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Cointegration and Tests of Present Value Models

  • John Y. Campbell
  • Robert J. Shiller

In a model where a variable Y[sub t] is proportional to the present value, with constant discount rate, of expected future values of a variable y[sub t] the "spread" S[sub t]= Y[sub t] - [theta sub t] will be stationary for some [theta] whether or not y[sub t]must be differenced to induce stationarity. Thus, Y[sub t] and y[sub t] are cointegrated. The model implies that S[sub t] is proportional to the optimal forecast of [delta Y{sub t+1}] and also to the optimal forecast of S*[sub t], the present value of future [delta y{sub t}]. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y[sub t] is the long-term interest rate and y[sub t] the short-term interest rate, we find in postwar U.S. data that S[sub t] behaves much like an optimal forecast of S*[sub t] even though as earlier research has shown it is negatively correlated with [delta Y{sub t+1}]. When Y[sub t] is a real stock price index and y[sub t] the corresponding real dividend, using annual U.S. data for 1871-1986 we obtain less encouraging results for the model, al-though the results are sensitive to the assumed discount rate.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 1885.

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Date of creation: Apr 1986
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Publication status: published as Campbell, John and Robert J. Shiller. "Cointegration and Tests of Present Value Models," Journal of Political Economy, Vol. 95, No. 5, October 1987, pp. 1062-1088.
Handle: RePEc:nbr:nberwo:1885
Note: ME
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  1. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
  2. John Y. Campbell & Robert J. Shiller, 1983. "A Simple Account of the Behavior of Long-Term Interest Rates," NBER Working Papers 1203, National Bureau of Economic Research, Inc.
  3. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-73, November.
  4. 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.
  5. 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.
  6. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
  7. 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.
  8. Marsh, Terry A. & Merton, Robert C., 1984. "Dividend variability and variance bounds tests for the rationality of stock market prices," Working papers 1584-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  9. 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.
  10. Robert J. Shiller & John Y. Campbell & Kermit L. Schoenholtz, 1983. "Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 14(1), pages 173-224.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Mankiw, N Gregory & Miron, Jeffrey A, 1986. "The Changing Behavior of the Term Structure of Interest Rates," The Quarterly Journal of Economics, MIT Press, vol. 101(2), pages 211-28, May.
  16. 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.
  17. 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.
  18. Sawa, Takamitsu, 1978. "Information Criteria for Discriminating among Alternative Regression Models," Econometrica, Econometric Society, vol. 46(6), pages 1273-91, November.
  19. 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.
  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.
  21. Robert J. Shiller, 1985. "Conventional Valuation and the Term Structure of Interest Rates," NBER Working Papers 1610, National Bureau of Economic Research, Inc.
  22. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
  23. 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.
  24. 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.
  25. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Cowles Foundation Discussion Papers 719R, Cowles Foundation for Research in Economics, Yale University.
  26. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
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