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Cointegration and Tests of Present Value Models

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.yale.edu/sites/default/files/files/pub/d07/d0785.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 785.

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Length: 41 pages
Date of creation: Mar 1986
Date of revision:
Publication status: Published in Journal of Political Economy (October 1987), 95: 1062-1088; also in Robert F. Engle and Clive W.J. Granger (eds.), Long-Run Economic Relationships: Readings in Cointegration, Oxford University Press, 1991, pp. 191-217; and Andrew W. Lo (ed.), Financial Econometrics, Edward Elgar, 2005
Handle: RePEc:cwl:cwldpp:785
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  1. 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.
  2. John Y. Campbell, 1986. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," NBER Working Papers 1805, National Bureau of Economic Research, Inc.
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  6. 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.
  7. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 15(2), pages 457-510.
  8. N. Gregory Mankiw & David Romer & Matthew D. Shapiro, 1985. "An Unbiased Reexamination of Stock Market Volatility," Cowles Foundation Discussion Papers 758, Cowles Foundation for Research in Economics, Yale University.
  9. Robert J. Shiller, 1980. "Alternative Tests of Rational Expectations Models: The Case of the Term Structure," NBER Working Papers 0563, National Bureau of Economic Research, Inc.
  10. 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.
  11. Gregory Mankiw, N. & Shapiro, Matthew D., 1985. "Trends, random walks, and tests of the permanent income hypothesis," Journal of Monetary Economics, Elsevier, vol. 16(2), pages 165-174, September.
  12. Marsh, Terry A & Merton, Robert C, 1986. "Dividend Variability and Variance Bounds Tests for the Rationality ofStock Market Prices," American Economic Review, American Economic Association, vol. 76(3), pages 483-98, June.
  13. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
  14. Thomas J. Sargent, 1978. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Staff Report 26, Federal Reserve Bank of Minneapolis.
  15. 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.
  16. 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.
  17. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
  18. Robert J. Shiller, 1985. "Conventional Valuation and the Term Structure of Interest Rates," NBER Working Papers 1610, National Bureau of Economic Research, Inc.
  19. Sawa, Takamitsu, 1978. "Information Criteria for Discriminating among Alternative Regression Models," Econometrica, Econometric Society, vol. 46(6), pages 1273-91, November.
  20. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
  21. 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 for Research in Economics, Yale University.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
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