Tests of a representation of the efficient markets model (the dividend-rtaio model of Campbell and Shiller (1988a)) of the stock market can be made by regressing (transformed) ex-post values on (transformed) actual values and testing whether the slope coefficient is one. Such tests are run here with some improvements. The results of the tests are that the efficient markets model is strongly rejected with U.S. data 1901-1987 in favor of an alternative that stock prices should have been much less volatile.

Robert J. Shiller, Fumiko Kon-Ya, Yoshiro Tsutsui, Why Did the Nikkei Crash? Expanding the Scope of Expectations Data Collection, The Review of Economics and Statistics, Vol. 78, No. 1 (Feb., 1996), pp. 156-164

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 ant. forecasts: the American Statistical Association and National Bureau of Economic Research Survey (ASA), Data Resources Incorporated (DRI), and Wharton Economic Forecasting Associates (UEFA). 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).