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Exchange rates, monetary policy, and the international transmission mechanism Betts, Caroline M. 1994

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EXCHANGE RATES, MONETARY POLICY, ANDTHE INTERNATIONAL TRANSMISSIONMECHANISMbyCAROLINE M. BETTSBA. (ions.), University of Durham, 1987M.A., Queens University, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(Department of Economics)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1994® Caroline Marie Betts, 1994in presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_____________________Department of CCOVOvAi’CThe University of British ColumbiaVancouver, CanadaDate__________________DE4 (2188)AbstractThe three chapters of this thesis address two questions. First, how are real and nominal exchangerates between different national currencies determined? Second, how does this determination influence the international transmission of macroeconomic fluctuations and, especially, monetary policydisturbances?Chapter 1 comprises an empirical evaluation of long-run purchasing power parity as a theory ofequilibrium nominal exchange rate determination for the post-Bretton Woods data. Structural timeseries methods are used to identify bivariate moving average representations of nominal exchangerates and relative goods prices and to test whether these empirical representations are consistentwith the implications of purchasing power parity. Long-run purchasing power parity can be unambiguously rejected for the G- 7 countries. There are permanent deviations from parity whichaccount for almost all of the variance of real exchange rates, and which are driven by permanentdisturbances to nominal rates which are never reflected in relative goods prices.Chapter 2 presents an empirical evaluation of the hypothesis that the global Depression of the1930’s was attributable to international transmission of (idiosyncratic) U.S. monetary policy actionsthrough the International Gold Exchange Standard - fixed exchange rate - regime. Specifically, theanalysis evaluates whether the interwar output collapse in Canada was caused by transmitted U.S.monetary policy disturbances. A multivariate structural time series representation of the Canadian macroeconomy is estimated which is consistent with the dynamic and long-run equilibriumproperties of a Mundell- Fleming small open economy model and in which U.S. data represent the‘rest of the world’. The empirical results show that U.S. monetary disturbances play a negligiblerole for both Canadian and U.S. output movements in the 1930’s. Permanent common real shocksto outputs can account for the onset, depth and duration of the Depression in both economies.There is little evidence to support a Gold-Standard transmitted global output collapse through thetransmission mechanisms usually associated with purchasing power parity theories of real exchangerate determination.Chapter 3 develops an alternative theory of real and nominal exchange rate determination andof the international transmision mechanism which can account for many stylized facts regardingthe empirical behaviour of real and nominal exchange rates that long-run purchasing power parityfails to explain. In a two-country, two-currency overlapping generations model, the role of optimalportfolio choices between internationally traded assets is emphasized - rather than goods markettrade - as the source of currency demands. These demands, and supplied of assets generated bydomestic monetary policies, determine both real and nominal exchange rates. Here, monetaryUpolicy changes can induce permanent international and intra-national reallocations through realexchange rate and real interest rate adjustments. This transmission mechanism differs markedlyfrom that implied by purchasing power parity.ifiTable of ContentsAbstract 11Table of Contents ivList of Tables viiList of Figures viiiAcknowledgements XvDedication XViIntroduction 10.1 Overview: Identifying Disturbances ToPurchasing Power Parity 30.2. Overview: A Small Open Economy In Depression:Lessons From Canada In The 1930’s 70.3 Overview: Money, Banking And The DeterminationOf Real And Nominal Exchange Rates 9CHAPTER 1 : Identifying Disturbances To Purchasing Power Parity 131.1 Introduction 131.2 The Maintained Economic Model 171.3 Empirical Representations OfDisturbances To PPP 191.3.1 Univariate Representations 191.3.2 Bivariate Representations 221.3.3 Representation And Identification 231.3.4 Tests Of Long-Run PPP 261.4 Results 281.4.1 Reduced Form Estimation 281.4.2 Structural Model Estimation 291.4.3 Long-Run Multiplier Estimates 291.4.4 Impulse Response Functions 301.4.5 Forecast Error Variance Decompositions 331.5 Conclusion 34ivCHAPTER 2: A Small Open Economy In Depression: Lessons From Canada In The 1930’s 752.1 Introduction 752.2 A Small Open Economy Model 792.2.1 Overview 792.2.2 The Model 802.2.3 Testable Implications Of The Model 842.3 Econometric Methodology 862.3.1 Overview 862.3.2 The Structural Moving Average Representation 862.3.3 Model Specification Tests 892.4 Data Analysis 902.4.1 The Jnterwar Data 912.4.2 Tests For Non-Stationarity And Cointegration 922.5 Identification Of The Empirical Model 952.6 Estimation Results 982.6.1 The Reduced Form Triangular VAR 982.6.2 Computation Of The Structural MAR 992.6.3 The Identified Innovations 992.6.4 Impulse Response Functions 1012.6.5 Forecast Error Variance Decompositions 1032.6.6 Historical Decompositions 1052.6.7 A Note On Robustness 1072.7 Conclusions 107CHAPTER 3: Money, Banking And The Determination Of Real And Nominal Exchange Rates 1373.1 Introduction 1373.2 The Environment 1403.3 Trading, And The Role Of Banks 1423.3.1 The Timing Of Trade 1423.3.2 Bank Behaviour 1433.4 General Equilibrium: Flexible Exchange Rates 1473.4.1 Government Activity 1483.4.2 Asset Markets 1493.4.3 Goods Market Clearing 1503.4.4 The Initial Period 1503.5 Characterization Of Equilibrium: Flexible Exchange Rates 1513.5.1 Steady State Equilibria 1513.5.2 Characterization 1523.5.3 Comparative Statics 1533.5.4 Comparative Statics: Money Growth Rates 1533.5.5 Comparative Statics: Relative Output Levels 1543.5.6 Comparative Statics: Liquidity Preference Parameters 1553.5.7 An Example: The Case Of A Small Open Economy 1553.6 On The Indeterminacy Of The Real Exchange Rate 156V3.6.1 Dynamical Equilibria 1563.6.2 Inflation Rates In Non-Stationary Equilibria 1573.6.3 Nominal Exchange Rate Depreciation 1583.6.4 Discussion 1583.6.5 A Conjecture 1593.7 Fixed Exchange Rates 1593.7.1 Government Activity 1603.7.2 A Steady State Equilibrium 1603.7.3 Comparative Statics 1613.8 Reserve Requirements And Exchange Controls 1633.8.1 Domestic (Small) Country Reserve Requirements 1633.8.2 Foreign (Large) Country Reserve Requirements 1643.8.3 Foreign (Large) Country Exchange Controls 1663.9 Conclusion 168References 173viList of TablesTables for Chapter 1:Table 1.1: Data Sources 36Table 1.2: Reduced Form VECM Results 37Table 1.2a: Error-Correction Terms (CPI’s) 37Table 1.2b: Error Correction Terms (WPI’s) 37Table 1.3: Estimated Long-Run Multipliers 38Table 1.3a: Model (1) Estimates (CPI’s) 38Table 1.3b: Model (1) Estimates (WPI’s) 39Table 1.3c: Model (2) Estimates (CPI’s) 40Table 1.3d: Model (2) Estimates (WPI’s) 41Table 1.3e: Model (3) Estimates (CPI’s) 42Table 1.3f: Model (3) Estimates (WPI’s) 43Table 1.4: Forecast Error Variance Decompositions 44Table 1.4a: Model (1) Estimates (CPI’s) 44Table 1.4b: Model (1) Estimates (WPI’s) 45Table 1.4c: Model (4) Estimates (CPI’s) 46Table 1.4d: Model (4) Estimates (WPI’s) 47Tables for Chapter 2:Table 2.1: Data Sources and Notation 109Table 2.2: Descriptive Statistics 110Table 2.2a: Descriptive Statistics (Log Levels) 110Table 2.2b: Cross Correlation Matrix (Log Levels) 110Table 2.2c: Descriptive Statistics (Log Differences) 111Table 2.3 Non-Stationarity Tests Results 112Table 2.3a: Tests For Non-Stationarity (Log Levels) 112Table 2.3b: Tests For Non-Stationarity (Log Differences) 112Table 2.4: Cointegration Tests Results 113Table 2.4a: Univariate Cointegration Tests 113Table 2.4b: Univariate Cointegration Tests (Constrained Coefficients) 113Table 2.4c: Multivariate Cointegration Tests 113Table 2.4d: Multivariate Cointegrating Vector Estimates 114Table 2.5: VAR Results (1925:1-1939:12) 115Table 2.5a: VAR F-statistics 115Table 2.6: Structural Model (1925:1-1939:12) 116Table 2.6a: Forecast Error Variance Decomposition For Canadian Output 116Table 2.6b:Forecast Error Variance Decomposition For US Output 116Table 2.6c: Forecast Error Variance Decomposition For Canadian Money 117Table 2.6d: Forecast Error Variance Decomposition For US Money 117Table 2.6e: Forecast Error Variance Decomposition For Canadian Prices 118Table 2.6f: Forecast Error Variance Decomposition For US Prices 118vuList of FiguresFigures for Chapter 1:Figure 1.1: 48Figure 1.la: Canada/US Nominal Exchange Rate And Relative CPI’s 48Figure l.lb: France/US Nominal Exchange Rate And Relative CPI’s 48Figure 1.lc: Germany/US Nominal Exchange Rate And Relative CPI’s 48Figure 1.ld: Italy/US Nominal Exchange Rate And Relative CPI’s 48Figure l.le: Japan/US Nominal Exchange Rate And Relative CPI’s 48Figure l.lf: UK/US Nominal Exchange Rate And Relative CPI’s 48Figure 1.2: 49Figure 1.2a: Canada/US Nominal Exchange Rate And Relative WPI’s 49Figure 1.2b: France/US Nominal Exchange Rate And Relative WPI’s 49Figure 1.2c: Germany/US Nominal Exchange Rate And Relative WPI’s 49Figure 1.2d: Italy/US Nominal Exchange Rate And Relative WPI’s 49Figure 1.2e: Japan/US Nominal Exchange Rate And Relative WPI’s 49Figure 1.2f: UK/US Nominal Exchange Rate And Relative WPI’s 49Figure 1.3: 50Figure 1.3a: Canada/US Real Exchange Rate 50Figure 1.3b: France/US Real Exchange Rate 50Figure 1.3c: Germany/US Real Exchange Rate 50Figure 1.3d: Italy/US Real Exchange Rate 50Figure 1.3e: Japan/US Real Exchange Rate 50Figure 1.3f: UK/US Real Exchange Rate 50Figure 1.4: 51Figure 1.4a: Canada/US pp response to permanent p.-p shock 51Figure 1.4b: Canada/US pp response to transitory pp shock 51Figure 1.4c: Canada/US e response to permanent pp shock 51Figure 1.4d: Canada/US e response to transitory p.-p shock 51Figure 1.4e: Canada/US ep+p* response to permanent pp shock 51Figure 1.4f: Canada/US ep+p* response to transitory pp shock 51Figure 1.4(wp): 52Figure 1.4(wp)a: Canada/US pp response to permanent pp shock 52Figure 1.4(wp)b: Canada/US pp* response to transitory pp* shock 52Figure 1.4(wp)c: Canada/US e response to permanent pp* shock 52Figure 1.4(wp)d: Canada/US e response to transitory pp shock 52Figure 1.4(wp)e: Canada/US ep+p* response to permanent pp< shock 52Figure 1.4(wp)f: Canada/US ep+p* response to transitory pp shock 52vii-’Figure 1.5:Figure 1.5a: France/US pp* response to permanent pp shockFigure 1.5b: France/US p—p response to transitory pp* shockFigure 1.5c: France/US e response to permanent pp* shockFigure 1.5d: France/US e response to transitory p.-p shockFigure 1.5e: France/US ep+p* response to permanent pp shockFigure 1.5f: France/US ep+p* response to transitory pp shockFigure 1.5(wp):Figure 1.5(wp)a: France/US pp* response to permanent pp shockFigure 1.5(wp)b: France/US pp response to transitory p-p shockFigure 1.5(wp)c: France/US e response to permanent pp shockFigure 1.5(wp)d: France/US e response to transitory pp shockFigure L5(wp)e: France/US ep+p* response to permanent pp shockFigure 1.5(wp)f: France/US epIp* response to transitory pp shockFigure 1.6:Figure 1.6a:Figure 1.6b:Figure 1.6c:Figure 1.6d:Figure 1.6e:Figure 1.6f:Figure 1.6(wp):Figure 1.6(wp)a:Figure 1.6(wp)b:Figure 1.6(wp)c:Figure 1.6(wp)d:Figure 1.6(wp)e:Figure 1.6(wp)f:Figure 1.7:Figure 1.7a: Italy/US pp response to permanent pp’ shockFigure 1.7b: Italy/US pp response to transitory pp shockFigure 1.7c: Italy/US e response to permanent pp shockFigure 1.7d: Italy/US e response to transitory pp’ shockFigure 1.7e: Italy/US ep+p* response to permanent pp shockFigure 1.7f: Italy/US ep+p* response to transitory pp shockFigure 1.7(wp):Figure 1.7(wp)a: Italy/US pp response to permanent pp shockFigure 1.7(wp)b: Italy/US pp* response to transitory pp shockFigure 1.7(wp)c: Italy/US e response to permanent pp shockFigure 1.7(wp)d: Italy/US e response to transitory pp’ shockFigure 1.7(wp)e: Italy/US ep+p* response to permanent pp shockFigure 1.7(wp)f: Italy/US ep+p* response to transitory pp shockGermany/US p-.p response to permanent pp shockGermany/US pp response to transitory pp shockGermany/US e response to permanent pp shockGermany/US e response to transitory pp shockGermany/US ep+p* response to permanent pp shockGermany/US ep+p* response to transitory pp shockGermany/US p-p response to permanent pp shockGermany/US pp* response to transitory pp shockGermany/US e response to permanent pp” shockGermany/US e response to transitory pp shockGermany/US ep+p* response to permanent pp* shockGermany/US ep+p* response to transitory pp* shock535353535353535454545454545455555555555555565656565656565757575757575758585858585858ixFigure 1.8: 59Figure 1.8a: Japan/US pp response to permanent pp< shock 59Figure 1.8b: Japan/US pp response to transitory pp’ shock 59Figure 1.8c: Japan/US e response to permanent pp shock 59Figure 1.8d: Japan/US e response to transitory pp* shock 59Figure 1.8e: Japan/US ep+p* response to permanent pp shock 59Figure 1.8f: Japan/US ep+p* response to transitory pp* shock 59Figure 1.8(wp): 60Figure 1.8(wp)a: Japan/US pp’ response to permanent p..p* shock 60Figure 1.8(wp)b: Japan/US pp response to transitory pp shock 60Figure 1.8(wp)c: Japan/US e response to permanent pp< shock 60Figure 1.8(wp)d: Japan/US e response to transitory pp shock 60Figure 1.8(wp)e: Japan/US ep+p* response to permanent pp shock 60Figure 1.8(wp)f: Japan/US ep+p* response to transitory p.p shock 60Figure 1.9: 61Figure 1.9a: UK/US pp* response to permanent pp* shock 61Figure 1.9b: UK/US pp response to transitory pp shock 61Figure 1.9c: UK/US e response to permanent p-.p shock 61Figure 1.9d: UK/US e response to transitory pp shock 61Figure 1.9e: UK/US ep+p* response to permanent p..p shock 61Figure 1.9f: UK/US ep+p* response to transitory pp shock 61Figure 1.9(wp): 62Figure 1.9(wp)a: UK/US pp response to permanent pp shock 62Figure 1.9(wp)b: UK/US pp response to transitory p-p shock 62Figure 1.9(wp)c: UK/US e response to permanent pp* shock 62Figure 1.9(wp)d: UK/US e response to transitory p.-p shock 62Figure 1.9(wp)e: UK/US ep+p* response to permanent pp shock 62Figure 1.9(wp)f: UK/US e=p+p* response to transitory pp* shock 62Figure 1.10: 63Figure 1.lOa: Canada/US pp< response to permanent pp shock 63Figure 1.lOb: Canada/US pp response to transitory pp* shock 63Figure 1.lOc: Canada/US ep+p* response to permanent pp shock 63Figure 1.lOd: Canada/US ep+p* response to transitory pp shock 63Figure 1.10(wp): 64Figure 1.10(wp)a: Canada/US pp response to permanent p—pt shock 64Figure 1.10(wp)b: Canada/US pp response to transitory p-.p shock 64Figure 1.10(wp)c: Canada/US epfp* response to permanent pp shock 64Figure 1.10(wp)d: Canada/US ep+p* response to transitory pp shock 64xFigure 1.11: 65Figure 1.lla: France/US p—p response to permanent pp shock 65Figure 1.llb: France/US pp response to transitory pp shock 65Figure 1.llc: France/US ep+p* response to permanent pp shock 65Figure 1.lld: France/US epFp* response to transitory pp shOck 65Figure 1.11(wp): 66Figure 1.11(wp)a: France/US pp”< response to permanent pp shock 66Figure 1.11(wp)b: France/US pp response to transitory pp shock 66Figure 1.11(wp)c: France/US ep+p* response to permanent pp shock 66Figure 1.11(wp)d: France/US ep+p* response to transitory pp* shock 66Figure 1.12: 67Figure 1.12a: Germany/US pp* response to permanent pp shock 67Figure 1.12b: Germany/US pp response to transitory pp’ shock 67Figure 1.12c: Germany/US ep+p* response to permanent pp shock 67Figure 1.12d: Germany/US ep+p* response to transitory pp shock 67Figure 1.12(wp): 68Figure 1.12(wp)a: Germany/US pp response to permanent pp> shock 68Figure 1.12(wp)b: Germany/US pp’ response to transitory pp< shock 68Figure 1.12(wp)c: Germany/US ep+p* response to permanent pp shock 68Figure 1.12(wp)d: Germany/US ep+p* response to transitory pp shock 68Figure 1.13: 69Figure 1.13a: Italy/US p-pt response to permanent pp shock 69Figure 1.13b: Italy/US pp response to transitory pp shock 69Figure 1.13c: Italy/US ep+p* response to permanent pp shock 69Figure 1.13d: Italy/US ep+p* response to transitory p-.p shock 69Figure 1.13(wp): 70Figure 1.13(wp)a: Italy/US pp response to permanent pp shock 70Figure 1.13(wp)b: Italy/US pp response to transitory pp shock 70Figure 1.13(wp)c: Italy/US ep+p* response to permanent pp shock 70Figure 1.13(wp)d: Italy/US ep+p* response to transitory p.-p shock 70Figure 1.14: 71Figure 1.14a: Japan/US pp response to permanent ppK shock 71Figure 1.14b: Japan/US pp response to transitory pp shock 71Figure 1.14c: Japan/US ep+p* response to permanent pp shock 71Figure 1.14d: Japan/US eplp* response to transitory pp shock 71Figure 1.14(wp): 72Figure 1.14(wp)a: Japan/US pp’ response to permanent p..p shock 72Figure 1.14(wp)b: Japan/US pp response to transitory pp shock 72Figure 1.14(wp)c: Japan/US ep+p* response to permanent pp shock 72Figure 1.14(wp)d: Japan/US ep+p* response to transitory pp shock 72xiFigure 1.15:Figure 1.15a: UK/US p..p response to permanent pp shockFigure 1.15b: UK/US pp response to transitory p-.p shockFigure 1.15c: UK/US ep+p* response to permanent pp> shockFigure 1.15d: UK/US ep+p* responseto transitory pp’ shockFigure 1.15(wp):Figure 1.15(wp)a:Figure 1.15(wp)b:Figure 1.15(wp)c:Figure 1.15(wp)d:Figures for Chapter 2:UK/US pp* response to permanent pp shockUK/US pp* response to transitory pp shockUK/US ep+p* response to permanent pp* shockUK/US ep+p* response to transitory pp shockIndustrial Production IndicesMl Velocity Indices‘Wholesale Price IndicesMl Money Stock IndicesCommon Currency Price IndicesCommon Currency Ml IndicesPermanentPermanentPermanentTransitoryTransitoryFigure 2.1:Figure 2.la:Figure 2.lb:Figure 2.lc:Figure 2.ld:Figure 2.le:Figure 2.lf:Figure 2.2:Figure 2.2a:Figure 2.2b:Figure 2.2c:Figure 2.2d:Figure 2.2e:Figure 2.3:Figure 2.3a:Figure 2.3b:Figure 2.3c:Figure 2.3d:Figure 2.3e:Figure 2.4:Figure 2.4a:Figure 2.4b:Figure 2.4c:Figure 2.4d:Figure 2.4e:Figure 2.5:73737373737474747474120120120120120120120121121121121122122123123123123124124123123123123124124125125125125126126Supply ShockMoney ShockVelocity ShockU.S. ShockCanadian ShockTo Supply ShockTo Money ShockTo Velocity ShockTo U.S. Transitory ShockTo Cdn. Transitory ShockYc ResponseYc ResponseYc ResponseYc ResponseYc ResponseYus Response To Supply ShockYus Response To Money ShockYus Response To Velocity ShockYus Response To U.S. Transitory ShockYus Response To Cdn. Transitory ShockMc Response To Supply ShockMc Response To Money ShockMc Response To Velocity ShockMc Response To U.S. Transitory ShockMc Response To Cdn. Transitory ShockFigureFigureFigureFigureFigure2.5a:2.5b:2.5c:2.5d:2.5e:Figure 2.6: 125Figure 2.6a: Mus Response To Supply Shock 125Figure 2.6b: Mus Response To Money Shock 125Figure 2.6c: Mus Response To Velocity Shock 125Figure 2.6d: Mus Response To U.S. Transitory Shock 126Figure 2.6e: Mus Response To Cdn. Transitory Shock 126Figure 2.7: 127Figure 2.7a: Pc Response To Supply Shock 127Figure 2.7b: Pc Response To Money Shock 127Figure 2.7c: Pc Response To Velocity Shock 127Figure 2.7d: Pé Response To U.S. Transitory Shock 128Figure 2.7e: Pc Response To Cdn. Transitory Shock 128Figure 2.8: 127Figure 2.8a: Pus Response To Supply Shock 127Figure 2.8b: Pus Response To Money Shock 127Figure 2.8c: Pus Response To Velocity Shock 127Figure 2.8d: Pus Response To U.S. Transitory Shock 128Figure 2.8e: Pus Response To Cdn. Transitory Shock 128Figure 2.9: 129Figure 2.9a: Pc-Pus-e Response To Supply Shock 129Figure 2.9b: Pc-Pus-e Response To Money Shock 129Figure 2.9c: Pc-Pus-e Response To Velocity Shock 129Figure 2.9d: Pc-Pus-e Response To U.S. Transitory Shock 129Figure 2.9e: Pc-Pus-e Response To Cdn. Transitory Shock 129Figure 2.10: 130Figure 2.lOa: Yc Historical Decomposition (Supply) 130Figure 2.lOb: Yc Historical Decomposition (Money) 130Figure 2.lOc: Yc Historical Decomposition (Velocity) 130Figure 2.lOcl: Yc Historical Decomposition (U.S. Transitory) 131Figure 2.lOe: Yc Historical Decomposition (Cdn. Transitory) 131Figure 2.11: 130Figure 2.lla: Yus Historical Decomposition (Supply) 130Figure 2.llb: Yus Historical Decomposition (Money) 130Figure 2.llc: Yus Historical Decomposition (Velocity) 130Figure 2.lld: Yus Historical Decomposition (U.S. Transitory) 131Figure 2.lle: Yus Historical Decomposition (Cdn. Transitory) 131Figure 2.12: 132Figure 2.12a: Mc Historical Decomposition (Supply) 132Figure 2.12b: Mc Historical Decomposition (Money) 132Figure 2.12c: Mc Historical Decomposition (Velocity) 132Figure 2.12d: Mc Historical Decomposition (U.S. Transitory) 133Figure 2.12e: Mc Historical Decomposition (Cdn. Transitory) 