This paper presents estimates indicating that, for aggregate U.S. stock market data 1871-1986, a long historical average of real earnings is a good predictor of the present value of future real dividends. This is true even when the information contained in stock prices is taken into account. We estimate that for each year the optimal forecast of the present value of future real dividends is roughly a weighted average of moving average earnings and current real price, with between 2/3 and 3/4 of the weight on the earnings measure. This means that simple present value models of stock market prices can be strongly rejected.
We use a vector autoregressive approach which enables us to compute the implications of this for the behavior of stock prices and returns. We estimate that log dividend-price ratios are more variable than, and virtually uncorrelated with, their theoretical counterparts given the present value models. Annual returns on stocks are quite highly correlated with their theoretical counterparts, but are two to four times as variable.
Our approach also reveals the connection between recent papers showing forecastability of long-horizon returns on corporate stocks, and earlier literature claiming that stock prices are too volatile to be accounted for in terms of simple present value models. We show that excess volatility directly implies the forecastability of long-horizon returns.
The informational content of different forecasts can be compared by regressing the actual change in a variable to be forecasted on forecasts of the change. We use the procedure in Fair and Shiller (1987) to examine the informational content of three sets of ex ante forecasts: the American Statistical Association and National Bureau of Economic Research Survey (ASA). Data Resources Incorporated (DRI), and Wharton Economic Forecasting Associates (WEFA). We compare these forecasts to each other and to “quasi ex ante” forecasts generated from a vector autoregressive model, an autoregressive components model and a large-scale structural model (the Fair model).
JEL Classification: 132, 212
Keywords: Forecasts, Ex ante forecasts, Informational content
This paper uses data on nearly a million homes sold in four metropolitan areas — Atlanta, Chicago, Dallas and San Francisco — to construct quarterly indexes of existing home prices between 1970 and 1986. We propose and apply a new method of constructing such indexes which we call the method of constructing such indexes which we call the weighted repeat sales method (WRS). We believe the results give an accurate picture of the actual rate of appreciation in home prices in the four cities. The paper explains the construction of the index, discusses the results and compares them with the National Association of Realtors data on the median price of existing single family homes for the period 1981-1986.
JEL Classification: 026, 012
Keywords: Noncooperative games, agreements, repeated games
The information contained in the forecasts from two econometric models can be compared by regressing the actual change in the variable forecasted on the two forecasts of the change. We do such comparisons in this paper, where the forecasts are based only on information through the period prior to the first period of the forecast. If a model’s forecast is statistically significant in such a regression, we conclude that the model captures information not in the other model whose forecast is also included in the regression.
The models studied include the Fair model, vector autoregressive (VAR) models estimated by ordinary least squares, vector autoregressive models estimated with Litterman priors, and a new class of models, which we call “autoregressive components: (AC) models. The AC models divide GNP into components and estimate an autoregressive equation for each component.
Our results show that the Fair model’s forecasts contain information not in the forecasts of the VAR and AC models. The AC models contain no information not in the Fair model, which indicates that the Fair model uses all the useful information in the components. The VAR models contain information not in the Fair model for the four-quarter-ahead forecasts but not the one-quarter-ahead forecasts. The best AC model contains information not in the best VAR model, which indicates that there is useful information in the components that the VAR models are not using. The best VAR model contains information not in the best AC model for the four-quarter-ahead forecasts but not the one-quarter-ahead forecasts.
JEL Classification: 132, 211
Keywords: Forecasting, Autoregressive components model
A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for United States time series 1981-1986: versions using real interest rate data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio.
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.
JEL Classification: 211, 313
Keywords: Contegration, Present value methods, Stock price index, Interest rates, Term structure, Volatility, Efficient markets