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92 CHAPTER 3. THE MONETARY MODEL=∞Xj=1ψ j E t ∆f t+j . (3.18)(3.17) and (3.18) allow you to represent the deviation of the exchangerate from the fundamental as the present value of future fundamentalsgrowthζ t = s t − f t =∞Xj=1ψ j E t ∆f t+j . (3.19)Since s t and f t are cointegrated they can be represented by a vectorerror correction model (VECM) that describes the evolution of(∆s t , ∆f t , ζ t ), where ζ t ≡ s t − f t . As shown in chapter 2.6, the lineardependence among (∆s t , ∆f t , ζ t ) induced by cointegration impliesthat the information contained in the VECM is preserved in a bivariatevector autoregression (VAR) that consists of ζ t and either ∆s t or ∆f t .Thus we will drop ∆s t and work with the p−th order VAR for (∆f t , ζ t )Ã∆ftζ t!=à pX a11,j a 12,jj=1a 21,j!à !∆ft−j+a 22,j ζ t−jòtv t!. (3.20)The information set available to the econometrician consists of currentand lagged values of ∆f t and ζ t . We will call this informationH t = {∆f t , ∆f t−1 ,...,ζ t , ζ t−1 ,...}. Presumably H t is a subset of economicagent’s information set, I t . Take expectations on both sides of(3.19) conditional on H t and use the law of iterated expectations toget 4 ∞Xζ t = ψ j E(∆f t+j |H t ). (3.21)j=1What is the point of deriving (3.21)? The point is to show that youcan use the prediction formulae implied the data-generating process(3.20) to compute the necessary expectations. Expectations of marketparticipants E(∆f t+j |I t ) are unobservable but you can still test thetheory by substituting the true expectations with your estimate of theseexpectations, E(∆f t+j |H t ).4 Let X, Y, and Z be random variables. The law of iterated expectations saysE[E(X|Y,Z)|Y ]=E(X|Y ).