133xmFigure 2.13: 132Figure 2.13a: Mus Historical Decomposition (Supply) 132Figure 2.13b: Mus Historical Decomposition (Money) 132Figure 2.13c: Mus Historical Decomposition (Velocity) 132Figure 2.13d: Mus Historical Decomposition (U.S. Transitory) 133Figure 2.13e: Mus Historical Decomposition (Cdn. Transitory) 133Figure 2.14: 134Figure 2.14a: Pc Historical Decomposition (Supply) 134Figure 2.14b: Pc Historical Decomposition (Money) 134Figure 2.14c: Pc Historical Decomposition (Velocity) 134Figure 2.14d: Pc Historical Decomposition (U.S. Transitory) 135Figure 2.14e: Pc Historical Decomposition (Cdn. Transitory) 135Figure 2.15: 134Figure 2.15a: Pus Historical Decomposition (Supply) 134Figure 2.15b: Pus Historical Decomposition (Money) 134Figure 2.15c: Pus Historical Decomposition (Velocity) 134Figure 2.15d: Pus Historical Decomposition (U.S. Transitory) 135Figure 2.15e: Pus Historical Decomposition (Cdn. Transitory) 135Figure 2.16: 136Figure 2.16a: Yc Permanent Component 136Figure 2.16b: Yc Total Transitory Component 136Figure 2.17: 136Figure 2.17a: Yus Permanent Component 136Figure 2.17b: Yus Total Transitory Component 136Figures for Chapter 3:Figure 3.1: Timing Of Transactions 170Figure 3.2: Determination Of A Steady State Equilibrium 171Figure 3.3: An Increase In 171Figure 3.4: An Increase In o 172Figure 3.5: Dynamical Equilibria 172xivAcknowledgementsI would like to thank my thesis committee members, Michael B,. Devereux, James M. Nason andAngela Redish, and Michael D. Bordo and Bruce B. Smith for their guidance, support, valuablecomments and suggestions. In addition, I am grateful for useful comments and suggestions to;Brendan McCabe, Jeremy Rudin and Timothy Vogelsang who gave advice on the the first chapterof this thesis; Lawrence Shembri, Deborah Glassman and seminar participants at the 1993 AnnualMeetings of the Canadian Economics Association in Ottawa, the 1993 Canadian MacroeconomicsStudy Group Meetings in Victoria and the 1993 Conference on Monetary History at Cornell University regarding the second chapter; and, concerning the third Chapter, David Backus, ShouyongSki, Henry Wan and seminar participants at the Board of Governors of the Federal Reserve System>at Concordia, Cornell, Duke, Edinburgh, MacMaster, McGffl, Miami, Queens, Rutgers, SouthernIllinois, Toronto, U.S.C. and Wayne State Universities, at the 1994 Annual Meetings of the Canadian Economics Association in Calgary, and the 1994 Annual Meetings of the Society for EconomicDynamics and Control.xvI dedicate this thesis to my family.xvi0 IntroductionThe three chapters of this thesis each address some dimension of the following two questions.First, how are real and nominal exchange rates between different countries’ currencies determined?Second, what is the role of this determination in the international transmission of macroeconomicfluctuations and, especially, monetary policy disturbances?The hypothesis of purchasing power parity dominates contemporary international macroeconomic analysis as a theory of real and nominal exchange rate determination. That free international trade in consumption goods ultimately determines the relative prices of the flat currencies ofdifferent countries is a key implication of most two-country (monetary) models of nominal exchangerate determination and international fluctuations. More generally, many international macroeconomic models assume that international goods market arbitrage wifi equalize the common currencyprice of a given basket of goods in spatially separated economies under either market determinedor institutionally fixed nominal exchange rates. Under this assumption, there are no disturbancesthat (permanently) move the real exchange rate from its (initial) mean value of unity. Equivalently,there are no (permanent) disturbances to purchasing power parity. (Of course, under flexible ratesit is the nominal exchange rate that adjusts to re-establish parity following disturbances to relative goods prices, while under fixed rates the work of re-adjustment to parity is achieved throughnational price level movements.)In addition, the assumption that purchasing power parity holds under any given nominal exchange rate regime implies that a particular set of mechanisms operate for the international transmission of macroeconomic disturbances. These implications, also, are reflected in most contemporary analyses of international business cycles.It has long been accepted that parity values for common currency goods’ prices will not be observed to hold instantaneously. Purchasing power parity is now typically viewed (in fact, generatedby general equilibrium two-country models) as a ‘long-run’ or steady state relationship; as one thatholds in the absence of changes in fundamental macroeconomic variables. Yet there exists mixedevidence on the validity of this theory of (long-run) real and nominal exchange rate determination.Alternative methods for the empirical evaluation of long-run purchasing power parity have beenemployed and applied to various data sets with mixed and sometimes ambiguous results. Further,casual observation suggests that, for the post-Bretton Woods flexible exchange rate era, real andnominal exchange rates move together very closely and appear to be approximately equally volatile.This observation may be viewed as a manifestation of the failure of purchasing power parity in thisdata. Finally, the behaviour of real exchange rates not only fails to accord with purchasing power1parity doctrine during many different exchange rate regimes, but it also significantly differs acrossregimes. This, again, is inconsistent with the presence of regime-invariant parity relations betweencommon currency goods prices.In this thesis I study a number of aspects of exchange rate determination - both empirically andtheoretically- and its implications for international transmission of monetary and real economicdisturbances across countries, with a view to evaluating the validity of purchasing power paritytheory.Chapter 1 comprises an empirical evaluation of long-run purchasing power parity as a theoryof equilibrium nominal exchange rate determination in the post-Bretton Woods data. Structuraltime-series methods are used to identify bivariate stochastic representations of nominal exchangerates and relative goods prices and to test whether these are consistent with the implications ofpurchasing power parity. The bivariate representations are capable of separately identifying anddirectly measuring transitory and permanent shocks to real and nominal exchange rates and to relative prices. Using these methods, the hypothesis of purchasing power parity can be unambiguouslyrejected for the G-7 countries and I find that sources of real and nominal exchange rate variationare orthogonal to sources of relative goods price movements. There are permanent deviations frompurchasing power parity which account for almost all of the variance of real exchange rates in thissample at forecast horizons exceeding six to twelve months. These deviations are almost entirelydriven by permanent disturbances to nominal exchange rates which do not affect relative prices atany horizon.Chapter 2 comprises an empirical evaluation of the hypothesis that aggregate fluctuations in theU.S., and U.S. monetary policy actions in particular, were the source of the inter-war Depressionexperience of Canada. Specifically, using Canada as a case-study the paper assesses the pre-eminentview that the international nature of the Great Depression can be explained by transmission ofsuch U.S. monetary policy disturbances through prices under the fixed nominal exchange rate(International Gold Standard) regime.A multivariate structural time-series model is estimated of the Canadian macroeconomy. Thisempirical representation is consistent with the long-run and dynamic implications of a standardsmall open economy model in which the U.S. represents the ‘rest of the world’ relative to Canada andin which Canada is assumed to be on a fixed nominal exchange rate. Weak (or relative) purchasingpower parity is found to hold here, but the disturbances identified with U.S. monetary policy shocksappear to play an insignificant role for even short-run output fluctuations in Canada. While thesepolicy disturbances strongly influence the time-paths of both Canadian and U.S. money and prices2they have no significant real balance, relative price (real exchange rate) or output effects. It is notpossible to identify aggregate fluctuations m this small, open economy with externally originatingmacroeconomic disturbances that are transmitted through a mechanism associated with the fixedexchange rate (long-run purchasing power parity) regime. These results are, of course, predicatedon an empirical representation that assumes the existence of such mechanisms.Chapter 3 presents an alternative theory of real and nominal exchange rate determinationthat can account for the stylized facts of real and nominal exchange rate behaviour that long-run purchasing power parity fails to explain. In the model presented, the role of optimal portfoliochoices between internationally traded assets is emphasized as the source of demands for alternativecurrencies, rather than international trade in consumption goods. The consequences of changes inmonetary policy, the nominal exchange rate regime, and financial market regulations for real andnominal exchange rates and for asset returns are studied. The results suggest that there existimportant mechanisms for domestic and international reallocations through these media whichsignificantly differ from those associated with purchasing power parity theories of exchange ratedetermination. In particular, the role of monetary policy in international transmission for aneconomy where asset market interactions dominate exchange rate determination is quite differentfrom that typically assumed; in fact, here monetary policy can generate permanent internationaland intra-national reallocations through real exchange rate and real interest rate adjustments.The model presented in Chapter 3 suggests that future empirical evaluation of the determinantsof real and nominal exchange rates, and empirical work designed to identify sources of internationaltransmission of macroeconomic disturbances, should account for variables, relationships and transmission mechanisms that are not illuminated by purchasing power parity theories of exchange rates.The following overviews provide more detailed description of the three Chapters.0.1 Overview: ‘Identifying Disturbances To Purchasing Power Parity’In Chapter 1, titled ‘Identifying Disturbances To Purchasing Power Parity’, a new methodologyfor identifying disturbances to real exchange rates is proposed. This allows both an evaluation ofthe Casselian purchasing power parity hypothesis and identification of specific sources of deviationsfrom bilateral parity relations between nominal exchange rates and relative goods prices. Thepaper critiques existing univariate tests of purchasing power parity. The empirical implications ofpurchasing power parity for the bivariate time-series properties of the nominal exchange rate andrelative prices are described and an associated bivariate econometric representation is presented.A methodology for testing long-run purchasing power parity is derived that uses these bivariaterepresentations and this is applied to data from the floating exchange rate period for the G-73countries.Equilibrium models of exchange rate determination that deliver purchasing power parity as asteady state relationship have the following empirical implications. First, any permanent stochasticdisturbance to relative goods prices (due to permanent shocks to relative money stocks and outputs,for example) is both equally and permanently reflected in the nominal exchange rate. Second, anyother disturbance to relative prices or nominal exchange rates should be purely transitory for bothvariables. Consequently, nominal exchange rates and relative prices should be observed empiricallyto share a common stochastic trend, and the real exchange rate should exhibit mean reversion orpurely transitory dynamics around a fixed mean. Empirical evidence for such mean reversion ismixed.Application of standard univariate tests of mean reversion to real exchange rate data dominatesempirical evaluation of long-run purchasing power parity. Yet it is well known that such tests havelow power to discriminate between variables which exhibit high degrees of persistence and thosethat have permanent components. In particular, we know that any univariate series found to benon-stationary by such tests comprises both a permanent and a transitory component with theformer having arbitrarily small variance. Univariate tests cannot inform on the relative size ofthese permanent and transitory components in non-stationary univariate data series. Such testsare, therefore, argued to be uninformative for evaluating long-run purchasing power parity.An alternative method for testing purchasing power parity is proposed. This involves identification of a bivariate structural moving average representation for the nominal exchange rate andrelative prices which is consistent with, but does not impose, the maintained hypothesis of long-runpurchasing power parity. This representation can express the current level of the nominal exchangerate and of relative prices as the outcome of contemporaneous and historical realizations of twofundamental disturbances. In particular, it decomposes the variance of these two variables intosources due to permanent and purely transitory disturbances, and allows direct measurement ofthe relative importance of each type of disturbance for the variance of the real exchange rate.The common stochastic trend implication of purchasing power parity implies that the reducedform parameterization of this bivariate system takes the form of a vector error correction model.This is estimated and inverted to generate a reduced form moving average representation. Purchasing power parity is then evaluated in the following ways.A structural moving average representation of an equilibrium exchange rate model can alwaysbe identified from a reduced form representation by imposing restrictions on the long-run responsesof the nominal exchange rate and relative prices to particular types of disturbance. First, by im4posing the restriction that relative prices have a zero long-run (infinite horizon) response to oneshock, an empirical representation is derived which decomposes fluctuations in nominal exchangerates and relative prices into sources due to disturbances which permanently affect relative pricesand to disturbances which only transitorily affect relative prices. Under the maintained model, permanent relative price disturbances should have an equal permanent effect on the nominal exchangerate. Transitory relative price disturbances should induce purely transitory nominal exchange ratedynamics. Inspection of the estimated long-run multiplier matrix for the moving average providesa (weak) test of the satisfaction of these conditions. Analysis of the impulse response functions ofthe two variables and of their forecast error-variance decompositions then informs on whether anypermanent real exchange rate disturbances found, due to the failure of either of these conditions,are large and significant.Alternative decompositions are also considered. A permanent-transitory decomposition forthe nominal exchange rate should deliver identical results as that for relative prices under themaintained hypthesis. A decomposition which imposes an equal long-rim effect for both variablesof one disturbance should deliver an equal (possibly zero) effect for both variables of the seconddisturbance. Finally, purchasing power parity can be imposed directly on the bivariate system andthe implied short-run dynamics of the system inspected for their consistency with theory. In fact,under the maintained hypothesis that long-run purchasing power parity holds, these four alternativerepresentations should be identical (subject to sampling error).The models are estimated and small sample statistical inference based on standard errors andbiases computed by Monte Carlo integration. The following empirical results are obtained formonthly data over the sample period 1975:1-1991:12. For no G-7 country does purchasing powerparity hold according to the criteria discussed for bilateral nominal exchange rates against the $US.This is true whether consumer prices or wholesale and producer prices are employed. Some strikingempirical regularities are found.While permanent shocks to relative prices typically do have approximately equal long-run effectsfor nominal exchange rates, such disturbances account for a negligible fraction of nominal andreal exchange rate variance. However, for all countries there are large and significant permanentmovements of the nominal exchange rate due to shocks which are identified as purely transitory forrelative prices. In fact, these transitory relative price disturbances insignificantly affect (the varianceof) relative prices at all horizons, yet they can account for more than 50% of both nominal and realexchange rate variation in every case. There is, then, a large and significant permanent componentin real exchange rates due to disturbances that never affect relative goods prices but generate5almost all nominal exchange rate fluctuations. It is such nominal exchange rate disturbances thatcan account for the empirical observation that real and nominal exchange rates are approximatelyequally volatile.These results are mirrored in decompositions that impose equal long-run effects for one of thetwo disturbances for nominal exchange rates and relative prices; this disturbance turns out tobe exactly (has identical properties to) the permanent shock to relative prices identified in thepermanent/transitory relative price decompositions.In the permanent/transitory nominal exchange rate decompositions, both the identified permanent and transitory disturbances to the nominal exchange rate cause permanent deviations frompurchasing power parity. This decomposition generates permanent relative price responses following both types of nominal rate disturbance, while the variance of nominal exchange rates isprimarily attributable to permanent nominal exchange rate shocks. These results are consistentwith the preceding finding that nominal exchange rates and relative prices do not share a commonpermanent component, and with the previous observation that relative price movements appear tobe driven at both short and long horizons by (their cown) permanent disturbances.Finally, the decomposition that imposes long-run purchasing power parity generates transitoryrelative price shocks with very long-lived effects for real exchange rates, and which induce exchangerate and relative price dynamics that are difficult to reconcile with theory.The results suggest that sources of variance in exchange rates and relative prices are orthogonal.Permanent deviations from purchasing power parity are observed, in almost every sample studied,due to permanent nominal exchange rate shocks which do not affect relative prices at any horizon.Some extensions of the empirical investigation are considered. In particular, finer decompositions of variance might allow a more structural interpretation of the permanent nominal and realexchange rate shocks identified here. For example, decompositions of exchange rate variation usingdata on (relative) money stocks and outputs to identify explicitly monetary and real disturbancesmay be appropriate. Moreover, as shown in Blanchard and Quah (1989), results derived frombivariate models are conditional on the appropriateness of an aggregation assumption on the transitory and permanent disturbances identified. If multiple underlying disturbances of either typegenerate different dynamics in the two variables, the assumption that all permanent and all transitory disturbances can be treated as single (average) disturbances is invalid. Richer decompositionsof exchange rate variance could help alleviate this potential misspecification problem, in additionto generating more information on the sources of real and nominal exchange rate determination.60.2 Overview: ‘A Small Open Economy In Depression: Lessons From CanadaIn The 1930’s’In Chapter 2, titled ‘A Small Open Economy In Depression: Lessons From Canada In The 1930’s’,an empirical investigation of the sources of the Great Depression in Canada is conducted. The goalsof the paper are to contribute to the economic history of the Canadian Depression experience andto generate evidence towards an explanation of the international nature of the output collapse inthe 1930’s. In particular, I seek to evaluate the role of the fixed exchange rate regime in propagatingmacroeconomic disturbances across national (economic) borders.It is argued that, because Canada is well characterized as a small open economy, the Canadiandata provide a fertile testing ground for theories regarding international transmission of businesscycle fluctuations. Two facts suggest that especially powerful transmission mechanisms may haveoperated between Canada and the U.S. during the Great Depression. First, the U.S. was Canada’smost important trading partner during the 1930’s and, second, the Canadian govermnent maintained a fixed exchange rate against the U.S. dollar throughout the 1930’s despite the breakdownof the interwar gold exchange standard. Consequently, analysis of Canadian interwar data canpotentially help explain if and how the Depression was propagated internationally from the U.S.economy.Given these observations, the paper addresses three questions. First, what were the sources ofaggregate fluctuations in Canada during the years, 1929-1933, of output collapse ? Second, wereaggregate fluctuations in Canada during this era primarily caused by disturbances transmitted fromthe U.S. economy as the conventional view of the source of international output collapse asserts?Third, if international transmission from the U.S. economy was the source of Canadian outputcollapse, were monetary disturbances identifiable with Federal Reserve policy actions the mostimportant factor, as frequently proposed in explanations both of the U.S. and global Depression ?Two alternative views of the international nature of the Depression are considered and empirically evaluated. First, an extensive literature on the U.S. Depression assumes that the global outputcollapse reflected international transmission through some combination of goods and financial market forces of a recession originating in the U.S., initiated by Federal Reserve stringency in 1928,and exacerbated by financial crises following the Stock Market collapse during which the FederalReserve failed to provide necessary liquidity to the banicing system. In contrast, analyses of theCanadian and European Depression experience, while recognizing the importance of internationaltransmission, also emphasize the role of idiosyncratic factors in each country’s economic history.In the Canadian case, recognition is given to the peculiar vulnerability of the small open economy7to fluctuations in the external demand for her primary export goods. However, structural changesin the late 1920’s reflecting the end of prairie settlement and of the post-war investment boom innew primary manufacturing (processing) industries are also proposed to have induced recession.An empirical representation of the Canadian economy is developed in which Canada is explicitlymodeled as a small open economy on a fixed exchange rate and U.S. data is used to represent the‘rest of the world’. Specifically, a structural moving average representation of the Canadian economyis proposed in which the current values of Canadian variables are described by contemporaneousand historical realizations of a set of macroeconomic disturbances which may originate domestically,externally or be common to the domestic and external economies.Monthly, seasonally adjusted data for the sample period 1925:1-1939:12 on industrial production, the Ml money stock and wholesale prices for the two countries is analyzed prior to estimation.Tests for common stochastic trends in the U.S. and Canadian series reveal that outputs, moneystocks and prices share such trends. Consequently, I can identify three disturbances which haveequal, permanent effects on the levels of Canadian and U.S. variables. The first is interpreted asa common supply shock which drives the long-run trend in output for both economies and whichmay permanently affect both money stocks and price levels. The second is interpreted as a policy-driven money supply shock which generates a nominal long-run trend in each economy. This canbe viewed as the outcome of Federal Reserve policy actions and is transmitted to the Canadianeconomy through the fixed exchange rate. The money supply shock is identified by assuming long-run neutrality of monetary shocks for output. The third is a permanent disturbance to the demandfor real balances in each economy. This is interpretable as a common shock to the demand forliquidity, deriving from common asset market conditions, and is identified by allowing only pricelevel adjustments to this disturbance in the long-run.I also identify two country-specific disturbances by assuming that sources of aggregate fluctuations originating in Canada have no immediate (direct) impact on U.S. variables. These are purelytransitory disturbances which can be interpreted as real expenditure or demand shocks, in the U.S.case, and also as transitory domestic monetary disturbances in the Canadian case.The moving average representation for the six variables of interest is estimated under theseidentifying assumptions. I analyze the estimated structural innovations, the impulse responsefunctions, forecast error variance decompositions and historical decompositions of variance whichare derived from this dynamic representation. The results obtained are as follows.The estimated structural innovations do identify the U.S. monetary contraction in 1928, and theattendant rise in transactions money demand emphasized by Hamilton (1987) and Field (1984).8However these shocks are absorbed by prices and have an insignificant effect on output in bothCanada and the U.S. Similarly, I find evidence in the estimates of deflationary monetary policy in1930, and the historical decompositions reveal a significant unanticipated money stock contractionduring 1931 and 1932 to which Friedman and Schwartz (1963) attribute the depth and persistence ofthe U.S. Depression. Yet the former has no significant output effects in the historical decompositionsand the latter I find to be primarily an endogenous response to the permanent output disturbancesas argued by Temin (1976). Idiosyncratic U.S. demand disturbances during 1929 can be identified,to which Temin (1976) and Romer (1990) attribute significance, but do not induce important outputeffects in either economy. Consequently, these results reject explanations of the global Depressionwhich emphasize international transmission of autonomous monetary and real disturbances uniqueto the U.S. economy.I find that the onset, depth and persistence of the Depression in both Canada and the U.S.is attributable to the common, permanent output (supply) shock leaving little significant role foridiosyncratic disturbances in either economy. From 1929-1936, the twelve month ahead forecasterror in both output series is almost entirely due to this disturbance. Similarly, I find that the levelof output through this sub-sample is almost exclusively accounted for by the cumulative effectsover time of the supply shock. There is a striking symmetry in the behaviour of production in thetwo countries for the Depression subsample.Some interpretations are offered. The results are consistent with Fisher’s (1933) hypothesis thatdeclines in expected and actual productivity initiated both the 1929 U.S. recession and the StockMarket Crash in October of that year. They are also supportive of explanations for the Depressionsuch as Bernstein (1987) and Safarian (1959) that emphasize secular factors, and the importance ofsupply shocks during the 1931-1933 subsample is consistent with Bernanke’s (1983) assertion thatdisruptions to bank intermediated credit during the banking crises had real, long-lived effects forefficiency, productivity and output. While the results interpret the Depression as an international,‘collapse in trend’ event, the underlying source of that trend cannot be uncovered. Finally, it isobserved that if secular factors which were continental, if not global, can explain the Depressionin Canada and the U.S., this provides a potential rationalization for observed synchronicity in thetiming and pattern of international output collapse.0.3 Overview: ‘Money, Banking And The Determination Of Real And NominalExchange Rates’Chapter 3, titled ‘Money, Banking And The Determination Of Real And Nominal Exchange Rates’,presents a theoretical model of real and nominal exchange rate determination. The objective of this9analysis is to develop a model that can account for a number of important stylized facts regardingthe behaviour of real and nominal exchange rates in the post-war data; namely, the failure ofpurchasing power parity and several manifestations of that fact.A two country, single good, pure exchange model is considered in which the single good is non-traded (subject to prohibitive transportation costs). In each country there is a government whichissues both fiat currency and interest-bearing bonds. While trade in goods is limited, internationaltrade in these four assets is unrestricted. It is, then, the monetary policies that control suppliesof these assets, and the demands for assets by private agents in international capital and currencymarkets, that ultimately determine real and nominal exchange rates.The demands for alternative currencies and for bonds are generated by the following mechanism.Within each country there are two, symmetric locations and agents move between domestic andinternational locations stochastically, with stochastic relocation playing the role of liquidity, orportfolio, preference shocks. In particular, if relocated, agents must carry with them currencywhich is assumed to have superior liquidity characteristics over bonds in the presence of spatialseparation and limited communication between locations. Furthermore, inter-location exchangerequires the currency of the country in which the seller is located so that only the currency ofultimate destination is of value to an agent, ex post, if relocated. These assumptions, in anenvironment in which currency is dominated in rate of return by the bonds of each country, inducesex ante portfolio diversification among all four assets in the economy by private agents.In fact, since stochastic relocation plays the role of liquidity preference shocks in the DiamondDybvig (1984) model, banks naturally arise in this economy to insure agents against their randomneeds for currency-specific liquidity; against the risk of premature asset liquidation. To providethis insurance, banks in each country hold both foreign and domestic currencies as reserves and inaddition invest in interest-bearing government bonds.Since trade in goods between countries is limited, purchasing power parity need not hold. Thedetermination of the real exchange rate is examined in a model where all markets are competitiveand clear at each date, all prices are flexible, and all agents have equal access to all asset markets.Real exchange rate determination is analyzed under a variety of policy regimes, including fixed andflexible exchange rates, and regimes which differ with respect to the degree of domestic or foreignbatik regulation and the presence or absence of exchange controls.The results obtained are as follows. Monetary policy, portfolio preference parameters and relative endowments are all fundamentals in any steady state equilibrium for both real and nominalexchange rates. The importance of monetary factors is consistent with recent empirical evidence10supporting an important role for nominal shocks in real exchange rate fluctuations. There is aunique steady state equilibrium under both flexible and fixed exchange rates which is, for identical money growth rates, invariant to the choice of regime. In addition, the choice of nominalexchange rate value under fixed nominal rates has no aflocative consequences and does not affectthe equilibrium real exchange rate at any date.Under a regime of flexible exchange rates, an increase in the rate of growth of the domestic(foreign) money supply causes the real interest rate to rise and generates a real and nominaldepreciation of the domestic (foreign) country’s currency. The former effect is due to the factthat money creation finances debt repayment, while the latter is due to the fact that an increasein the money growth rate of either country taxes the holders of that country’s currency therebyreducing their demand for the goods of that country. Goods markets are re-equilibrated by areal exchange rate movement that raises the purchasing power of foreign (domestic) agents inthe domestic (foreign) economy. In addition, the impact on the initial nominal exchange rate ofmonetary changes is necessarily equal to the impact on the real exchange rate, which is consistentwith the observation that real and nominal exchange rates are approximately equally volatile.Under a regime of fixed exchange rates, an increase in the rate of growth of (all) money suppliestends to move the real exchange rate, but the impact is necessarily smaller than that under a regimeof flexible rates. This finding is consistent with the stylized fact that real exchange rate movementstend to be more pronounced under flexible than under fixed exchange rate regimes.The use of reserve requirements or exchange controls by a foreign country will also influencethe real interest rate and real exchange rate of the domestic country. An increase in the foreigncountry’s reserve requirements (a tightening of the foreign country’s exchange controls) tends toraise (reduce) the world real interest rate and to raise (have an ambiguous effect for) the domesticcountry’s real exchange rate. Both reserve requirements and exchange controls affect the efficacyof monetary policy changes in manipulating real and nominal exchange rates. These results hint atthe importance of reductions in exchange controls and reserve requirements since 1973 in helpingto account for the observed change in real exchange rate behaviour since that date relative to theBretton Woods era.Notably, while the effects of monetary policy changes in the theoretical model can account forthe stylized facts of real and nominal exchange rate behaviour cited here, changes in real factors(relative endowments) have counterfactual properties. The impact on the real exchange rate of achange in relative endowments is identical under fixed and flexible exchange rate regimes, and thereal exchange rate movement induced by such a change is never reflected in nominal exchange rates11under flexible nominal exchange rate regimes.Several extensions of the analysis can be contemplated. These include an investigation of moresophisticated monetary policies, more general utility functions, the introduction of more stochasticelements, and an analysis of a version of the model with production. The latter extension wifipermit an analysis of how output levels, real and nominal exchange rates, and price levels are jointlydetermined. It will thereby make possible statements about how policies that are designed to movereal exchange rates in favour of a particular country affect that country’s level of development.121 CHAPTER 1: Identifying Disturbances To PurchasingPower Parity1.1 IntroductionThe proposition that purchasing power parity (PPP) determines the long-run equilibrium value offreely traded currencies is both a central proposition of traditional open-economy macroeconomicrepresentations and a key implication of equilibrium in many two-country monetary business cyclemodels. This proposition implies that permanent disturbances to relative goods prices should bereflected one-for-one in nominal exchange rates and that nothing else (no transitory price shock)matters at distant horizons for the variance of either variable. Consequently, the real exchangerate (the PPP deviation) should exhibit long-run mean reversion in response to either type ofdisturbance; a long-run neutrality result holds. Yet tests of long-run PPP based on analyses of theunivariate properties of real exchange rates have returned mixed results.Here, bivariate time-series representations of nominal exchange rates and relative prices areused to identify and measure transitory and permanent deviations from PPP. In contrast to univariate models, both the specification and identification of these representations is conditional oninformation derived from economic models that deliver PPP as a long-run equilibrium condition.Consequently, there are a number of well-defined implications for the bivariate system that mustbe satisfied under the maintained hypothesis, each of which takes the form of a long-run neutralityproposition. Application of the bivariate methodology to G- 7 data for the floating exchange rateperiod reveals that several of these neutrality propositions are consistently violated across countriesand that long-run PPP can be rejected without exception.In its strongest form PPP asserts that international goods market arbitrage ensures instantaneous equalization in spatially separated economies of the common currency price of a givencommodity basket. While impediments to free trade in goods may prevent the relation from holding exactly, changes in common currency prices are assumed to be exactly contemporaneouslycorrelated by weaker forms of the doctrine. Under flexible exchange rate regimes, market determined spot currency prices eliminate goods market arbitrage opportunities. Static open economymodels in the spirit of the Mundell-Fleming monetary approach assume satisfaction of such arbitrage conditions, yet casual observation from the floating exchange rate regime reveals that no suchinstantaneous PPP relation holds in the data. Specifically, the data are characterized by volatilecurrency prices which diverge widely and persistently from the parity values implied by relativeprice series.Yet, since at least Cassel (1918) it has been recognized that PPP should be viewed as an equi13librium rather than instantaneous condition for exchange rate determination. Traditional modelsadapted to incorporate dynamics (Dornbusch (1976) and Mussa (1982) are leading examples) implythat any observed divergences from PPP in the data represent purely transitory deviations fromequffibrium. Slower adjustment of goods than asset prices following unpredictable (permanent)macroeconomic disturbances causes nominal exchange rates to overshoot the new fundamentallevel of relative goods prices. Two-country, two currency dynamic general equilibrium models, extending Lucas’s (1982) framework, derive PPP as the implication of an optimal consumption planfor a rational, forward looking agent who transacts in two, distinct goods markets which require theagent to offer different currency units in exchange for goods.’ Equilibrium relative goods prices,and hence nominal exchange rates, are determined endogenously as functions of cross-country differentials in fundamentals; taste, technology and money stock parameters. In the absence of newdisturbances to these fimdamentals this equilibrium is realized.2These models each have a version of PPP as a long-run equilibrium condition for nominalexchange rate determination, while allowing for transitory dynamics from equilibrium characterizedby PPP deviations. While alternative hypotheses exist,3 PPP still dominates as a condition forlong-run exchange rate determination in open economy models.Ultimately, whether PPP can explain real and nominal exchange rate behaviour in the long-runis an empirical issue that cannot be resolved by mere inspection of the data but requires estimationof long-run equilibria. Most tests of long-run PPP have been predicated on the univariate propertiesof the real exchange rate. Such tests use the fact that if equilibrium currency values are pinned downby goods market arbitrage then their long-run (low-frequency) behaviour wifi reflect this. Bilateralnominal exchange rates and relative goods prices should share a common permanent component,or cointegrate in the sense of Granger (1983), and their log difference, the real exchange rate,should be covariance stationary exhibiting purely transitory deviations from mean. A finding of anon-stationary real exchange rate is then taken to imply the failure of long-run PPP.41See, for example, Grill and Roubini (1992) and Schlagenhauf and Wrase (1992a,1992b).2Grilli and Roubini (1992) show how asset market disturbances originating in government open market operationscan generate liquidity effects for equilibrium exchange rates which are ‘non-fundamental’ (have no relative priceeffects). However, these liquidity effects have zero expectation.3See Blanchard and Watson (1982), Meese (1986) and Frankel and Froot (1990) in which rational and irrationalspeculative bubbles in exchange rates are posited as potential explanations for apparent failures of PPP to hold in thedata. In general, models with extrinsic uncertainty can explain volatility of real and nominal exchange rates whichare unrelated to movements in fundamentals with sunspot equilibria.4Studies that employ univariate tests of purchasing power parity are too numerous to document fully. Roll (1979),Meese and Singleton (1982), Adler and Lehmann (1983), Mussa (1986) and Diebold (1988) are among those studiesthat reject long-run PPP with univariate non-stationarity tests applied to real exchange rates. (These tests originate inthe work of Dickey and Fuller (1979, 1981) and Phillips (1987) in particular.) By contrast, Diebold, Husted and Rush(1991), Cheung (1993) and Cheung and Lai (1993) reject the martingale hypothesis in long spans of data, modelingreal exchange rates as long memory but fractionally integrated processes. Huizinga (1987), Kaminsky (1988), and14Yet there are two (now familiar) objections to such a univariate approach which together implythat univariate stationarity tests have (arbitrarily) low power to detect the presence of long-runPPP in the data. First, the low power of standard tests for non-stationarity to discriminatebetween highly persistent and non-stationary time-series has long been recognized.5 In particular,Cochrane (1991) and Quah (1992) demonstrate that any stochastic process which can be identifiedas non-stationary has a permanent component with arbitrarily small variance. Yet univariaterepresentations of such processes can neither identify nor measure the relative size of permanentand transitory components of a series without imposing additional structure on the covarianceproperties of the two components (which derives from information extraneous to the empiricalmodel specified). Consequently, the finding of a non-stationary real exchange rate may have littlestatistical or economic relevance.A second, and related objection, is that univariate methods cannot inform on the sources of PPPdeviations relative to any economic model. In the absence of information that permits structuralinterpretation of the permanent (or long-lived) components frequently found in real exchange rates,univariate tests for stationarity have little insight to offer on the validity of specific theoreticalpropositions regarding exchange rate determination.In this paper, structural vector autoregressions (VAR’s) are used to generate more informativetests of long-run PPP. Long-run neutrality propositions about the effects of alternative disturbancesfor real exchange rates can be straightforwardly evaluated when the maintained model allows forpermanent components in both nominal exchange rates and relative prices. The class of modelsthat delivers PPP as a long-run relation, while having no unique set of implications for transitoryexchange rate and relative price dynamics, does have a unique set of implications for the effects ofpermanent disturbances for relative prices and nominal exchange rates. Specifically, any permanent disturbance to relative goods prices, whether due to monetary or real shocks, has an equalpermanent effect on nominal exchange rates. All other disturbances in this class of models have nopermanent effect for either variable. Long-run PPP therefore implies that two long-run neutralitypropositions should hold for the real exchange rate when nominal rates and relative prices aresubject to permanent disturbances.A bivariate structural moving average representation is identified which expresses these twovariables as the outcome of current and historical realizations of permanent and transitory disturGnu and Kaminsky (1991) find evidence of mean reversion in real rates using univariate variance ratio tests, whileAbuaf and Jorion (1990) following Hakkio (1984) also support long-run PPP when cross-sectional information isincorporated into variance ratio statistics.5See, for example, Schwert (1987) and Gregory (1991) and, in the exchange rate context, Hakkio (1984)15bances to relative prices, which is parameterized as a bivariate VAR of an error-correcting form inrelative goods prices and nominal exchange rates. 6 This allows long-run hypotheses to be testeddirectly. Estimates of the infinite horizon multipliers for permanent and transitory relative priceshocks are derived and inspected with the impulse response functions for evidence that the long-runrestrictions are satisfied. Forecast error-variance decompositions then inform on the relative size ofthe implied transitory and permanent components in real exchange rates.Three other, complementary tests of long-run PPP are conducted. The maintained modelimplies that a bivariate representation in which permanent and transitory disturbances to nominalexchange rates are identified should mirror exactly that in which a permanent/transitory relativeprices variance decomposition is invoked, at least in its long-run behaviour. This representation isestimated and results compared to those from the relative price decomposition described above. Themaintained model also implies that if an underlying structure is identified in which one disturbanceis imposed to have an equal long-run effect on relative prices and nominal exchange rates thenthe second disturbance should also have an equal long-run impact on the two variables which maybe zero. The results from this model should reflect those for the preceding two. Finally, if astructure is identified in which long-run PPP is imposed, the estimated dynamics of that systemshould be reconcilable with at least one standard idea about the effects over time of permanentand transitory relative price shocks in economic models that predict long-run PPP and, under themaintained hypothesis, also should be identical to those generated by the preceding decompositions.Each of these tests is applied to monthly G-7 data for the sample period 1975:1-1991:12. The$US is used as the numeraire (foreign country) currency in all cases, where the exchange rate isdefined as the price of foreign currency in domestic currency units. Both consumer and wholesaleprices are used to measure aggregate relative price levels across countries so that sensitivity of theresults to alternative data sets can be evaluated.The results show that for no bilateral exchange rate according to the long-run neutrality criteriais long-run PPP satisfied. While permanent shocks to relative prices are typically reflected one-for-one in the nominal exchange rate, these disturbances account for a small and insignificantpercentage of both nominal and real exchange rate variance. Disturbances identified to be purelytransitory for relative prices, however, engender large, significant and permanent movements innominal and real exchange rates that account for almost all of the total variance in these variables.6The error-correcting form is appropriate for a maintained economic model which implies that relative prices andnominal rates cointegrate. See Engle and Granger (1987) for the source of this result. Cochrane (1992) uses a similarmethodology in evaluating the source of permanent and transitory components in GNP and stock prices.71n particular, this addresses criticisms of the use of consumer prices, which incorporate a high percentage ofnon-traded goods, in tests of PPP.16Consequently, disturbances that are only transitory for relative prices cause permanent violations ofPPP. Moreover, these disturbances are never significantly reflected in relative price variation at anyforecast horizon. Almost all of the variance of relative prices is accounted for by its ‘own’ permanentdisturbance so that relative prices have an insignificant transitory component, approximating a purerandom walk. Since nominal exchange rate variance is primarily attributable to transitory relativeprice shocks, in ten of twelve cases in the sample sources of fluctuations in relative prices andexchange rates are orthogonal.Given the equality of nominal exchange rate and relative price effects of permanent relativeprice shocks under this decomposition, the decomposition that imposes this equality identifies(in ten of twelve cases) identical disturbances with identical dynamics and long-run effects. Incontrast, the permanent/transitory decomposition for nominal exchange rates cannot retrieve thesame disturbances as the permanent/transitory decomposition for relative prices since the twovariables do not share a (single) common permanent component. The decomposition that imposeslong-run PPP likewise cannot replicate the dynamics implied by the permanent/transitory relativeprice decomposition, and by forcing permanent real exchange rate disturbances to be zero at theinfinite horizon generates transitory relative price shocks with real effects that persist beyond a fiveyear horizon.The results mirror the empirical observation that real and nominal exchange rates are approximately equally volatile. Importantly, they suggest that while the permanent component of prices isfully reflected in nominal exchange rates, the important source of (permanent) variation in nominaland real exchange rates is ‘non-fundamental’ relative to sources of fluctuations in relative goodsprices. It is this component of nominal exchange rate variation that generates the permanentcomponent in real exchange rates and so permanent disturbances to PPP.The remainder of this paper is organized as follows. Section 1.2 briefly describes the maintainedeconomic model, and Section 1.3 presents the mapping from this model to the empirical representation and tests. Section 1.4 describes the results of applying the test to G-7 data and Section 1.5concludes.1.2 The Maintained Economic ModelThe strong form of purchasing power parity asserts that under conditions of free trade spatial arbitrage will ensure that the currencies of different countries command the same bundle of goods whenmeasured in common units. The bilateral nominal exchange rate between any two currencies shouldtherefore equal the ratio of domestic to foreign price indices pertaining to a common commodity17basket. This condition is expressed in logarithms aset =Pt —P (1)where et is the log of the domestic currency price of foreign exchange, and Pt and p are the loglevels of the domestic and foreign prices.It has long been accepted that PPP is unlikely to hold at any given point in time. Weakerforms of the doctrine account for constant wedges between bilateral nominal exchange rates andnational indices of purchasing power due to impediments to free trade which are unchanging overshort periods of time. This weaker form of PPP allows for constant deviations from (1) due totransportation costs, international transactions costs, policy related trade restrictions and otherobstacles to trade which prohibit exact parityet=c+pt—p (2)However, common currency prices still are assumed to be closely related and highly arbitraged.Equation (2) implies that the change in an exchange rate is determined by the change in twocountries’ relative price levels, or that ‘relative purchasing power parity’ holdsIXet = Pt—Ip (3)Casual inspection of data from the floating exchange rate regime since 1974 indicate that (1), (2)and (3) have little validity as explanations of nominal exchange rate movements over short horizons.Figure 1.1 plots monthly time-series of the six G-7 bilateral currency prices, where the $U.S. is thenumeraire currency, against relative consumer price indices and Figure 1.2 plots the same exchangerates against relative wholesale price indices. In both cases, movements in nominal exchange ratesappear to little reflect movements in relative prices month by month. This phenomenon has beenexplained by many models that allow for transitory deviations from PPP, but which deliver PPPas a long-run equilibrium condition.8Transitory deviations from PPP have traditionally been attributed to divergent speeds of adjustment by wages and prices relative to nominal exchange rates following permanent, country-specificshocks to money stocks and output levels which are ultimately reflected in permanent relative priceschanges. if wages are fixed by long-term contracts, goods prices based on normal unit costs may adjust only slowly to these disturbances. In contrast, currency prices are determined in spot marketsand can respond immediately to new disturbances to goods and asset markets. These responses are8Notably, the price index used to measure wholesale prices for France is in fact an import price index and (ascan be seen in the results) generates some perverse results relative to the other data series. Its dynamic behaviour isnoticeably more similar to that of the exchange rate than for any other index.18argued to clear international asset markets in the short run following any disturbance that affectsinternational interest rate differentials, and the return to alternative currency deposit holdings, buthas no immediate price impact. The divergent dynamics of goods and asset prices causes nominal exchange rates to overshoot their new long-run values and induces potentially persistent, buttransitory, deviations from PPP following permanent shocks to fundamentals.Neoclassical two country, two good, two currency models deliver equilibrium (steady state)exchange rates that conform to some PPP arbitrage condition (subject to potential shifts in preferences or the marginal rate of substitution function). In these models also, steady state price levelsand so exchange rates are determined by relative money stocks and outputs, ‘fundamentals’. Suchmodels must be linearized and parameterized to generate simulated dynamics out of equilibriumfor exchange rates and relative prices, and few unambiguous conclusions emerge.The literature thus proposes that while (1)-(3) may not hold instantaneously, some versionwill hold in the absence of new disturbances and when the transitory dynamics of all previousdisturbances have been fully worked out. Long-run parity is asserted. Empirically, we observe thatreal exchange rates which are deviations from (strong) PPP given byrt = et— (Pt—p) (4)diverge widely from their mean (zero) values. Figure 1.3 plots (demeaned) log real exchange ratesfor the G-7 countries (where prices are measured by both consumer and wholesale indices) andifiustrates this point clearly. However, mere inspection of the data is insufficient to inform onwhether the real rate tends to revert to mean following permanent and transitory disturbances tofundamentals. This observation is discussed in the context of testing for long-run PPP in nextsection.1.3 Empirical Representations Of Disturbances To PPP1.3.1 Univariate RepresentationsRelative prices and the nominal exchange rate are typically characterized as linear stochastic processes driven by underlying stochastic shocks in the fundamentals which determine macroeconomicprices and quantities. In particular, long-run PPP has been taken to imply that the real exchangerate is a covariance stationary, or a mean reverting, stochastic process with time invariant firstand second moments. Any innovation in such a stationary process has finitely-lived effects which9See Schiagenhauf and Wrase (1992a,1992b) for some investigation of these dynamics in models that allow forliquidity effects of monetary injections through limited participation constraints on agents’ receipts of these injections.19eventually die out. Further, the long-run expected value of such a process is a time-invariant constant. 10 This is an appealing representation of long-run PPP since it implies that deviations fromparity exchange rate values are finitely lived, and that ultimately the real exchange rate returns toa time-invariant constant (zero) mean value.The condition that r be stationary is trivial if both e and (p — pj are stationary processes.However, if fundamentals follow non-stationary processes (tastes, technology, money supplies) thenlong-run PPP requires cointegration of the nominal exchange rate and relative prices. Granger(1983) and Engle and Granger (1987) show that even if two variables are individually non-stationary,there may be a unique linear combination of them in which the non-stationary components cancelout and which is stationary as a consequence. In short, any permanent disturbance to relative pricesoriginating in permanent disturbances to fundamentals must be ultimately and equally reflected innominal exchange rates and all other disturbances transitory for both variables.The evidence of Nelson and Plosser (1982) and numerous studies since indicates that manymacroeconomic time-series can be characterized as unit root processes suggesting that underlyingfundamentals may be non-stationary. Relative goods prices and nominal exchange rates may beexpected to inherit this property and the perceived conventional wisdom is that this is indeedthe case. Long-nm PPP then implies these two variables wifi be cointegrated with uniquecointegrating vector (1,-i). The real exchange rate may be very persistent but will be stationary ifthis condition holds.Typically, univariate tests of covariance stationarity of rt take as their alternative hypothesis astationary univariate process of a first order autoregressive moving average (ARMA) form= C + C1’1 + Vt (5)where c is a constant, c can take any value less than unity, and Vj 1S a moving average process suchasVt = a(L)ct (6)with a(L) a lag polynomial satisfying conditions for stationarity and invertibi]ity. The long-nmequilibrium real exchange rate is defined as the unconditional mean of this process,(7)‘°In fact, long-run PPP requires only that the fir8t unconditional moment of the real exchange rate be timeinvariant. Covariance stationarity is a stronger condition which has been imposed by empiricists as a condition to besatisfied in the data, but which has strong intuitive appeal as an equilibrium condition.‘1See Meese and Singleton (1982) and Schotman (1989) on the case for non-stationarity of nominal exchange ratesand Nelson and Plosser (1982) for evidence supporting non-stationarity of aggregate price indices.20Strict or short-run PPP is violated whenever the instantaneous real exchange rate does not equalthis long-run value. Long-run PPP is violated whenever a is greater than or equal to unity.12 Ifa equals unity, then every shock in the Vt process has a permanent effect on r through Vt_i. If ais less than one then each shock to the system is corrected at the rate of (1 — a) per period andtherefore eventually dies out.For the purposes of studying the dynamic properties of real exchange rates, one can also invertthe uuivariate ARMA process (5) to generate an infinite order moving average representation(MAR)Vt = é+d(L)e (8)where ê is a constant function of c and a, and d(L) is a lag polynomial function with coefficientsdepending on a and a(L). The coefficients in d(L) summarize completely the dynamic behaviourof Vt in reponse to any shock Ct. Once a suitable time-series representation for Vt is found, one candirectly measure the persistence of deviations from PPP by studying the moving average coefficients(its univariate impulse response function).Most empirical tests of long-run PPP have employed tests of non-stationarity (non-cointegration)of Vt based on (5). These involve a test of the null of a unit root in rt, or a equal to unity, againstthe alternative that a is less than unity. Most tests of non-stationarity in exchange rate data cannotreject the null for nominal rates or relative prices. However, they also frequently fail to reject thenull for the real exchange rate and conclude that long-run PPP is violated.Yet there are three important criticisms of the univariate approach which suggest its invalidityas a method for evaluating the hypothesis of long-run PPP. First, and most generally, it is well-documented (with Monte Carlo evidence) by Schwert (1987), Blough (1988), Gregory (1991) andothers, that univariate non-stationarity tests have low power to discriminate between the null andclose alternative hypotheses in small samples. Lo and MacKinlay (1989) show that similar resultshold for the variance-ratio tests of non-stationarity which have been applied to real exchange ratesalso (by Gnu and Ka.minsky (1991) to evaluate PPP for the US/UK data, for example). If thehypothesis of long-run PPP is correct, tests for unit roots have low power to detect this in the data.More specifically, Cochrane (1991) and Quaia (1992) show formally that any non-stationaryprocess has both a permanent and a transitory component, the former having arbitrarily smallvariance so that unit root tests have arbitrarily low power against some stationary alternatives in12J fact, long-run PPP is also violated if either a or c is time-varying. This source of violation is not consideredin the current paper.21small samples.’3 A meaningful test of the hypothesis of long run PPP therefore relies on beingable to identify the relative size of the permanent component in real rates. If a real exchangerate, for which the unit root hypothesis cannot be rejected, has a permanent component with smallvariance, then deviations from PPP (fluctuations in real exchange rates) may be prirriarily transitorydespite non-rejection of a univariate test for non-stationarity. Yet, as shown in (8), univariateestimation and testing