# Cointegration and Tests of Present Value Models

*John Campbell* () and
*Robert Shiller*

No 1885, NBER Working Papers from National Bureau of Economic Research, Inc

**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.

**Date:** 1986-04

**Note:** ME

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (9) Track citations by RSS feed

**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.

**Downloads:** (external link)

http://www.nber.org/papers/w1885.pdf (application/pdf)

**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)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:nbr:nberwo:1885

**Ordering information:** This working paper can be ordered from

http://www.nber.org/papers/w1885

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.

Bibliographic data for series maintained by ().