficult to distinguish between the null and the alternative.

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File URL: http://www.federalreserve.gov/pubs/ifdp/2008/928/default.htm
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File URL: http://www.federalreserve.gov/pubs/ifdp/2008/928/ifdp928.pdf
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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 928.

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Date of creation: 2008
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Handle: RePEc:fip:fedgif:928
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  1. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  2. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
  3. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  4. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
  5. Richardson, Matthew & Stock, James H., 1989. "Drawing inferences from statistics based on multiyear asset returns," Journal of Financial Economics, Elsevier, vol. 25(2), pages 323-348, December.
  6. Campbell, John & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Scholarly Articles 3122601, Harvard University Department of Economics.
  7. Richardson, Matthew & Smith, Tom, 1991. "Tests of Financial Models in the Presence of Overlapping Observations," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 227-54.
  8. Richardson, Matthew P & Smith, Tom, 1994. "A Unified Approach to Testing for Serial Correlation in Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(3), pages 371-99, July.
  9. Richardson, Matthew, 1993. "Temporary Components of Stock Prices: A Skeptic's View," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 199-207, April.
  10. John Y. Campbell, 1993. "Why Long Horizons: A Study of Power Against Persistent Alternatives," NBER Technical Working Papers 0142, National Bureau of Economic Research, Inc.
  11. Campbell, John & Shiller, Robert, 1988. "Stock Prices, Earnings, and Expected Dividends," Scholarly Articles 3224293, Harvard University Department of Economics.
  12. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-79, June.
  13. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
  14. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
  15. Kirby, Chris, 1997. "Measuring the Predictable Variation in Stock and Bond Returns," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 579-630.
  16. Lanne, M., 2000. "Testing the Predictability of Stock Returns," University of Helsinki, Department of Economics 488, Department of Economics.
  17. Walter Torous & Rossen Valkanov & Shu Yan, 2004. "On Predicting Stock Returns with Nearly Integrated Explanatory Variables," The Journal of Business, University of Chicago Press, vol. 77(4), pages 937-966, October.
  18. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  19. Nelson, Charles R & Kim, Myung J, 1993. " Predictable Stock Returns: The Role of Small Sample Bias," Journal of Finance, American Finance Association, vol. 48(2), pages 641-61, June.
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