allows derivation only of one, reduced form error process which may bea linear combination of multiple underlying disturbances some with permanent and some withtransitory effects. Univariate time-series methods cannot identify and measure alternative sourcesof disturbance to PPP in the absence of additional information that imposes some structurallyinterpretable decomposition of variance for Vt.The third, and related, objection to univariate methods is that they may lead to at worstmisleading and at best uninformative representations of real exchange rate dynamics. Notably,Cochrane emphasizes that there exist unit root processes (with permanent components havingsmall innovation variance) whose autocorrelation and likelihood functions are arbitrarily close tothose of given stationary series. For such processes, the asymptotic distribution theory derivedunder the false alternative may be a better guide for statistical inference in small samples thanthe non-standard (correct) distribution theory derived under the assumption of non-stationarity.This calls into question the use of unit root test results as information for specifying univariaterepresentations for exchange rate dynamics in borderline cases. Huizinga (1987) presents evidencethat exchange rates lie in this ‘borderline’ category.More generally, without the means to identify multiple, structurally interpretable sources ofreal exchange rate disturbances univariate methods have little potential to inform theory withexplanations of the failure of long-run PPP.1.3.2 Bivariate RepresentationsUnivariate evaluations of long-run real exchange rate behaviour fail to exploit additional informationthat is available in multivariate systems. This extra information can be used to identify multiple13 response to these criticisms, some empirical evaluations of long-run PPP have used fractional integrationmethods which allow for more general forms of long memory or time-dependence in real exchange rates. Dieboldet al (1991), Cheung (1993) and Cheung and Lai (1993) are examples. In this work, r is represented as following anear unit root process given by b(L)(l — = c + v where d is allowed to be non-integer (the fractional orderof integration), equal to unity under a unit root null, qf(L) is a polynomial in the lag operator satisfying conditionsfor stationarity and invertibility, and i, is again a stationary (MA) error process. A stationary process is said tohave long-memory if there are non-negligible autocorrelations between observations widely separated in time, yetzero effects of shocks at the infinite horizon for the level of the variable. ARFIMA modeling of real exchange ratesinvolves estimation of d and of the associated moving average representation, and has found strong evidence to favourlong-memory alternatives to non-stationary behaviour in real exchange rates.22sources of disturbance to real exchange rates, to measure their relative size in accounting for thevariance of real rates, and to characterizations of exchange rate dynamics that inform theory on therole and importance of different fundamental processes. In particular, multivariate systems admitidentification of both transitory and permanent components in exchange rates.Quah (1992) shows that multivariate vector autoregressive (VAR) representations can identifyboth the (orthogonal) permanent and transitory components of non-stationary series. One appealof Quah’s multivariate method is that it allows for direct estimation of the two components in asimple vector-autoregressive (VAR) system specified to have meaningful structural interpretation.14 Additionally, King and Watson (1992) suggest that such structural VAR decompositions can beused to evaluate propositions about long-run neutrality in the presence of non-stationarity in theendogenous variables of an economic model. The permanent/transitory decompositions suggestedby Quali (1992) are invoked in the testing process. This methodology can be readily applied as a testof long-run PPP where, as noted above, this hypothesis translates directly into long-run neutralitypropositions concerning the effects of permanent and transitory relative price disturbances fornominal exchange rates. This section shows how bivariate structural VAR’s can be used to identifyand measure disturbances to bilateral PPP relations and suggests how to test directly long-runPPP in this framework.1.3.3 Representation And IdentificationModels which predict long-run PPP assert that prices in each of any two economies are driven bymultiple disturbances to nominal and real fundamental variables some of which are permanent andothers transitory. These are the only disturbances that affect nominal exchange rates albeit withdifferent dynamic effects. Since long-run PPP holds, permanent disturbances to prices have equallong-run effects for the nominal exchange rate, and all transitory disturbances have zero long-runeffects for both variables. Consequently, both permanent and transitory disturbances are neutralfor the real exchange rate in the long-run.This suggests that bivariate structural representations of bilateral nominal exchange rates andrelative prices, which allow identification of only two fundamental disturbances, are ‘complete’provided that all of the underlying fundamental disturbances can be aggregated into two orthogonalrepresentative disturbances. Given non-stationarity of nominal rates and relative prices, a bivariatesystem in one (aggregate) permanent relative price disturbance and one (aggregate) transitory14Structural VARs have been proposed and applied by Blanchard and Quah (1989), Quah (1992) and Cochrane(1992) as alternative methods for estimating the permanent and transitory components in time series which arecharacterized by stochastic non-stationarity.23relative price disturbance can potentially represent such models.Blanchard and Quah (1989) and Quah (1992), show that representations in which all permanentand all transitory disturbances are aggregated into single stochastic variables in this manner, mustsatisfy some regularity conditions to be valid. Specifically, two conditions must hold. First, thepermanent shocks must elicit very similar dynamic responses of the two variables.’5 Second, thetransitory disturbances can have different dynamic effects for the variables but must leave (nearly)unchanged the dynamic relation between them. It is assumed that these regularity conditions aremet.Assume that the vector of non-stationary economic variables, X = [et, ( p*)tlI is jointly,completely and fundamentally determined by a fixed set of underlying disturbances which can beaggregated into a single permanent relative price disturbance and a single transitory relative pricedisturbance as i. From Wold’s Theorem, the (2 x 1) jointly covariance stationary stochastic vectorprocess, then has infinite (causal) vector moving average representation (MAR)= I’(L)rft (9)where = [set, I.(pt—pr]’, F(L) is a matrix lag polynomial summarizing the dynamics of thesystem and satisfying conditions for stationarity and invertibility, and tmlt is a (2 x 1) vector oforthogonal fundamental disturbances, one of which is permanent and the other transitory for X,with variance- covariance matrix. Estimation of the parameters in T(L) and identification ofthe orthogonal innovations generate a complete description of the system’s dynamics.While the MAR (9) cannot be estimated directly, it can be identified from the parameters ofa reduced form parameterization under the maintained hypothesis.’6 From Engle and Granger(1987) we know that if the 2 x 1 vector X is non-stationary, or integrated of order 1 (1(1)), but thelinear combination given by rt is stationary, the covariance stationary exchange rate/relative pricesystem can be parameterized in one of two ways. First, a vector error-correction model (VECM)given by= —7rt_1 + B(L)/X_, + t (10)can be estimated, where rt is the ‘error-correction term’ which captures the common permanentcomponent in et and (p — p*)t. Its inclusion restores the spectral density of the model to full rank(accounts for the singularity in I’(1) due to the presence of this common permanent component).’7These cointegrated representations are correct under the maintained hypothesis.15This condition appears to be satisfied in the impulse response functions estimated below.‘6Direct estimation of the system is possible if there exist strictly exogenous variables which can be used asinstruments allowing identification of any non-zero contemporaneous multipliers.17See Yoo (1985).24This parameterization can be inverted and transformed to produce a reduced form MAR of theform= (11)where C(O) = I and the variance-covariance matrix of t is given by . From (9) and (11)I’(L)qt = C(L)e (12)and since C(O) = I the structural innovations are given by= F(O)’e (13)and the dynamic multipliers byI’(L) = C(L)F(O) (14)Hence, the structural innovations and parameters can all be identified given knowledge of I’(O).From (13), the covariance condition= r(o)r(o)i (15)provides 3 restrictions which must be satisfied by the elements of I(O).18 However, there are4 distinct elements to be estimated in I’(O), and so multiple representations of (9) aclniissablefrom (11) conditional on the fourth identifying restriction imposed, each of which allows for thecontemporaneous joint determination of the elements of Xt by orthogonal disturbances.Notably, the hypothesis of long-run PPP assumed in (9) involves two restrictions on the elementsof I’(l)=Fj, the long-run multiplier matrix for the two disturbances.’9 These are= I’(1)2, (16)(17)= r(1)22 (18)= 0 (19)where the first disturbance in the system. is (arbitrarily) identified as the permanent relative priceshock and the second as the transitory relative price shock. These two restrictions overidentify theI:n fact, E,, is normalized to be the identity matrix and the diagonal elements of r(O) estimated as the impactmultipliers.19F(l) represents the cumulative impact of each disturbance on the elements of (If X is a covariancestationary vector, then these long-run effects are zero.) If X is non-stationary in levels and the VAR is thus specifiedin first differences of X, r(1) reflects both the cumulative impact of a given disturbance on the first difference of thevariable and the infinite horizon effect on the level of the variable.25model, but imposition of either one in some form should, under the maintained model, retrievethe structural representation of interest. One of these constraints can therefore be imposed as arestriction on the elements of C(1)F(0) = F(1).An alternative representation, which directly imposes long-run PPP, is a reduced form cointegrated VAR in Y = [(p — p*)t,rt]l which is estimated asYt = B(L)Y_ + t (20)In this instance the same identification problem arises. Now, however, a single restriction will sufficeto identify the maintained model since long-run PPP is embodied in the specification through theinclusion of Vt as a dependent variable. Specifically, imposing that the long-run effect of onedisturbance for (p — p*)t is zero will retrieve (9) directly. Such a zero restriction on r(1) impliesa representation for i in terms of permanent and transitory disturbances for relative prices a laBlanchard and Quah (1989).For both parameterizations, the underlying structural model can be retrieved in the form ofinterest (as a description of the levels behaviour of exchange rates and prices following alternativedisturbances) asX = F(L)/(1— (21)by appropriate transformation of the estimated parameters. The levels behaviour of the real exchange rate is directly estimated from the second parameterization and can be derived by appropriate transformations from the first.1.3.4 Tests Of Long-Run PPPFollowing King and Watson (1992), two tests of long-run PPP are proposed which use the twoparameterizations of (9) described above.First, three alternative long-run restrictions are imposed on the reduced form MAR (11) andthe overidentifying restrictions used to evaluate the validity of the joint hypotheses (16) and (18).These restrictions areT(1)22 = 0 (22)F(1)12 = 0 (23)= P21 (24)26(22) identifies the second disturbance in the system as purely transitory for (p — p*)t 2O Theresulting structural model is referred to as Model (1). Under the maintained hypothesis, thisrestriction generates a representation in which the following (necessary) conditions are observed:I’(1)21 = (25)= 0 (26)Consequently, both the first (permanent relative price) disturbance and the transitory relative pricedisturbance are neutral for the real exchange rate at the infinite horizon.(23) identifies the second disturbance in the system as purely transitory for et. The resultingstructural model is referred to as Model (2). Under the maintained hypothesis, this restrictiongenerates a representation in which the following (necessary) conditions are observed:= r(1)1 (27)I’(l)22 = 0 (28)Consequently, both disturbances are neutral for the real exchange rate at the infinite horizon. Theidentified system should be identical to that identified by Model (1).(24) identifies the first disturbance as having equal long-run effects for et and (, — p*)t Theresulting structural model is referred to as Model (3). Under the maintained hypothesis, thisrestriction generates a representation in which the following (necessary) condition is observed:I’(1)12 = F(1)22 (29)Again, both disturbances are neutral for the real exchange rate at the infinite horizon and the identified system should be identical to that identified for Models 1 and 2. Both the long-run multipliermatrix and the parameters in (L)/(1 — L) are inspected for evidence of significant deviationsfrom long-run PPP. 21 However, even if one of the conditions required for the system to satisfylong-run PPP according to the preceding criteria fails, the forecast error variance decompositionscould indicate that the implied source of the PPP deviation accounts for a negligible fraction ofreal exchange rate variance. This trivariate of statistics therefore are used together to evaluate thehypothesis.20The choice of ordering for the identified disturbances involves a normalization; the point estimates are unique upto a column sign change. Notably, there may be differences across choice of ordering in small sample inference dueto sampling error. In general, the inference based on simulated standard errors computed in this paper is robust tosuch changes in ordering.21In all tests, statistical inference is based on empirical distributions computed by Monte Carlo integration using2500 replications and based on standard distributional assumptions for the reduced form VECM parameters.27The second test of the long-run PPP hypothesis involves use of the identified system (21), whichwill be referred to as Model (4). Tn this case, there is no unique set of overidentifying restrictionssupplied by theory which can be used to evaluate the model’s performance. Since long-run PPP isdirectly imposed on the system, a test of this hypothesis involves evaluating the compatibility ofthe resulting dynamics of the system to those of economic models that predict that long-run PPPwill hold. These dynamics, moreover, should be consistent with those generated by Models (1)-(3).Finally, this model informs theory on the dynamics that should be generated by any theoreticalstructure that has long-run PPP as an equilibrium condition.1.4 ResultsAll estimation is conducted for the sample period 1975:1-1991:12 (except for the Italian data whichwere available only to 1989:12) for the G-7 countries Canada, France, Germany, Italy, Japan, theUnited Kingdom and the United States. For data sources and definitions see Table 1.1. Thenominal exchange rate is defined as the (log of) the price of one U.S. dollar in units of domesticcurrency. Relative prices are defined as the log of the relative consumer (wholesale) price index ofthe domestic price index minus the log of the relevant price index in the U.S. Each series demeanedprior to estimation. Two price indices were used in order to assess robustness of the results to theuse of alternative data series, where one of these (the consumer price index) is commonly attributedwith partial responsibility for rejections of long-run PPP in the data due to its including a relativelylarge component of non-tradeable goods’ prices.1.4.1 Reduced Form EstimationFor each country, two VECM’S and two VAR’s (each with four lags included of each endogenousvariable)22 are estimated where, in the second VAR relative consumer prices are replaced by relative wholesale prices. The coefficients on the lagged error-correction term (lagged value of the realexchange rate) in the VECMs are shown in Tables 1.2a and 1.2b. These indicate that the laggedlevel (error-correction) variable appears to play the appropriate ‘correcting’ role for the nominalexchange rate; a positive deviation from PPP (due either to a positive shock to nominal rates ora negative relative price disturbance) causes a negative nominal exchange rate response in the following period. Furthermore, relative prices rise in the period following a positive PPP disturbance.There therefore appears to be a tendency for all currencies and relative prices to act to eliminate22This lag length is selected primarily by standard information criteria, and appropriate for most data sets. Consistency of lag length across different country data sets was the deciding criterion in marginaL cases.28short-run ‘disequilibria’. However, in few cases are the coefficients on the error-correction termsignificant, suggesting weak support for the error-correcting specification.1.4.2 Structural Model EstimationThe reduced form VECM’s and VAR’s are inverted and the structural moving average Models(1)-(4) estimated using the identification procedures described above. 231.4.3 Long-Run Multiplier EstimatesEstimated long-run multiplier matrices for each country (and price index) are shown in Table 1.3.(These are based on the response of each variable to alternative innovations after 204 months.)This provides information directly on the validity of long-run PPP in this data for Models (1)-(3).In many cases the estimates are significant, however, in some the estimates are highly imprecisewhich is inevitable in direct estimation of long-run responses. Consequently, the impulse responsefunctions (elements of F(L)) are also reported in the following section for a one year horizon, andthese provide additional inference.For Canada, the results for Model (1) indicate that while permanent relative price disturbanceshave an approximately equal effect on nominal exchange rates and relative prices, there is a largeand significant permanent effect for nominal exchange rates of disturbances that only transitorilymove relative prices. The size and significance of this effect is independent of which price index isused to identify relative price shocks. The results for Model (3) reflect those for Model (1). Thepermanent relative price shock identified in Model (1) appears to be exactly that identified in Model(3) as the disturbance with equal long-run nominal exchange rate and relative price effects. Thelong-run multiplier estimates for Model (2) are consistent with the finding of permanent nominalexchange rate effects of transitory price disturbances and comparatively small nominal rate long-run effects of permanent relative price disturbances. The relative price infinite horizon response topermanent exchange rate shocks is barely significant, while its response to transitory exchange rateshocks is highly significant and is close in value to the relative price response to its own permanentshock in Model (1). The permanent exchange rate component generated by Model (2) is apparentlynot identifiable with the permanent relative price disturbance generated by Model (1).In the German data, the equality of relative price and nominal exchange rate responses topermanent price shocks in Model (1) is subject to more uncertainty but remains consistent with23AJ1 identilication is computed by solving the implied nonlinear system of equations given by (16) and the relevantlinear restrictions on the elements of C(1)r(O) in the GAUSS NLSYS package using the default non-linear solutionalgorithm and program settings.29the Canadian results. The German VECM’s based on alternative price indices generate a similarsize for the ‘excess’ permanent nominal exchange rate component. Again, Model (3) reflects theresults of Model (1) and Model (2) implies a significant permanent relative price response onlyfollowing disturbances identified as being transitory for the nominal exchange rate. A remarkablysimilar pattern of infinite horizon responses emerges in the Italian and UK data.The French and Japanese cases warrant further comment. In these cases, the additional inference afforded by the impulse response analysis is especially valuable in assessing the long-run effectsof alternative disturbances for the real exchange rate. For both countries, the nominal exchangerate response to permanent relative price disturbances in Model (1) is imprecisely estimated andinsignificantly different from zero when consumer prices are used. For France, the relative priceresponse is also imprecisely estimated in this instance. However, a significant ‘excess’ permanentnominal exchange rate component is observed when both consumer and wholesale price measuresof relative prices are used for both countries.In general, these results show that there exist large permanent nominal exchange rate movementswhich occur independently of permanent relative price movements and despite the approximatelyequal effect of the latter for nominal rates predicted by models of long-run PPP. Consequently,the results for Models (1) and (3) coincide for ten of the twelve cases studied , and the results ofModel (1) and Model (2) are significantly different. Given this indication of rejection of long-runPPP, the remaining results reported focus on Model (1) and Model (4) in further evaluating thehypothesis. 