The objective of the paper is to test the hypothesis that the structure of the economy is recursive with disturbances flowing from income to prices, but not back to income. Under this hypothesis, inflation shocks result in corresponding changes in output of the opposite sign. Tests are based on analysis of the vector stochastic process of GNP, the price deflator, and real GNP for the United States from 1954 to 1970. The results are consistent with the recursive structure hypothesis and would seem to reinforce evidence that stock prices and real interest rates vary inversely with inflation.

In an innovative and provocative paper in this Review, Eugene Fama presents evidence which appears to be consistent with the joint hypothesis that the real rate of interest, ignoring taxes, is a constant and that the market for U.S. Treasury Bills is efficient in the sense of embodying rational expectations.' Those findings are strikingly at variance with a long list of previous studies which seemed to support the view that the real rate of interest varies over time and can be related to economic variables such as real output, monetary policy, and so forth.2 The methodologies which lead to these contradictory conclusions are quite different. Previous studies had followed the lead of Irving Fisher by relating nominal interest rates to distributed lags on past rates of inflation.3 These distributed lags are generally interpreted as approximations to the market's expected rate of inflation and thus any remaining variation is attributed to variation in the real rate.4 Fama's methodology, on the other hand, draws on the fact that the difference between the market interest rate and the subsequently observed rate of inflation, the ex post real interest rate, consists by definition of the ex ante real interest rate plus a pure forecasting error.5 The hypothesis of market efficiency implies that these forecasting errors must be serially random. Thus, observing ex post real rates is equivalent to observing ex ante real rates with random measurement error. These errors of course confound the problem of identifying variation in the ex ante real rate. In this paper, we will argue that the relative magnitude of these measurement errors is such that the tests carried out by Fama were not powerful enough to reject the joint hypothesis that the ex ante real rate is a constant and expectations are rational. More powerful tests which are presented in this paper using the same data do lead to rejection of that hypothesis. Of course, rejection

ABSTRACT Predictive regressions are subject to two small sample biases: the coefficient estimate is biased if the predictor is endogenous, and asymptotic standard errors in the case of overlapping periods are biased downward. Both biases work in the direction of making t ‐ratios too large so that standard inference may indicate predictability even if none is present. Using annual returns since 1872 and monthly returns since 1927 we estimate empirical distributions by randomizing residuals in the VAR representation of the variables. The estimated biases are large enough to affect inference in practice, and should be accounted for when studying predictability.