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# Advanced International Economics ECON 872

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This 17 page Class Notes was uploaded by April Jerde on Thursday September 17, 2015. The Class Notes belongs to ECON 872 at University of Wisconsin - Madison taught by Charles Engel in Fall. Since its upload, it has received 74 views. For similar materials see /class/205143/econ-872-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.

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Date Created: 09/17/15

Notes on EngelWest Exchange Rates and Fundamentals JPE 2005 What guestion does the paper address The question is Whether presentvalue models of nominal exchange rates are good models of the exchange rate A present value model for the exchange rate is one in Which the exchange rate depends on the expected present discounted value of current and future fundamentals 00 139 st a2 9 EtxHj 10 Where a is some constant I is a discount factor 0 lt I lt1 and XI represents the economic fundamentals For example we have seen that the Dombusch model can be written as w 1 st 2 A EtxH where xt Emt mt qt 1 0 11 J The Taylor rule model can be written as 00 I St 1 EtZHj 7 Where F0 157 5 as 7 pt pt LEt tl 7 7r v v l57 l 7 H1 l57 I I ZtE Why is this an interesting question There is substantial doubt in the literature that exchange rate models have any empirical validity This doubt arises principally because the models cannot be used to forecast the change in the exchange rate st1 st That is time t information cannot be used to produce forecasts of changes in the exchange rate that are signi cantly better have a signi cantly lower mse than the forecast of no change st1 st 2 0 The most important paper in this vein is Meese and Rogoff J IE 1983 They build stickyprice and exibleprice variants of the monetary model They form forecasts of the exchange rate based on the model but nd that the forecast of no change has a lower mse than the model One surprising thing about MeeseRogoff is that they use actual ex post values of fundamentals to make the model forecasts but they still do no better than the forecast of no change This is not as bad for the models as it at first sounds Why 1 First under the MeeseRogoff methodology the no change forecast at least gets to use st in its forecast of SW But MeeseRogoff do not allow the models to have that information 2 This methodology can always be manipulated to give the model really good or really bad ex post information While it wasn t intentional MeeseRogoff did not give the models good ex post information Here is an example Suppose we take the case of the exibleprice model that posits that the nominal exchange rate is determined by relative money supplies less relative money demand levels S 2m m lit l39ut u Hk m Mink 11k as the forecast of the k period ahead exchange rate If the model were true the forecast would miss because of the error terms perhaps money demand shocks qu uquot But there are equally valid ways of writing the equation for the exchange rate These produce different ex post forecasts that might have smaller errors Meese and Rogoff use tk m tk For example we could use covered interest parity to write ft st 1 1 where ft is the log of the oneperiod forward rate Then we have st mt m lft stut u We can rewrite this as st mm m Mm at 1 l If our forecast using ex post information was A l SW MOI51 Mme fnkv l the forecast error would be only WWW Link The var1ance of the forecast A gtllt error 1s much smaller than when we use SM 2 m k mnk Ml k Ink My point is that it might seem surprising that we cannot do better than the forecast of no change even using ex post information but it all depends on what ex post information you use However in general the performance of exchangerate models in genuine outofsample forecasting exercises is not good Mark 1995 has some success using models to forecast exchange rates at longhorizons Mark de nes the fundamental determining exchange rates as xt mt m yt He then posits an forecasting equation Etstk St Bkxt St He finds some success forecasting dollar exchange rates for Canada Switzerland Germany and Japan at long horizons 16 quarters However that paper has been criticized The paper originally used data through 1991 Other researchers for example Faust Rogers and Wright HE 2003 found that as the sample was extended into the 1990s the forecasting power of the models disappeared Others questioned whether the bootstrapped significance levels in Mark s paper were correct since he presupposed cointegration between the exchange rate and the fundamentals Chinn Cheung and Garcia Pascual J IMF 2005 nd little consistent support for the claim that models have outofsample forecasting power Mark and Sul HE 2001 and Groen 2000 use panel methods to derive some support for the claim that the models have power in outofsample forecasts at long horizons However it is fair to say that there is little agreement that exchange rate models are useful in making forecasts of exchange rate changes out of sample How do Engel and West address the guestion The paper has two main points 1 Many exchange rate models actually have the implication that the