The Present Value Model of Stock Prices: Regression Tests and Monte Carlo Results

Abstract

The variance bounds tests of the present value model of stock prices are re-examined in this paper. A direct test of the model based on ordinary least squares estimation of a simple regression equation is proposed as an alternative and it is shown that this regression approach has several advantages over the variance bounds tests. This test is easily adapted to the important case in which the percentage changes in real dividends and real stock prices are stationary processes. The tests are applied to quarterly data for the Standard & Poor's Index of 500 Common Stocks and the results are much more conclusive than those obtained by previous tests. S HILLER (1981a and 1981b) and LeRoy and Porter (1981) have tested the present value model of stock prices by examining the implicit restrictions of this model on the variation of stock prices. Their results suggest that actual stock prices vary too much to be consistent with this model. If we examine their results closely, we find that Shiller does not construct formal statistical tests of the model and that most of the tests in LeRoy and Porter are not statistically significant because the standard errors of the variance estimates are quite large. In addition, some critics have argued that the time series used are not stationary, even after the removal of a time trend, and that the variance estimates are unreliable. This argument has been made by Kleidon (1982,1984) and by Marsh and Merton (1983,1984). An alternative would be to model the percentage changes in dividends, earnings, and stock prices as covariance stationary time series. Shiller (1981a) considers this alternative specification, but notes that it does not lead to tractable variance bounds for stock prices. In this paper, a direct regression test of the present value model is developed as an alternative to the variance bounds test, and the test is extended to handle the case in which the percentage changes in dividends, earnings, and stock prices are covariance stationary. The present value model of stock prices has the following form: