Cointegration and Tests of Present Value Models

John Campbell and Robert Shiller

No 785, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Cointegration; present value methods; stock price index; interest rates; term structure; volatility; efficient markets (search for similar items in EconPapers)
Pages: 41 pages
Date: 1986-03
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Citations: View citations in EconPapers (6)

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

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Related works:
Journal Article: Cointegration and Tests of Present Value Models (1987)
Working Paper: Cointegration and Tests of Present Value Models (1987)
Working Paper: Cointegration and Tests of Present Value Models (1986)
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