JIANG WANG INTERTEMPORAL ASSET PRICES 257 where hnp(>0),hun,hep (>0),hen are constants,b,is a (2x3)matrix.The innovation process of the filters,w,is a standard Wiener process with respect to g"(t)DP(t). Furthermore,the information structure generated by(t)is equivalent to that generated by D.P(t). Proof.See Appendix A. As specified in equation(2.1),II governs the expected changes in dividends.Not observing II,the uninformed investors rationally draw inferences about II from dividends and prices.They rationally attribute a shock in dividend to reflect partially a change in II.This gives rise to the positive contribution of dividend shocks to innovations in II, as shown in equation (4.3).Thus,E[dnIdD]=hnp>0 even though dwp and dwn are independent.From equation (4.3),we observe that also positively responds to dividend shocks.For the uninformed investors,a positive innovation in D suggests an increase in II.Conditioned on A=PnII+pe,the increase in II must be offset by an increase in (given pe<0).Hence,E[dodD]=hep>0 although and D are independent.The joint esimation of II and based on both D and P generates the induced correlation between the filters and dividends and prices.The induced correlation between the uninformed investors'estimates and dividends as well as prices are important in understanding the behaviour of stock prices and returns. Furthermore,the uninformed investors'estimation error,A=II-II,follows a stan- dard O-U process: d△=-aa△dt+badw, (4.5) where as is a positive constant and ba is a(1 x 3)constant matrix given in Appendix A. The fact that A is mean-reverting to zero implies that the estimation errors of the uninformed investors are only temporary.As a matter of fact,the continuous flow of dividends as well as changes in prices provide a flow of new information about the underlying growth rate of dividends and supply shocks.The uninformed investors constantly update their estimates about II(and )based on the newly arrived information and correct the errors made in their previous estimation.Suppose that there has been a positive shock in D while there has been no shock to II.Not observing II,the uninformed investors rationally attribute the dividend shock to partially reflect a high value of II, hence increase their estimate II.However,the future dividend will not grow as expected since II has not increased.When new levels of D are realized,the uninformed investors will revise their estimate and lower II,eliminating the error in their previous estimation. 4.2.Investment opportunities Given the process of filter II,the stock price follows the process: dP=[p(Π-kD)+anpt(i-I)-aePe⊙-aapa△]dt+bpdw, (4.6) where bp is a(1 x 3)constant matrix as given in Appendix A.In order to characterize investment opportunities in the economy,we consider the instantaneous excess return to one share of stock:dQ=(D-rP)dt+dp.dQ is also the return on a zero-wealth portfolio long one share of stock fully financed by borrowing at the risk-free rate.Q gives the undiscounted cumulative cash flow from the zero-wealth portfolio