RATIONAL EXPECTATION: Deviations from Rationality. Certain imperfections and biases in the expectations may also be analyzed with the methods of this paper. Allowing for cross-sectional differences in expectations is a simple matter, because their aggregate effect is negligible as long as the deviation from the rational forecast for an individual firm is not strongly correlated with those of the others. Modifications are necessary only if the correlation of the errors is large and depends systematically on other explanatory variables. We shall examine the effect of over-discounting current information and of differences in the information possessed by various firms in the industry. Whether such biases in expectations are empirically important remains to be seen I wish only to emphasize that the methods are flexible enough to handle th Let us consider first what happens when expectations tently over- or under-discount the effect of current events. Equation(3.8), which gives the optimal price expectation, will then be replaced by (3.18) p=AW1et-1+∑Wet-4 In other words the weight attached to the most recent exogenous dis- turbance is multiplied by the factor fi, which would be greater than unity if current information is over-discounted and less than unity if it is under discounted If we use(3. 18) for the expected price instead of (3.8)to explain market orice movements, then (3. 11)is replaced by W0=--o (319b 8+fy l (3.19c) (=2,34…) The effect of the biased expectations on price movements depends on the statistical properties of the exogenous disturbances If the disturbances are independent(that is, wo= l and we=0 fori> 1) the biased expectations have no effect. The reason is that successive obser- vations provide no information about future fluctuations. On the other hand, if all the disturbances are of a permanent type(that =1), the properties of the expectations function are significantly affected. To illustrate the magnitude of the differences, the parameters of the function p=∑VRATIONAL EXPECTATIONS 321 Deviations from Rationality. Certain imperfections and biases in the expectations may also be analyzed with the methods of this paper. Allowing for cross-sectional differences in expectations is a simple matter, because their aggregate effect is negligible as long as the deviation from the rational forecast for an individual firm is not strongly correlated with those of the others. Modifications are necessary only if the correlation of the errors is large and depends systematically on other explanatory variables. We shall examine the effect of over-discounting current information and of differences in the information possessed by various firms in the industry. Whether such biases in expectations are empirically important remains to be seen. I wish only to emphasize that the methods are flexible enough to handle them. Let us consider first what happens when expectations consistently over￾or under-discount the effect of current events. Equation (3.8), which gives the optimal price expectation, will then be replaced by 00 (3.18) Pt = fi Wiet-i + I Wi Et-i i=2 In other words the weight attached to the most recent exogenous dis￾turbance is multiplied by the factor f1, which would be greater than unity if current information is over-discounted and less than unity if it is under￾discounted. If we use (3.18) for the expected price instead of (3.8) to explain market price movements, then (3.1 1) is replaced by (3.19a) Wo wo (3.19b) WW WI (3.19c) Wi Wi (i = 2,3,4,...). /3+y The effect of the biased expectations on price movements depends on the statistical properties of the exogenous disturbances. If the disturbances are independent (that is, wo =1 and wj = 0 for i > 1), the biased expectations have no effect. The reason is that successive obser￾vations provide no information about future fluctuations. On the other hand, if all the disturbances are of a permanent type (that is, w0 = w, = ... = 1), the properties of the expectations function are significantly affected. To illustrate the magnitude of the differences, the parameters of the function 00 pt - V}fit-