exchange rate change should be nearly unforecastable That is they imply that the exchange rate is nearly a random walk 2 How then do we judge exchange rate models Since exchange rate models are forward looking then the exchange rate ought to incorporate useful information about the future fundamentals One test of the models then is to test the implication that the exchange rate is useful in forecasting future fundamentals They nd weak evidence in favor of this hypothesis Theorem in EngelWest Suppose the exchange rate is determined by a presentvalue model st a2 bjEtxHj j0 Theorem states that if xt is 10 then as the discount factor gets large I gt 1 the exchange rate approaches a random walk Here is the intuition of the theorem Do a BeveridgeNelson decomposition of fundamentals xt rwt t1 Then st iobjEler ZfzobjEltII rwl l b 2390 bjEltrl 1 1 Sr Sz l Srwz rwz 11 b fzobJIEZ lj Z0bjEt ltrz lj V b gt 1 VAR gt 00 VAR gtconstant When the discount factor is close to one markets put a high weight on the future In the distant future the in uence of the transitory component diminishes Uncertainty about the future values of fundamentals in the future primarily arises from uncertainty about the permanent component As the discount factor goes to one more and more weight is put on the future and the in uence of the permanent component of fundamentals is larger and larger In the limit the fraction of the variance of the exchange rate explained by the transitory component goes to zero Is this theory useful in practice How close does I have to be to one Population Auto and Crosscorrelations of ASI St C 3bjl7flCZJ xi AR2 with roots 7 and p b 77 p ASr l ASz z ASz 3 sz l sz z sz 3 05 1 05 027 014 007 028 014 007 08 052 042 034 056 044 036 09 1 05 005 003 001 006 003 001 08 009 007 006 013 011 009 095 1 05 003 001 001 003 001 001 08 004 004 003 007 005 004 090 090 05 004 001 003 002 003 005 090 095 05 005 001 001 004 000 002 095 095 05 002 000 001 001 002 003 095 099 05 002 001 000 003 001 000 How do we validate the models Engel and West suggest that the exchange rate should have forecasting power for future fundamentals Indeed there is a wellknown methodology for testing presentvalue models derived by Campbell and Shiller JPE 1987 They exploit the fact that if the true model is st a2 bJ39Eth then st should contain all the information relevant j0 for forecasting the sum aijxH That is at time I only st should be used in J390 forecasting aijxH They show how we can test the restriction that the J390 best forecast of aijxt J390 is given by st j Engel and West argue that the CampbellShiller methodology is too stringent because it applies to models where we can measure exactly the fundamental xt In exchange rate models some fundamentals are unobserved or mismeasured So EngelWest propose testing the weaker restriction which is just that the exchange rate contains useful information in forecasting future values of xt They test whether the exchange rate Granger causes xt They find weak evidence in favor of this hypothesis The exchange rate seems to be useful in forecasting some fundamentals for some countries but the success is not uniform They conclude that we should not judge models by whether the model is useful in forecasting the exchange rate But the model is supported by evidence that the exchange rate forecasts the future fundamentals Critigue of EngelWest l The most obvious problem is the one just mentioned that the exchange rate doesn t do all that well in forecasting future fundamentals 2 It is possible that the theorem really does not apply to most models after all In particular if uncovered interest parity does not hold the behavior of the exchange rate may not depend much on the economic fundamentals as b gt 1 Let me explain by way of an example using the monetary model To recall we started with mt pt m plit We then used uncovered 1nterest parity It It 2 E s t H1 st to wr1te mt mt qt St lEtStl St Instead though let s assume there is a deviation from uncovered interest parity 0 that represents a foreign exchange risk premium or a liquidity premium or maybe a deviation from rational expectations lt lt ESHI St 10t39 t Then we have mt mt qt St iEtStl St 10t Then the exchange rate model is written as s m m L LES t t 1 qt ttl Iterating forward we get 00 j w 139 St I li39l lljlur7 1 0 11 J 1 0 11 J gtllt where x E m m qt as before This can be rewritten as s 1 bijEtxHj 19219115ij j0 r0 As Engel and West note if the second term is present then as b gt 1 it becomes increasingly important relative to the rst term As I gt 1 the behavior of 0 dominates This is problematic for two reasons 1 0 is unobserved So we have a model where the main driving force of the exchange rate is not observed 2 Most people would think 0 is stationary If it is stationary the EngelWest theorem does not apply though if its largest root is close to one the EngelWest theorem still may apply approximately Example St 1 bm but bEZS1 Amt Amz 1 I AI 7Auz 1 8r gt ASIIZMAmI 1 1 b 1 b uz1 Al 197 8H1 1 b7 1 b1 b7 1 Ifluz 0 then as b gt 1 ASI1 gt nut If yr 7 0 then as b gt 1 Asz1 gt large number x 8H1 NOTE s is n0t a random walk unless b gt 1

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