241.4.4 Impulse Response FunctionsThe impulse response functions provide information regarding the behaviour of nominal exchangerates, relative prices and the real exchange rate for one year following a disturbance of one standarddeviation (unity) in an orthogonal innovation. The results for Model (1) are shown in Figures 1.4-1.9for consumer price indices and in Figures 1.4(wp)-1.9(wp) for wholesale price indices. The Canadianresults indicate negligible differences in nominal exchange rate, relative price and real exchangerate dynamics following permanent and transitory relative price disturbances when alternativeprice indices are employed. In both cases, the long-run effects are complete for the levels of eachvariable by the twelve month horizon. The permanent price disturbance raises relative prices andthe nominal exchange rate permanently by equal amounts and has no significant real exchange rateimpact at any lag since the nominal rate and price dynamics are insignificantly different from each24Results for Models (2) and (3) are available from the author upon request.30other. The transitory price disturbance accounts for no significant movement in relative prices atany lag but engenders a large, significant nominal exchange rate response at all lags. This suggeststhat relative prices follow a pure random walk (have an insignificant transitory component) andthat if long-run PPP fails in the Canadian data it is due to the response of the nominal exchangerate to disturbances which have no effect for relative prices, or ‘fundamentals’ as they are measuredhere. 25The results for France are similar in the latter respect. Transitory relative price disturbanceshave no significant effect for relative prices at any lag, but a large, positive and increasing effect forthe nominal exchange rate. This is true for both wholesale and consumer price indices. There are,however, some differences in responses to the permanent price disturbance compared to the Canadian model, and conditional on the definition of prices used. Again, this disturbance permanentlyraises both relative prices and the nominal exchange rate but there is a small, significant effect forthe real exchange rate. ‘When consumer prices are used, while the relative price and nominal raterespsonses are indistinguishable at low lags they diverge at longer lags with the nominal exchangerate impact exceeding that for relative prices. This generates a significant and positive effect forthe real exchange rate after six months although this effect is estimated with a large standarderror even at this horizon. ‘When wholesale prices are used, the real exchange rate is significantlyand negatively affected by the permanent price disturbance at all lags, although again this effectis estimated somewhat imprecisely. In this case, the relative price response exceeds that of thenominal rate at all lags. 26The German data reflects the Canadian results. There are no significant differences in dynamicsthat depend on which price index is used and in both cases there are insignificant real exchange rateeffects at all lags following a permanent relative price shock. Again, the real rate is permanentlyraised at all horizons after a transitory price disturbance which has no significant effect for relativeprices but a large, significant positive impact for the nominal exchange rate. The Italian modelsand the Japanese consumer price index case also reproduce these results in Figures 1.7, 1.7(wp),and in Figure 1.8. The use of wholesale price indices in the Japanese case, however, generates asignificant and positive real exchange rate response following a permanent price disturbance. Yet,disturbances to PPP due to the transitory price shock retain the properties exhibited in all previouscases.25The impulse response functions for Model (2) aiso suggest that relative prices contain no significant transitorycomponent; there are significant permanent relative price responses following both permanent and transitory exchangerate disturbances.26The results’ sensitivity to the use of alternative price indices may be attributable to the use of an importedmaterials price index to proxy for wholesale prices in the absence of an alternative series being available.31Finally, the results for the UK/US system are shown in Figures 1.9 and 1.9(wp). The dynamiceffects of the transitory relative price disturbance reflect all previous results. There are permanentcomponents in nominal and real exchange rates that are never reflected in relative prices. Similarly,the permanent price shock generates no significant real exchange rate response at any lag, corroborating the earlier results concerning the long-run neutrality of the permanent price component formost currency prices.Model (4) produces impulse responses (those for relative prices and the real exchange rateare shown in Figures 1.10-1.15 and in Figures 1.10(wp)-1.15(wp)) which show how the dynamicsgenerated from a representation which imposes long-run PPP differ from those in Model (1). Theimpulses are plotted to a five year horizon at which not all disturbances, which are by assumptiontransitory for the real exchange rate, have dissipated.Clearly, there are significant differences in the estimated parameters of the impulse responsefunctions from Models (1) and (4) for all countries and both prices indices at most horizons following transitory relative price disturbances. Imposing long-run PPP on a relative price permanent/transitory decomposition requires that both disturbances be neutral for the real exchange rateat the infinite (204 month) horizon. From Model (1), we know that Model (4) is misspecified andthis reflects in the differences across the two Models. In particular, the long-run PPP model identifies ‘transitory’ relative price disturbances with effects for the real exchange rate that die out moregradually than those that are identified as being permanent for relative prices.This is due, in the case of the consumer price models, to a large and significant nominal exchangerate response to the transitory shock which, while restricted to have no real effects at the infinitehorizon, is clearly highly persistent. The ‘excess’ permanent nominal exchange rate componentin Model (1) is forced to satisfy an infinite horizon zero restriction in Model (4) which generatesthis result. This is true for all countries and both measures of prices. The permanent relativeprice disturbance is neutral for the real exchange rate at all lags for the Canadian and UK models,but has significant real effects to at least a one year horizon for the remaining cases. Model (4)apparently induces these prolonged real effects of the permanent relative price disturbance byforcing all permanent real effects to be zero in this decomposition of variance.In the wholesale price models, permanent relative price shocks also have prolonged real effectsin the Canadian and German data, while the same protracted transitory price shock is observed asin the consumer price models. Notably, there are significant negative relative price responses to thisdisturbance while the implied nominal exchange rate response is positive. This pattern of responsesis difficult to reconcile with the implications of standard models of exchange rate dymtaniics.321.4.5 Forecast Error Variance DecompositionsThe preceding results show that there exist large permanent nominal exchange rate disturbanceswith no significant price effects that force most disturbances to long-run PPP. However, the relativeimportance of these long-run PPP disturbances can only be ascertained by evaluating the percentageof the total real exchange rate variance accounted for by them at any given forecast horizon.Forecast error variance decompositions are therefore constructed for each country and price indexfor Models (1) and (4) which show the percentage of the total forecast error variance accounted forby each disturbance at various forecast horizons. The results for Model (1) are shown in Tablesl.4a and l.4b.The results for Canada indicate that the permanent price disturbance accounts for a small andinsignificant fraction of the total variance in the real exchange rate although it can explain almostall of the variance in relative prices. Further, almost all of the variance in nominal exchange rates isaccounted for by the transitory price shock, so that the percentage forecast error variance of bothreal and nominal exchange rates explained by this disturbance are very similar. These observationssuggest that while relative prices are approximately a pure random walk with respect to somepermanent shock(s), real exchange rate variation is largely due to sources of ‘non-fundamental’permanent nominal exchange rate movements not reflected in relative prices. Moreover, the factthat long and short-run neutrality of permanent relative price disturbances holds in the data istypically irrelevant for real exchange rate behaviour. Finally, given these results, one would expectto observe the variation in real and nominal exchange rates to be very similar in the data and fornominal exchange rates and relative prices to look more alike than real exchange rates and relativeprices.These results are mirrored in the reports for the remaining five countries with few exceptions.In the French consumer price index (Model (1)) case, long-run PPP violations attributable to thepermanent price disturbance which were observed in the impulse response functions account forabout one quarter of all violations. However, in the (perverse) wholesale price case this source oflong-run PPP deviations accounts for an insignificant percentage of real exchange rate variance.Consequently, the ‘excess’ permanent nominal exchange rate variation retains dominance in generating permanent real exchange rate movements in both cases. In the Italian wholesale price data,nominal exchange rate variation is more strongly associated with the permanent price disturbancethan is typically the case, however this has no impact on the relative importance of transitory pricedisturbances for purchasing power parity deviations in the long-run which is negligible.While the results for Japan in which consumer prices are used reflect the Canadian case, the33use of wholesale prices introduces a significant change. Here, permanent relative price shocks canaccount for almost one half of all real exchange rate variation, and are especially important atshort horizons. Since the impulse responses indicate the existence of permanent real exchange rateshocks due to this disturbance when wholesale prices are used, deviations from long-run PPP occurwith approximately equal frequency due to permanent and transitory price disturbances here.Overall, the results from Model (1) therefore indicate that in ten of twelve cases there aresignificant permanent disturbances to PPP that are almost entirely attributable to permanentnominal exchange rate shocks which are never reflected in relative prices.The forecast error variance decompositions from Model (4) which imposes long-rim PPP therefore look very different to those for Model (1) in several cases. At the (relatively short) forecasthorizons considered, relative price variance is accounted for less by the disturbance identified tobe permanent than in Model (1), and real exchange rate variance is accounted for more by thisdisturbance although in most cases the fraction of real exchange rate variance attributable to thisshock is insignificant over all but very short horizons. Notably, when wholesale prices are used inthe decompositions significant differences are observed over these (short) horizons in the Canadianand German models. Here, most real exchange rate forecast variance is accounted for by the permanent relative price disturbance. While this sensitivity of the results to alternative price indicesis surprising, it remains true that in ten of twelve cases an insignificant fraction of real exchangerate variation is caused by permanent relative price shocks.1.5 ConclusionThe results indicate that in ten of the twelve cases studied, there are deviations from PPP atall horizons that are almost entirely attributable to disturbances that have permanent nominalexchange rate effects but which are never reflected in relative prices. This is despite the fact thatpermanent relative price disturbances are typically reflected one-for-one in nominal exchange ratesas predicted by models that deliver long-run PPP as an equilibrium condition. There is a large andsignificant permanent component in real exchange rates.In fact, permanent relative price disturbances account for a insignificant percentage of nominaland real exchange rate variance at most forecast horizons but account for approximately 100%of the variance of relative prices. This suggests that there are important sources of (permanent)nominal and real exchange rate movements that are never captured in the ‘fundamentals’ proposedby many theoretical representations as long-run determinants of exchange rates. Notably, imposinglong-run PPP on the data induces decompositions of variance that generate dynamics which are34difficult to reconcile with the implications of standard models of exchange rate determination, andtransitory shocks with extraordinarily long-lived real exchange rate effects.The estimated (unrestricted) decompositions are consistent with the empirical observation thatnominal and real exchange rates are approximately equally volatile and that neither variable appearsto be closely related to relative price movements. In fact, sources of fluctuations in relative pricesand exchange rates in ten of twelve cases are orthogonal. Furthermore, in these cases, whetherconsumer or wholesale prices are used to construct a relative price variable is irrelevant for the mainresults, suggesting that previous criticisms of the use of consumer prices for evaluating propositionsabout PPP may be unfounded.Clearly, further empirical analysis is needed to uncover the source of the ‘excess’ permanentnominal and real exchange rate component identified here. Finer decompositions of exchange ratevariance would be required to achieve this, and this is left to future work.35Table 1.1: Data SourcesAll series are monthly, deterministically seasonally adjusted, logarithmically transformed and demeaned prior to estimation.• consumer price indices are averaged data from the Citibase database, available from 1974:1-1991:12 for all countries.• wholesale price indices are averaged data from the International Monetary Fund’s International Financial Statistics database, available from 1974:1-1991:12 for all but the Italian seriesfor which the sample is 1974:1-1989:12.1. for Canada this index is the aggregate industry selling price index2. for France this index is the price of imported materials index3. for Germany this index is the wholesale price index for industrials4. for Italy this index is a general wholesale price index5. for Japan this index is a general wholesale price index6. for the UK this index is the industrial output price index7. for the US this index is the price index of industrial output• nominal exchange rates are averages of daily noon spot rates from the Citibase database,available 1974:1-1991:12 for all series36Table 1.2: Reduced Form VECM ResultsTable 1.2a: Error Correction Terms (CPI’s)Country Equation Estimated t-statisticCoefficientCanada et -0.011 -1.222(p— P)t 0.002 0.468France-0.026 -1.909(i— P)t 0.002 1.026Germany et -0.016 -1.499‘(i— P)t 0.002 1.146Italy et -0.015 -1.413‘(i— P)t 0.005 1.344Japan et -0.015 -1.365i(1 — p*) 0.004 1.720UK et -0.021 -1.767.(p—p*)t 0.002 0.688Table 1.2b: Error-Correction Terms (WPI’s)Country Equation Estimated t-statisticCoefficientCanada et -0.000 -0.025(p— P)t 0.019 2.802France zket -0.013 -1.018(i — p*) 0.002 0.175Germany zet -0.013 -0.993(p_p*) 0.002 2.467Italy et -0.011 -0.843(p — p*)t 0.005 0.821Japan ket -0.021 -1.531z(i — p*) 0.000 0.015UK zet -0.014 -1.141(p — p*)t 0.006 1.83437Table 1.3: Estimated Long-Run MultipliersTable 1.3a: Model (1) Estimates (CPI’s)Country Variable Permanent Transitory_________(pp*) Shock (p-p) ShockCanada et 0.0067 0.0138(0.0058) (0.0033)( — 0.0066 0.0(0.0019) 0.0France iet 0.0466 0.0523(38.495) (0.0188)(p— P)t 0.0094 0.0(4.3218) 0.0Germany et 0.0221 0.0459(0.0468) (0.0133)( — *) 0.0114 0.0(0.0129) 0.0Italy et 0.0235 0.0461(0.0268) (0.020)(l— i)t 0.0201 0.0(0.0073) 0.0Japan et -0.0032 0.0565(0.0329) (0.0197)( — *) 0.0090 0.0(0.0011) 0.0UK et 0.0190 0.0480(0.0356) (0.0157)( — *) 0.0174 0.0(0.0087) 0.0Each element reports the response of the Variable to each alternative Shock at theinfinite horizon (204 months), which is also the cumulative impact on the level of eachVariable. Standard errors computed by Monte Carlo integration are in parenthesesand are based on 2500 random draws.38Table 1.3: Estimated Long-Run MultipliersTable 1.3b: Model (1) Estimates (WPI’s)Country Variable Permanent Transitory_________(p-p) Shock (p-p) ShockCanada et 0.0054 0.0131(0.0049) (0.0034)“(i— P)t 0.0056 0.0(0.0011) 0.0France et 0.0297 0.0383(0.0192) (0.0124)( — 0.0466 0.0(0.0141) 0.0Germany et 0.0165 0.0456(0.0043) (0.0195)( — *) 0.0087 0.0(0.0046) 0.0Italy et 0.0374 0.0371(0.0357) (0.0108)t( —*) 0.0246 0.0(0.0129) 0.0Japan iet 0.0458 0.0374(0.0506) (0.0149)( — *) 0.0164 0.0(0.0120) 0.0UK .et 0.0149 0.0467(3.9171) (0.0162)i( — p*) 0.0169 0.0(0.7075) 0.0Each element reports the response of the Variable to each alternative Shock at theinfinite horizon (204 months), which is also the cumulative impact on the level of eachVariable. Standard errors computed by Monte Carlo integration are in parenthesesand are based on 2500 random draws.39Table 1.3: Estimated Long-Run MultipliersTable 1.3c: Model (2) Estimates (CPI’s)Country Variable Permanent Transitorye Shock e ShockCanada Iet 0.0157 0.0(0.0052) 0.0(i— P)t 0.0029 0.0061(0.0029) (0.0013)France 0.0700 0.0(814.79) 0.0( — 0.0063 0.0070(58.761) (0.0025)Germany et 0.0510 0.0(0.0371) 0.0( — *) 0.0049 0.0103(0.0082) (0.0027)Italy et 0.0516 0.0(0.0101) 0.0(p— P)t 0.0091 0.0178(0.0101) (0.0046)Japan iet 0.0564 0.0(0.0331) 0.0( — *) -0.0005 0.0090(0.0046) (0.0021)UK et 0.0518 0.0(0.0383) 0.0i( — p*) 0.0064 0.0160(0.0140) (0.0043)Each element reports the response of the Variable to each alternative Shock at theiiiflnite horizon (204 months), which is also the cumulative impact on the level of eachVariable. Standard errors computed by Monte Carlo integration are in parenthesesand are based on 2500 random draws.40Table 1.3: Estimated Long-Run MultipliersTable 1.3d: Model (2) Estimates (WPI’s)Country Variable Permanent Transitorye Shock e ShockCanada et 0.0141 0.0(0.0043) 0.0‘(i— P)t 0.0022 0.0052(0.0017) (0.0008)France et 0.0485 0.0(0.0172) 0.0( — 0.0286 0.0369(0.0170) (0.0106)Germany zet 0.0514 0.0(0.0319) 0.0(p— P)t 0.0028 0.0083(0.0039) (0.0014)Italy et 0.0526 0.0(0.0356) 0.0(p— P)t 0.0175 0.0173(0.0167) (0.0039)Japan et 0.0591 0.0(0.1146) 0.0( — *) 0.0127 0.0104(0.0311) (0.0070)UK et 0.0489 0.0(0.3420) 0.0( — *) 0.0051 0.0161(0.0594) (0.0035)Each element reports the response of the Variable to each alternative Shock at theiiiflnite horizon (204 months), which is also the cumulative impact on the level of eachVariable. Standard errors computed by Monte Carlo integration are in parenthesesand are based on 2500 random draws.41Table 1.3: Estimated Long-Run MultipliersTable 1.3e: Model (3) Estimates (CPI’s)Country Variable Common SecondShock ShockCanada et 0.0066 0.0139(0.0017) (0.0052)( — 0.0066 0.0001(0.0017) (0.0026)France zet 0.0077 0.0697(0.0024) (4.7714)‘(i3 — 0.0077 0.0055(0.0024) (0.6291)Germany et 0.0111 0.0498(0.0038) (0.0437)( — *) 0.0111 0.0026(0.0038) (0.0125)Italy et 0.0199 0.0475(0.0055) (0.0561)i( — p*) 0.0199 0.0015(0.0055) (0.0242)Japan et 0.0088 0.0557(0.0021) (0.0266)(p— P)t 