TY  - JOUR
AU  - Campbell,John Y.
AU  - Shiller,Robert J.
TI  - Cointegration and Tests of Present Value Models
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 1885
PY  - 1988
Y2  - June 1988
UR  - http://www.nber.org/papers/w1885
L1  - http://www.nber.org/papers/w1885.pdf
N1  - Author contact info:
John Y. Campbell
Morton L. and Carole S.
Olshan Professor of Economics
Department of Economics
Harvard University
Littauer Center 213
Cambridge, MA 02138
Tel: 617/496-6448
Fax: 617/495-7730
E-Mail: john_campbell@harvard.edu

Robert J. Shiller
Yale University, Cowles Foundation
Box 208281
30 Hillhouse Avenue
New Haven, CT  06520-8281
Tel: 203/432-3708
Fax: 203/432-6167
E-Mail: robert.shiller@yale.edu
AB  - 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.
ER  -