Working Paper: NBER ID: w1885
Authors: John Y. Campbell; Robert J. Shiller
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.
Keywords: cointegration; present value models; financial markets
JEL Codes: C32; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| long-term interest rates (E43) | spread between long-term and short-term interest rates (st) (E43) |
| short-term interest rates (E43) | spread between long-term and short-term interest rates (st) (E43) |
| spread between long-term and short-term interest rates (st) (E43) | expected short rate changes (E43) |
| real stock prices (G19) | real dividends (G19) |
| real dividends (G19) | real stock prices (G19) |
| deviations from the present value model for stocks (G17) | long-term relationship between stock prices and dividends (G35) |