0.0088 -0.0019(0.0021) (0.0041)UK et 0.0174 0.0488(0.0051) (0.0262)i( — p*)t 0.0174 0.0006(0.0051) (0.0090)Each element reports the response of the Variable to each alternative Shock at theiaflnite horizon (204 months), which is also the cumulative impact on the level of eachVariable. Standard errors computed by Monte Carlo integration are in parenthesesand are based on 2500 random draws.42Table 1.3: Estimated Long-Run MultipliersTable 1.3f: Model (3) Estimates (WPI’s)Country Variable Commrnon SecondShock ShockCanada et 0.0057 0.0139(0.0009) (0.0052)( — *) 0.0057 -0.0001(0.0009) (0.0017)France et 0.0427 0.0130(0.0432) (0.0043)( — 0.0427 -0.0189(0.0432) (0.0279)Germany zet 0.0087 0.0506(0.0016) (0.1112)(p— P)t 0.0087 0.0014(0.0016) (0.0082)Italy zet 0.0232 0.0472(0.0082) (0.1989)( *) 0.0232 0.0080(0.0082) (0.0847)Japan et 0.0129 0.0577(0.0134) (0.0738)( — *) 0.0129 0.0101(0.0134) (0.0149)UK et 0.0168 0.0459(0.0042) (0.0234)(p— P)t 0.0168 -0.0007(0.0042) (0.0072)Each element reports the response of the Variable to each alternative Shock at theimfinite horizon (204 months), which is also the cumulative impact on the level of eachVariable. Standard errors computed by Monte Carlo integration are in parenthesesand are based on 2500 random draws.43Table 1.4: Forecast Error Variance DecompositionsTable 1.4a: Model (1) Estimates (CPI’s)Percentage Forecast Error Due To Permanent Relative Price ShockCountry Variable 1 month 6 months 12 months 24 monthsCanada et 4.24 8.36 12.66 16.00(9.42) (11.87) (14.30) (16.37)( — 93.81 97.20 98.83 99.52(10.14) (4.85) (2.12) (0.82)(e—p + P)t 2.19 1.04 0.52 0.24(8.18) (7.47) (7.98) (9.12)France et 4.84 14.00 25.55 35.51(13.38) (17.39) (20.88) (23.50)( — *) 93.13 94.88 97.64 99.10(14.37) (9.80) (5.32) (1.70)(e—p + P)t 0.71 5.58 14.70 24.21(10.34) (13.64) (18.18) (22.31)Germany et 5.93 7.64 11.49 14.99(12.17) (13.17) (15.94) (18.77)( — *) 96.83 98.49 99.38 99.77(10.17) (5.31) (2.53) (0.90)(e—p + P)t 0.22 1.27 2.42 3.65(7.95) (9.15) (11.51) (14.41)Italy et 1.59 13.43 16.53 18.68(10.98) (16.54) (18.00) (19.47)( — *) 99.08 99.90 99.96 99.98(9.90) (5.16) (2.69) (1.1)(e—p + p*)t 3.69 0.53 0.45 0.49(11.97) (9.77) (11.04) (12.65)Japan et 0.02 0.36 0.36 0.34(10.56) (11.50) (12.25) (13.09)( — *) 99.40 99.56 99.80 99.91(10.70) (6.58) (3.70) (1.62)(e—p + P)t 6.25 5.11 4.83 4.63(15.03) (14.62) (14.95) (15.46)UK et 2.88 5.15 8.07 10.75(11.31) (12.85) (14.98) (17.18)( — *) 95.06 97.70 99.04 99.62j (12.21) (6.85) (3.35) (1.26)(e — p + P)t 1.33 0.35 0.15 0.11(10.32) (10.35) (10.63) (12.16)44Table 1.4: Forecast Error Variance DecompositionsTable 1.4b: Model (1) Estimates (WPI’s)Percentage Forecast Error Due To Permanent Relative Price ShockCountry Variable 1 month 6 months 12 months 24 monthsCanada et 16.17 13.84 14.32 14.52(15.43) (14.47) (15.15) (15.57)(p— P)t 95.54 99.19 99.60 99.80(9.92) (3.55) (1.73) (0.29)(e—p + p)t 0.57 1.22 0.58 0.29(7.87) (8.41) (8.40) (8.74)France et 43.11 48.50 44.74 41.02(22.98) (21.25) (20.41) (20.51)(r— P)t 99.17 99.77 99.89 99.95(10.01) (5.68) (3.16) (1.41)(e—p + p)t 26.22 18.25 17.14 16.68(20.80) (18.36) (18.41) (18.88)Germany et 11.98 8.15 9.26 9.83(16.73) (14.93) (16.11) (16.94)( — *) 97.61 99.39 99.72 99.87(11.34) (6.18) (3.53) (1.84)(e—p + p’)t 1.59 0.85 1.57 2.05(10.85) (10.59) (12.00) (13.23)Italy et 43.59 44.58 47.19 48.97(21.75) (20.61) (20.80) (21.45)( — *) 90.49 97.33 98.95 99.58(14.28) (6.54) (3.01) (1.13)(e—p + p*)t 7.95 7.92 8.97 9.83(13.79) (14.44) (16.05) (17.79)Japan et 77.36 63.93 61.75 60.75(17.44) (18.05) (18.29) (18.78)( — *) 81.09 94.71 97.80 99.06(16.94) (7.70) (3.57) (1.40)(e—p + p*)t 51.61 37.25 37.11 37.70(20.35) (19.64) (20.48) (21.40)UK et 2.14 1.86 4.64 7.12(11.71) (11.76) (14.00) (16.22)( *) 99.66 99.74 99.87 99.94(9.86) (5.62) (2.87) (1.24)(e—p + p*)t 1.03 3.56 2.04 1.04(0.83) (12.88) (12.29) (12.66)45Table 1.4: Forecast Error Variance DecompositionsTable 1.4c: Model (4) Estimates (CPI’s)Percentage Forecast Error Due To Permanent Relative Price ShockCountry Variable 1 month 6 months 12 months 24 monthsCanada (p — p*)t 82.12 88.59 91.38 93.39(32.96) (31.19) (30.04) (27.91)(e—p + p*)t 0.22 1.13 1.75 2.25(29.68) (29.70) (29.91) (30.25)France (p — p*)t 80.07 87.15 92.90 96.46(26.17) (23.10) (19.54) (15.04)(e—p + P)t 7.95 18.84 32.72 43.75(22.08) (24.50) (26.27) (27.33)Germany (p— p’)t 53.71 65.06 68.54 76.12(30.92) (29.11) (28.05) (24.26)(e—p + p*)t 33.62 38.10 43.24 46.94(29.42) (29.36) (29.92) (30.42)Italy (p— P)t 59.01 75.74 83.27 89.23(33.08) (30.33) (28.01) (24.28)(e—p + p)t 15.14 34.20 36.22 37.14(29.23) (31.73) (31.98) (32.15)Japan (r— P)t 38.83 48.21 56.83 69.67(31.43) (31.11) (29.81) (25.60)(e—p + p*)t 43.71 46.24 46.35 46.38(30.95) (30.55) (30.44) (30.48)UK (p — p*)t 76.63 85.31 88.91 92.84(30.52) (28.13) (26.01) (21.58)(e—p + p*)t 2.58 5.05 6.89 8.38(25.11) (26.16) (26.86) (27.56)46Table 1.4: Forecast Error Variance DecompositionsTable 1.4d: Model (4) Estimates (WPI’s)Percentage Forecast Error Due To Permanent Relative Price ShockCountry Variable 1 month 6 months 12 months 24 monthsCanada (p — p*)t 2.84 24.89 37.42 55.32(16.12) (22.94) (23.55) (20.99)(e—p + p*)t 80.75 79.89 82.21 83.38(23.12) (22.33) (21.87) (21.76)France (p — p*)t 96.95 93.46 91.56 92.07(28.31) (28.49) (28.28) (26.28)(e—p + P)t 6.76 2.86 2.67 2.69(29.29) (28.27) (28.43) (28.66)Germany (p— P)t 22.81 46.21 59.79 75.39(24.87) (25.89) (23.91) (18.49)(e—p + p*)t 75.19 70.41 74.30 76.05(25.05) (24.65) (23.87) (23.67)Italy (p — p*)t 66.87 84.17 89.97 93.59(33.61) (30.15) (28.01) (24.63)(e—p + P)t 30.59 31.63 33.87 35.53(33.54) (33.47) (33.56) (33.74)Japan (p— P)t 99.69 97.24 96.18 96.63(26.19) (25.74) (25.91) (22.64)(e—p + p*)t 15.95 7.61 8.59 9.45(30.41) (28.13) (28.60) (29.03)UK (p — p*)t 43.39 65.86 79.26 88.21(31.29) (29.31) (25.28) (20.53)(e—p + P)t 40.77 32.80 37.89 42.12(30.77) (29.01) (29.21) (29.64)Each element reports the percentage of the Variable’s total forecast error varianceattributable to the permanent relative price disturbance in Model (1). 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II357911131517192123252720313535573041434547495155555759LagsFur...I5(wp)c:UK/USe—p+p.responsetopermanentpp5shock0I3579II131517102135302720313535375041454547495153555750LagsFuei15(wp)d:UK/US.—p+p.r.spon..totransitoryp—p.shock0 a 1. 0 0 0 aLagsa 0 0 0I50791115151719212325272031355057304143404749515555675913570II131517102123232729SI3536373041434647495153555750Lags2 CHAPTER 2: A Small Open Economy In Depression:Lessons From Canada In The 1930’s2.1 IntroductionThe conventional view of the global Depression of the 1930’s is that a recession originating in theUnited States during 1929, and initiated by Federal Reserve stringency, was exacerbated domestically by financial crises following the Stock Market Crash and transmitted internationally throughsome combination of goods and financial market forces. This view is challenged by coincidencein the timing of output collapse across countries early in 1929, yet it has never been subjected tosystematic empirical evaluation and remains the preeminent interpretation of events.Canada is perhaps the quintessential small open economy, and provides a fertile testing groundfor the hypothesis that idiosyncratic U.S. disturbances and their international propagation can account for the global Depression. I test this hypothesis by estimating a small open economy modelfor Canada in which the U.S. represents the rest of the world. This jointly identifies macroeconomicfluctuations in Canada and the U.S. with realizations from a set of country-specific and international disturbances. My results suggest that the onset, depth and persistence of output collapse inboth countries are attributable to permanent output disturbances which are common to the twoeconomies. I find no significant role in the output collapse for monetary, asset market or demanddisturbances originating in either the Canadian or U.S. economy.The experience of the Canadian economy during the interwar period and the remarkable parallels between economic performance in Canada and the U.S. can be seen in Figures 2.la-2.lf.’In each country, real production declined by 30% between 1929 and 1933 and subsequently roseto its 1929 level by 1937. From 1929-1933, private investment fell by 74% and 78% in the U.S.and Canada respectively.2 The time paths of nominal variables, Ml money stocks and velocitiesand (wholesale) prices, also exhibit remarkable symmetry. These similarities suggest that the twoeconomies were influenced by similar disturbances that they propagated in similar ways, yet theeconomic history of each country has emphasized idiosyncratic factors.The proximate source of the 1929 recession in the U.S. which precipitated the subsequent outputcollapse is widely held to be the tight money stance that the Fed undertook in 1928 to prevent goldoutflows following the Poincare deflation and to stem speculation in financial markets (Hamilton(1987) and Temin (1993)). Field (1984) and Hamilton (1987) argue that the contractionary effectsof this policy were exacerbated by rising demand for transactions balances to finance the excep1For data sources and definitions see Table 2.1.2See Urquhart and Buckley (1965) and the U.S. Department of Commerce (1975).75tional volume of asset trades, while Temin (1976) and Romer (1990) propose that an importantcontributing factor was the collapse of domestic consumption. Ternin asserts that an ‘inexplicable’decline in autonomous expenditure during 1929 is the source of this collapse in contrast to Romer’s(1990) emphasis on the decline induced by future income uncertainty following the Stock MarketCrash in October. Friedman and Schwarz (1963) attribute the persistence of the U.S. Depressionto monetary collapse following the Fed’s misguided base contraction policy of 1930 and aggravatedby the effects of banking crises throughout the early 1930’s. Their emphasis on the demand effectsof the attendant rise in real interest rates is disputed by Bernanke (1983) who argues that onlythe investment and aggregate supply effects engendered by the banking crises can explain the persistence of output collapse. Bernanke asserts that the loss of bank intermediated credit raised thecost of credit intermediation and so investment and Cecchetti and Karras (1992), using a similareconometric methodology to that applied in this paper, present some empirical support for thishypothesis.The onset and persistence of the global Depression is frequently attributed to internationaltransmission of real and nominal U.S. disturbances through strict nominal parity relations underthe gold exchange standard, at least until 1931. Temin (1991), Eichengreen (1992), Romer (1993)and Temin (1993) all support this view of the transmission mechanism. Bernanke and James (1991)and Calomiris (1993) argue that imported monetary contractions from the U.S., especially, explainthe duration as well as the onset of the worldwide output collapse. Debtor defaults associated withunanticipated ‘debt-deflation’, and the supply-side effects of attendant bankruptcies and bankingcrises can account for international persistence of a transmitted monetary contraction. Others haveemphasized the role of declining export markets and capital flows in highly integrated goods andcapital markets under the fixed exchange rate as the important source of transmission of the U.S.output collapse (Kindleberger (1984)). Yet typically, the economic history of Canada and Europestresses significant country-specific factors with potential to generate recession in the late 1920’squite independently of the U.S. collapse.Safarian’s (1959) informal Keynesian analysis remains the leading interpretation of events inCanada. Safarian emphasizes not only Canada’s dependence on primary commodity exports andpeculiar vulnerability to the collapse of world trade, but also declining investment opportunitiesin the domestic economy. These reflected overexpansion during the 1920’s in the new resourceintensive industries, such as pulp and paper, exacerbated by the completion of Western settlement.He notes that while Canadian exports had recovered their 1929 level by 1937, investment remainedat half its 1929 peak at that date. Similarly, Green and Sparks (1988) present empirical evidence to76suggest that, while both the onset and severity of the Depression in Canada are explicable by thedecline in exports, the initial domestic downturn is attributable to a reduction in the autonomousexport component. This is independent of changes in U.S. income and the terms of trade, implyingthat the export collapse did not simply reflect transmission of disturbances from the U.S.Haubrich (1990) examines the role of financial market disruptions in exacerbating the CanadianDepression. The absence of bank failures in Canada, despite substantial financial market disruptionand in contrast to the U.S. experience, allows Haubrich to isolate their contribution to the outputcollapse. He finds that neither debt level nor commercial failure measures can explain the declinein Canadian output implying that bank failures per se were the financial market source of outputfluctuations in the U.S. Haubrich also finds little explanatory power for U.S. monetary aggregatesor reduced export volume in accounting for Canadian output fluctuations.My objective in this paper is to evaluate systematically these competing views about the openeconomy experience of the Great Depression using data from the interwar Canadian macroeconomy.In particular, I test whether the transmission of idiosyncratic U.S. disturbances can explain theoutput collapse in Canada, whether shocks of domestic origin were more important, or whetherthe Depression in Canada and the U.S. originated from a common source. Using monthly data onoutput, prices and money stocks for the interwar sample 1925-1940, I estimate a small open economymodel for Canada in which data from the U.S. represent the rest of the world. Specifically, I identifya structural moving average representation which is consistent with the long-run equilibrium anddynamic properties of such a model. The representation decomposes output fluctuations in Canadainto sources due to five fundamental disturbances.First, I identify a permanent real output shock which is common to the two economies. Thisdrives the stochastic trend in both output series, permanently affects all of the variables in theempirical model and is interpretable as a supply shock- the result of disturbances to the levelof resources and to technology. Second, a permanent nominal shock to the U.S. money stock isidentified which I interpret as originating in U.S. monetary policy and which is inherited by theCanadian money stock under the fixed exchange rate regime. This permanent shock to moneystocks is also reflected in the permanent component of prices for both economies but has no longrun output effects. Third, I find a permanent common asset market (velocity) disturbance whichgenerates additional permanent shocks to prices in both Canada and the U.S. but is not reflected inoutput or monetary fluctuations. The fourth disturbance is a purely transitory U.S. shock, whichI associate with real demand disturbances, and the fifth an idiosyncratic Canadian shock, whichmay incorporate purely transitory real and monetary shocks originating in the domestic economy.77The empirical results are stark, although their interpretation is less so. From 1929-1936 thetwelve month ahead forecast error in Canadian output is almost entirely due to the common permanent output shock. Similarly, the level of Canadian output at each point in time is almostexclusively attributable to the cumulative effects over time of this disturbance. Equally striking isthe remarkable symmetry of the decompositions for Canadian and U.S. output fluctuations. Whilethe velocity and money supply shocks explain a significant component of the price deflation andmonetary contraction for both economies1 and the transitory ‘demand’ shocks can explain someoutput fluctuations in Canada in the pre and post Depression sample, the onset, depth and duration of the Depression in both economies is accounted for by the effects of the common permanentoutput disturbance. The global Depression is interpretable as an international ‘collapse in trend’event.This result has implications for analyses of the Depression in both Canada and the U.S. Itpresents a challenge to theories that emphasize the role of the 1928 U.S. monetary contraction in theonset of the U.S. Depression and its transmission to other economies through the Gold Standard.I find that although there were significant negative money supply shocks in early 1928 they donot explain the fall in U.S. or Canadian output in 1929. This does not prohibit an importantrole for monetary contraction in sustaining the output collapse however. While the identifiedmoney supply shocks are insignificant for output fluctuations in both economies throughout theDepression, the money stock responds endogenously and significantly to the permanent outputshocks. Consequently, I cannot rule out a role for the induced monetary contraction in aggravatingthe (international) output collapse. Additionally, the large supply shocks after 1930 which I identifymust reflect any unanticipated permanent effects for output due to the financial crises, implying apotentially important role for credit in the supply collapse.That the onset of the Depression is attributable to permanent ‘supply’ shocks is consistent withconsiderable historical evidence of secular change in both the Canadian and U.S. economies. Forexample, Wright (1990) argues that from 1879 to 1928 U.S. industrial success was founded on extraction of abundant supplies of industrial minerals. By 1940, this was no longer the case implyinga dramatic change in the structure of American industry. Bernstein (1987) argues that the U.S.Depression reflected long-term secular change caused by rising income levels during the 1920’s.He shows that patterns of consumer demand and, consequently, labour demand and investmentshifted as rising income levels promoted industry more heavily oriented to consumer than producergoods. Both arguments suggest a role for secular change in generating output fluctuations in the1930’s. My results are also consistent with Fisher’s (1933) argument that the decline in actual and78expected productivity in the late 1920’s induced a drop in investment demand, sufficient pessimismto engender the Stock Market Crash, and effects for the capital stock which took several years tocorrect. Safarian’s explanation of the Canadian Depression experience, as the outcome of overinvestment in the growth sectors of the economy during the early 1920’s, provides a complementaryaccount of a secular output collapse in Canada.These structural factors are potentially continent-wide, if not global, and can rationalize thecommonality of the identified negative supply disturbances which may either have been synchronousacross economies or have rapidly diffused across geographic boundaries.The remainder of the paper is organized as follows. Section 2.2 presents a small open economymodel which is consistent with theoretical frameworks employed in previous analyses of the GreatDepression in Canada and Section 2.3 develops an empirical representation of this model. Section2.4 evaluates the consistency of the interwar data with the long-run properties of my open economymodel and Section 2.5 shows how these long-run, and also some dynamic, implications of thetheoretical model are imposed to identify the empirical representation. Section 2.6 presents theestimation results and Section 2.7 concludes with some interpretations.2.2 A Small Open Economy Model2.2.1 OverviewCanada is modeled as a small open economy on a fixed exchange rate with the rest of the world inwhich goods and capital markets are internationally integrated and capital is mobile. Consequently,although the Canadian economy is too small to impinge on economic conditions in the rest of theworld, both domestically originating disturbances and shocks in the rest of the world can effectdomestic fluctuations. These fluctuations cannot be offset by Canada’s monetary authorities withautonomous policy actions since the domestic money supply is pinned down by the fixed exchangerate commitment.This representation is a reasonable approximation to Canada’s interwar international economicstatus. While the interwar gold exchange standard, which effectively fixed bilateral currency exchange values by specifying gold par values for each individually, broke down following Britain’sabandonment of the regime in 1931, the arguments posed by Bordo and Redish (1990) and casualobservation suggest that Canada pursued a fixed exchange rate policy against the U.S. dollar formost of the sample period studied here. Equally, although Canada’s capital markets were underdeveloped relative to those in many Western