Cointegration and Tests of Present Value Models

John Y. Campbell, Robert J. Shiller

NBER Working Paper No. 1885 (Also Reprint No. r1016)
Issued in April 1986
NBER Program(s):Monetary Economics

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.

download in pdf format
   (284 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/w1885

Published: 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. citation courtesy of

Users who downloaded this paper also downloaded* these:
Shiller w0456 Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?
Campbell and Shiller w8221 Valuation Ratios and the Long-Run Stock Market Outlook: An Update
Blanchard and Watson w0945 Bubbles, Rational Expectations and Financial Markets
Pindyck w4083 The Present Value Model of Rational Commodity Pricing
Grossman and Shiller w0564 The Determinants of the Variability of Stock Market Prices
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us