Cointegration and Tests of Present Value Models

39 Pages Posted: 6 Apr 2004 Last revised: 28 Aug 2022

See all articles by John Y. Campbell

John Y. Campbell

Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Robert J. Shiller

Yale University - Cowles Foundation; National Bureau of Economic Research (NBER); Yale University - International Center for Finance

Date Written: April 1986

Abstract

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.

Suggested Citation

Campbell, John Y. and Shiller, Robert J., Cointegration and Tests of Present Value Models (April 1986). NBER Working Paper No. w1885, Available at SSRN: https://ssrn.com/abstract=249498

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Robert J. Shiller

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Yale University - International Center for Finance ( email )

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