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Cointegration and Tests of Present Value Models

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Author Info
John Y. Campbell (Princeton University)
Robert J. Shiller () (Cowles Foundation, Yale University)

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Abstract

In a model where a variable Y is proportional to the present value, with constant discount rate, of expected future values of a variable y, the "spread" S - Y - qy will be stationary for some q whether or not y must be differenced to induce stationarity. Thus, Y and y are cointegrated. The model implies that S is proportional to the optimal forecast of S*, the present value of future changes in y. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y is the long-term interest rate and y the short-term interest rate, we find in postwar United States data that S behaves much like an optimal forecast of S* even though as earlier research has shown it is negatively correlated with next period's change in Y. When Y is a real stock price index and y the corresponding real dividend, using annual United States data for 1871-1986 we obtain less encouraging results for the model, although the results are sensitive to the assumed discount rate.

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File URL: http://cowles.econ.yale.edu/P/cd/d07b/d0785.pdf
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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 785.

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Length: 41 pages
Date of creation: Mar 1986
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Handle: RePEc:cwl:cwldpp:785

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Cointegration present value methods stock price index interest rates term structure volatility efficient markets

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  1. Quantitative Macroeconomics and Real Business Cycles (QM&RBC)
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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June. [Downloadable!] (restricted)
  3. Ito, Takatoshi, 1988. "Use of (Time-Domain) Vector Autoregressions to Test Uncovered Interest Parity," The Review of Economics and Statistics, MIT Press, vol. 70(2), pages 296-305, May. [Downloadable!] (restricted)
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  4. Kleidon, Allan W, 1986. "Variance Bounds Tests and Stock Price Valuation Models," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 953-1001, October. [Downloadable!] (restricted)
  5. Mankiw, N Gregory & Romer, David & Shapiro, Matthew D, 1985. " An Unbiased Reexamination of Stock Market Volatility," Journal of Finance, American Finance Association, vol. 40(3), pages 677-87, July. [Downloadable!] (restricted)
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  6. Shiller, Robert J., 1981. "Alternative tests of rational expectations models : The case of the term structure," Journal of Econometrics, Elsevier, vol. 16(1), pages 71-87, May. [Downloadable!] (restricted)
  7. Sargent, Thomas J., 1979. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Journal of Monetary Economics, Elsevier, vol. 5(1), pages 133-143, January. [Downloadable!] (restricted)
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  8. Scott, Louis O, 1985. "The Present Value Model of Stock Prices: Regression Tests and Monte Carlo Results," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 599-605, November. [Downloadable!] (restricted)
  9. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-74, May. [Downloadable!] (restricted)
  10. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis. [Downloadable!]
  11. Shiller, Robert J, 1979. "The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1190-1219, December. [Downloadable!] (restricted)
  12. Robert J. Shiller & John Y. Campbell & Kermit L. Schoenholtz, 1983. "Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates," Cowles Foundation Discussion Papers 667, Cowles Foundation, Yale University. [Downloadable!]
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  13. Campbell, John Y & Shiller, Robert J, 1984. "A Simple Account of the Behavior of Long-Term Interest Rates," American Economic Review, American Economic Association, vol. 74(2), pages 44-48, May. [Downloadable!] (restricted)
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  14. 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 421-36, June. [Downloadable!] (restricted)
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  15. Matthew D. Shapiro & N. Gregory Mankiw, 1984. "Trends, Random Walks, and Tests of the Permanent Income Hypothesis," Cowles Foundation Discussion Papers 725, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  16. Modigliani, Franco & Shiller, Robert J, 1973. "Inflation, Rational Expectations and the Term Structure of Interest Rates," Economica, London School of Economics and Political Science, vol. 40(157), pages 12-43, February. [Downloadable!] (restricted)
  17. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November. [Downloadable!] (restricted)
  18. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Cowles Foundation Discussion Papers 719R, Cowles Foundation, Yale University. [Downloadable!]
  19. Robert J. Shiller, 1985. "Conventional Valuation and the Term Structure of Interest Rates," NBER Working Papers 1610, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  20. Baillie, Richard T & Lippens, Robert E & McMahon, Patrick C, 1983. "Testing Rational Expectations and Efficiency in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 51(3), pages 553-63, May. [Downloadable!] (restricted)
  21. Sawa, Takamitsu, 1978. "Information Criteria for Discriminating among Alternative Regression Models," Econometrica, Econometric Society, vol. 46(6), pages 1273-91, November. [Downloadable!] (restricted)
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