MULTIVARIATE ESTIMATES OF THE PERMANENT COMPONENTS OF GNP AND STOCK PRICES

The economic assumption that a present value relation holds between consumption and income and between stock prices and dividends, or the statistical assumption that the consumption/ income ratio and the dividend/price ratio are stationary imply that the permanent or random walk component in each series of a pair must be the same as the permanent component in the other series of a pair. Either assumption then allows us to estimate the variance of the permanent component of one series (GNP, stock prices) from the variance of the permanent component of the other (consumption, dividends), or from the covariance of the two series’ permanent components. This paper presents such estimates, and finds that the permanent components are about half those estimated by similar univariate methods. A series of recent papers has examined the importance of a potential unit root to the behavior of real GNP [Campbell and Mankiw (1986, 1987), Cochrane (1986), Clark (1987)] and stock prices [Fama and French (1986) Lo and Mai if by 0, the series is stationary. The response can be any real number, which is the innovation in these estimates: instead of forcing us to ask the dichotomous question ‘is there a unit root or not’, they allow us to continuously measure the importance of a potential unit root. The actual estimating technique used in these papers varied somewhat. Cochrane, Poterba and Summers, and Lo and Mai if a series is stationary, the variance of k differences will tend to *A precursor to this paper appeared under the title ‘Spectral Density Estimates of Unit Roots’. We thank Masanao Aoki, Lam Hansen, Masao Ogaki, and Chris Sims for helpful suggestions. The computer programs and data used in this paper are available on request from the authors.