COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 785 "Cointegration and Tests of Present Value Models" John Y. Campbell and Robert J. Shiller March 1986 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. |
