Since the summation extends to infinity, we never observe p* without some error. However, with a long enough dividend series we may observe an approximate p . If we choose an arbitrary value for the terminal value of p* (in Figures 1 and 2, p* for 1979 was set at the average detrended real price over the sample) then we may determine p1* recursively by p* =Y(p*?I +dt) working backward from the terminal date. As we move back from the terminal date, the importance of the terminal value chosen declines. In data set (1) as shown in Figure 1, y is .954 and Y'08 =.0063 so that at the beginning of the sample the terminal value chosen has a negligible weight in the determination of pt*. If we had chosen a different terminal condition, the result would be to add or subtract an exponential trend from the p* shown in Figure 1. This is shown graphically in Figure 3, in which p* is shown computed from alternative terminal values. Since the only
thing we need know to compute p* about dividends after 1978 is p* for 1979, it does not matter whether dividends are "smooth" or not after 1978. Thus, Figure 3 represents our uncertainty about p*. There is yet another