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3.2. THE MONETARY MODEL OF THE BALANCE OF PAYMENTS83(chapter 4) and in the Redux model (chapter 9) as well. Why is that? ⇐(60)One reason frequently given is that we don’t have a good theory for whyPPP doesn’t hold so there is no obvious alternative way to provide internationalprice level linkages. A second and perhaps more convincingreason is that all theories involve abstractions that are false at somelevel and as Friedman [64] argues, we should judge a theory not by therealism of its assumptions but by the quality of its predictions.3.2 The Monetary Model of the Balanceof PaymentsThe Frenkel and Johnson [62] collection develops the monetary approachto the balance of payments under Þxed exchange rates. Toillustrate the main idea, consider a small open economy that maintainsa perfectly credible Þxed exchange rate ¯s. 1 i t is the domestic nominalinterest rate, B t is the monetary base, R t is the stock of foreignexchange reserves held by the central bank, D t is domestic credit extendedby the central bank. In logarithms, m t is the money stock,y t is national income, and p t is the price level. The money supply isM t = µB t = µ(R t +D t )whereµ is the money multiplier. A logarithmicexpansion of the money supply and its components about their meanvalues allows us to writem t = θr t +(1− θ)d t (3.1)where θ =E(R t )/E(B t ), r t =ln(R t ), and d t =ln(D t ). 2A transactions motive gives rise to the demand for money in whichlog real money demand m d t −p t depends positively on y t and negativelyon the opportunity cost of holding money i tm d t − p t = φy t − λi t + ² t . (3.2)1 A small open economy takes world prices and world interest rates as given.2 A Þrst-order expansion about mean values givesM t − E(M t ) = µ[R t − E(R t )] + µ[D t − E(D t )]. But µ = E(M t )/E(B t ) whereB t = R t + D t is the monetary base. Now divide both sides by E(M t )toget[M t − E(M t )]/E(M t )=θ[R t − E(R t )]/E(R t )+(1 − θ)[D t − E(D t )]/E(D t ). Notingthat for a random variable X t ,[X t − E(X t )]/E(X t ) ' ln(X t ) − ln(E(X t )), apartfrom an arbitrary constant, we get (3.1) inthetext.