nations during the interwar era they were well integratedwith equivalent U.S. and British markets. Inspection of interwar time-series for nominal interest79rates of similar maturity and risk characteristics in Canada and the U.S. also suggests that thecapital market integration assumption is tenable.3Specifically, I present a stochastic small open economy model in the Mundell-Fleming tradition.The domestic open economy is represented by an IS-LM construct augmented with an output supply function that permits permanent output growth due to stochastic changes in the quantity ofresources, the supply of labour and capital, and technology. Domestic output is exogenously determined in the long-run by this aggregate supply component; the ‘stochastic output trend’. However,the model admits short-run deviations from trend following unpredictable domestic and externaldisturbances to aggregate expenditure with nominal rigidities represented by an expectations augmented Phillips’ Curve.4This Mundell-Flerning framework accomodates short-run domestic output fluctuations in response to both real and nominal foreign disturbances and to local shocks. This contrasts withclassical small open economy representations in which foreign shocks are absorbed by domesticmoney and price level fluctuations, with output fixed at its supply determined level. The framework is consistent with previous analyses of the interwar years in Canada which discuss how ‘world’and, especially, U.S. real and nominal shocks caused Canadian output fluctuations.5 Since theMundell-Fleming analytic framework yields testable implications for the transmission of foreigndisturbances, dynamics and equilibrium for a small open economy, I can evaluate directly its validity in the interwar data by estimating an empirical system that is identifiable with models of thisclass.2.2.2 The ModelAssume that ‘Canada’ is a small, open, monetary economy in a multiple currency world andaccounts for a negligible fraction of total world output, trade, capital and money. The international3Whlle the magnitude and nature of domestic fluctuations induced by external disturbances is conditional on thedegree of capital market integration, for the purposes of exposition I present a model reflecting the most extremecase.4The model therefore accomodates the well-documented fact that output can be represented as a stochastic non-stationary (unit root or integrated) process. This property implies, as described in Quah (1992), that some of themultiple fundamental stochastic determinants of, or economic disturbances to, output have effects which never dieout. I follow standard macroeconometric interpretation of the permanent component of output as being ‘long-runaggregate supply’ with residual, purely transitory variation taken to be the result of ‘demand’ shocks. The originof this idea and its defence can be found in Blanchard and Quah (1989). Subsequent empirical applications includeCecchetti and Karras (1992), Gall (1992) and Ahmed et al (1993).5Safarian’s informal (1959) Mundell-Flerning open economy analysis and Green and Sparks’s (1988,1992) IS-LMBP framework are leading examples in the Canadian literature, while many of the models used by Temin (1989) andEichengreen (1990) in discussing international aspects of the Depression more generally involve similar structures.McCallum (1989) presents a thorough analysis of the properties of traditional classical and Mundell-Fleming modelsand of static small open economy equivalents.80monetary regime is exogenous and fixes the exchange rate of the domestic currency against the(average) currency in the rest of the world. A simple linearized representation for such an economyislit = 8t—ai(pt—p—e)—a2(Rt—Eipt+l)+ri’ (1)Pt = E_1p + b1(y— St) (2)St = Ot— + (3)(mt— Pt) = clyt — c2Rt +,1rnd (4)(5)where all variables are expressed in log-levels and as deviations from mean, except nominal interestrates which are specified as deviations from mean in levels. All coefficients and elasticities in themodel are measured as absolute values. The i ‘s represent the fundamental disturbances of themodel which generate stochastic fluctuations in the macroeconomy. Each element of the,t vectoris a white noise stochastic process, (it has zero mean, is serially uncorrelated and has constant finitevariance), which is orthogonal to the other disturbances in the model contemporaneously and atall leads and lags.(1) is an expenditure function. Expenditure on Canadian output in the public and privatesectors comprises consumption, investment and net exports which depend negatively on the terms oftrade with the rest of the world and the expected real interest rate and positively on an autonomousaggregate demand disturbance. This disturbance can represent fiscal policy and preference shocks,for example. Expenditure also depends on the term St which, in equation (2), represents the longrun level of output to which the economy returns in the absence of disturbances (price surprises). Iview this as fundamentally supply determined by the quantity of resources in the economy and bytechnology. The generating process for 6, is given in equation (3), where is the underlying whitenoise supply shock. This unit root specification implies that any supply shock has a permanent effecton the level of output and admits the standard macroeconometric interpretation of the permanentstochastic component of output.6 Long-run equilibrium is characterized by equalization of aggregateexpenditure to long-run aggregate supply so that output is determined only by the cumulative effectsof past supply shock realizations or its ‘permanent’ component. Supply shocks directly impactexpenditure through the effect of technology shocks on investment demand and, in aggregate data,any change in the level of demand due to permanent labour supply shifts.6To ifiustrate, if t = zt_i + Ut, where u can be any stationary invertible autoregressive moving average process,then x can be rewritten as Zti = ao u_; every realization of the stochastic error driving u has a permanent,equal effect on the level of x.81Equation (4) represents money market equilibrium. The demand for real balances is determinedby domestic income, the nominal interest rate and a fundamental money demand disturbance.Finally, equation (5) presents the condition for capital market integration under the assumptionthat the nominal exchange rate between Canada and the ‘rest of the world’ is fixed and whereCanada is small. Specifically, instantaneous uncovered interest rate parity holds.No independent policy rule or generating process is specified for the money stock which is determined endogenously for a small open economy on a fixed exchange rate with perfect capital mobility.Output and prices are determined in goods markets (equations (1) and (2)), taking as given external prices and interest rates. Given output and prices, domestic asset demand disturbances andthe world interest rate, the domestic money supply must respond with complete elasticity to equilibrate asset markets following both external and domestic disturbances. The small open economysystem is ‘recursive’ even in the short-run. In particular, any nominal or real external disturbancethat affects prices or interest rates in the rest of the world can invoke transitory fluctuations in thedomestic price level and output and, therefore, in the money supply.To close the system requires a specification for the ‘rest of the world’. I assume that thecoefficients and elasticities in the Canadian model economy are approximately equal to those in therest of the world. I also assume that the underlying fundamental stochastic processes satisfy thesame properties worldwide.=— a2(R’ — Ei.p1)+ if (6)Pt = E_1p+ b1(y — (7)= 8L + if (8)(m—j4) (9)m’ = rn+70 (10)= ñ_i+m8* (11)The interpretations of equations (6)-(9) are the same as for the Canadian economy, although there isby definition no role for ‘external’ determinants, and equations (10) and (11) specify the exogenousstochastic process for the money stock in the rest of the world.Equation (10) states that the money stock grows endogenously with permanent output growthand also has an exogenous permanent component which evolves according to equation (11). Under acommodity exchange standard which does not impose 100% reserve backing, the world money stockis roughly proportional to total reserves and monetary policy institutions have some autonomy indetermining the level of domestic reserves. I therefore allow for a non-zero monetary policy shock82in the rest of the world to reflect the aggregate effects of this leverage, which permanentlyaffects the level of the world money stock. This rationalizes a permanent nominal component inthe world economy. However, total world reserves of gold and foreign exchange also are drivenexogenously by variables such as world income and the level of world trade.7 I assume, therefore,that the money stock in the rest of the world is determined also by permanent output growth, 8.The general, short-run solution for the rest of the world’s economy has y,p and RZ as linearfunctions of past and current realizations of the four fundamental disturbances if* * rnd* andwhile the money stock, m, is determined only by the permanent money supply and outputshocks. Specifically,* — * (0* — * 8* ma*\ (iq— vt_i,mt_i,71t ,,lt ,— —8 ms d4 md4Pt — ,‘lt ‘1t ,‘7t*— \*(0, 8* m8* ct md* (i’Yt — yivt_i,•7t 1t ‘1t ,‘lt I Li-Z.C— ( s ma d* md*.LL.t— “R’Ylt ,71t 1t ,7twhere the )* ‘s are vectors of coefficients in the underlying structural parameters. These solutionsimply that Canadian output, prices, and money are determined in the short run by the fourexternal disturbances through the terms of trade and world interest rate in addition to all domesticdisturbances. By assumption there is no feedback from Canada to the rest of the world. Thesolutions are,nit = Am(O_i,fij_j,T* ,73* 77d* ,nd* (13a)* —** * d* d* dPt = ,(8t_1mt_ ,m8 (13b)—10 8* m8* d* md* 8 d hoYt — AyiVt_1,l7t ,‘lt ,% ,1t ‘‘lt’’lt) I.L.)Co — * 1 8* m8* d* md*—“Ri.’1t 1t ‘7t ,17tThe current value of each variable in the model except the common nominal interest rate dependson both a permanent, stochastic trend component driven by the non-stationary processes 8 and ñiand a second, transitory component due to current realizations of each white noise disturbance.The long-run equilibrium of the model is defined by the absence of new disturbances or pricesurprises, so that output lies at its exogenous supply-driven level in both the rest of the world andthe domestic economy, and transitory dynamics of external and domestic origin disappear. Onlypermanent components matter. This implies that nominal and real interest rates, and expected andactual inflation rates, are constant at their zero-mean levels in the rest of the world and domestic7McClosky and Zecher (1976) and Eichengreen (1990) Chapter 10 argue this point.83economy. Long-run outputs are given (from (1),(2),(6) and (7)) by(14)y = 0 (15)where the long-run levels of 8 and 9* are represented by their conditional expected values. Long-runmoney market equilibrium in the rest of the world, (9), and domestic goods market equilibrium forthe small open economy, (1) and (2), imply that long-run price levels are given by= 1h + (y — cj)0’ (16)p = p+e (17)The long-run price level in the rest of the world, p, is determined by the exogenous permanentcomponents of aggregate output and the money stock and, from (1), a long-run purchasing powerparity (PPP) relation pins down Canadian prices at this level. Long-run PPP is (implicitly) rationalized by international goods market integration in a single, composite commodity world. Despitethe presence of country-specific supply shocks, Canada is too small to affect the common currencyworld price of the composite commodity. External determination of long-run prices for Canadaalso determines the associated long-run domestic money stock. Sincem=(p*+e)+c10 (18)andm* = fi* + 78* (19)then, from (16), (18) and (19),m = m* + e + ci(8 — 9*) (20)m = ñi + e + (‘y — c1)0” + c10 (21)In the long-run, Canadian monetary authorities accomodate both the exogenously given aggregatesupply at home and exogenously fixed world prices for that output by elastically supplying theamount of currency required to ensure that all output is consumed and invested.2.2.3 Testable Implications Of The ModelThese solutions provide some testable implications for international transmission and macroeconomic dynamics. While for simplicity of exposition the model presented has very simple dynamics84and is subject to the strong restriction of white noise fundamental shocks, in the empirical workdisturbances are represented by any invertible, stationary and causal autoregressive moving average (ARMA) process in white noise. In this case, the elements of A’ and A associated with thedisturbances are lag polynomial, rather than coefficient, vectors.Three implications for the small economy’s dynamics hold in either case, with generalizationsin parentheses. First, domestic money stock fluctuations reflect contemporaneous (and historical) realizations of all disturbances in both the domestic and external economies and prevent thetransmission of contemporaneous domestic asset market shocks to output. Second, domestic pricefluctuations in Canada reflect contemporaneous (and historical) realizations of domestic goodsmarket disturbances and both nominal and real external disturbances which engender transitorydeviations from trend in output. Third, domestic output fluctuations reflect contemporaneous (andhistorical) realizations of all disturbances in the rest of the world and all domestic shocks exceptthose originating in domestic asset markets.Additionally, the model predicts that the impact and short-run responses of all variables in themodel will differ across the two economies due to international transmission even though long-runresponses may be identical. Since the domestic economy is subject to shocks of both domesticand external origin in the short-run, the vectors of (lag polynomial) parameters A and A’ will ingeneral differ across the two economies. Moreover, the rest of the world’s economy is not affectedby Canadian disturbances and the money stock in the rest of the world is unaffected by any butthe autonomous nominal and real permanent external shocks.The solutions also generate testable implications for long-run equilibrium. The theoreticalmodel rationalizes stochastic non-stationarity in the log level of output, prices and money both inthe domestic and world economies, so these implications take the form of conditions on commonstochastic trends or cointegrating relations between variables both within and across countries.8When variables share common stochastic trends, common sources of non-stationarity cancel outin the unique linear combination which represents a structural equilibrium relation. Consequently,although money stocks, prices and outputs are individually non-stationary, and so can wanderwidely with no mean reverting tendancy, their equilibrium linear combinations are stationary andthe variables trend together over time. The current representation in ARMA disturbances impliesthat we should observe purely transitory stationary deviations from three, long-run equilibriumconditions.First, there is a long-run money market equilibrium condition in the external economy which8See Engle and Granger (1987) for definition and discussion of cointegration in time-series.85implies that prices in the rest of the world inherit the stochastic trends in output and the nominalmoney stock (see (16)). Second, long-run purchasing power parity holds, that is, Canadian pricesshare this stochastic trend of prices in the rest of the world (as in (17)). Third, there is a long-run money market equilibrium condition for the domestic economy in which the nominal moneystock inherits the stochastic trends in money and output in the rest of the world and in domesticoutput ((20) and (21)). While the first two equilibrium conditions are shared by many closed andtwo-country models with long-run price flexibility, the third uniquely characterizes internationalmonetary equilibrium for a small open economy of this class.Additionally, given the similar behaviour of output across countries in the inter-war data, Ialso test for common supply shocks; for a common stochastic trend in the domestic and externaleconomies’ output series. This common trend could be rationalized by world technology shocks ortechnology shocks which are diffused rapidly across geographic and economic boundaries. Satisfaction of such a common trend characterization of the data would imply that, provided internationalmoney market equffibrium (20) holds, domestic nominal money, real money and velocity sharestochastic trends with their external counterparts.2.3 Econometric Methodology2.3.1 OverviewI estimate a moving average representation (MAR) for integrated macroeconomic data from theinterwar era for Canada that accounts for and uses information on common stochastic trends. TheCanadian macroeconomic variables of interest are assumed to be jointly determined by a set offundamental (orthogonal) disturbances with interpretation as internal and external shocks to asmall open economy with short-run non-neutralities due to nominal rigidities. The MAR expressesthe current value of each variable as the cumulative effect of current and past realizations of thisset of disturbances. It can represent the dynamics of the small open economy model maintainedas generating the Canadian macroeconomy, subject to the long-run equilibrium constraints of themodel which take the form of common stochastic trends. The estimated responses of the empiricalmodel to each type of disturbance can then be inspected and their consistency with the stylizedresponses predicted by the Mundell-Flemning small open economy framework evaluated.2.3.2 The Structural Moving Average RepresentationRecent advances in macroeconometric theory and practice mean that the methods required toconduct this empirical analysis are well documented and so only a brief review of the methodology86is presented here.9Assume that IX is an N-vector of jointly covariance stationary variables (X requires firstdifferencing to achieve stationarity) such as [yt, Lmt, I(m + e), zSp, i.(p + e)] where theelements of X are cointegrated. I posit the existence of a structural MAR for some appropriatetransformation of the elements of X in an N-vector of fundamental disturbances, t, which haveinterpretation as the shocks in a simple open economy Mundell-Fleming model when some of theshocks are known to be permanent for and common to the elements of X. This representation innt is assumed to be ‘complete’; given the maintained model, it fully captures the determination,dynamics and interrelations of the N variables.’0 The MAR also is assumed to be fundamental forand to account for common stochastic trends or long-run equilibrium relations between theelements of X.The objective is to study the dynamics and long-run properties of this structural system to shedlight on sources of output fluctuations by estimating an empirical representation. We know fromEngle and Granger (1987) that in the presence of cointegration in levels between the elements ofX simple MAR representations for IX in nt of the form= D(L)i7 (22)are misspecifled since there are fewer independent permanent shocks in the system than is impliedby the N-variable specification. One or more of the shocks must be purely transitory for all variablesand the long-run multiplier matrixD(1)= (23)which represents the cumulative effect of shocks on the first difference of X or the infinite horizoneffect on the level of X is singular, having one or more columns containing all zeros. The correctstructural representation for cointegrated X restores the long-run multiplier matrix to full rarLkby renormalizing the system to account for the cointegrating relations. The resulting vector-errorcorrection, or alternative triangular, system contain equivalent information and the triangular formis applied here. 12The structural MAR for the triangular representation is given by9See, for example, Blanchard and Quah (1989), and King, Plosser, Stock and Watson (1991).10See Quah (1992). I also assume that conditions required for an N-disturbance representation to approximatean underlying generating process for X of higher dimension are satisfied. Blanchard and Quah (1989) present adiscussion, Theorem and proof.11Lippi and Reichlin (1993) and Blanchard and Quah (1993) discuss conditions under which an assumption offundamentalness of the MAR may not be valid.‘2Phillips (1991) discusses the properties of triangular systems.87[(X21)]= (24)where X is partitioned into subvectors X and X2 of dimension Ni and N2, Ni+N2=N, and a isan (Nix N2) matrix of (known) cointegrating coefficients where N2 is the number of cointegratingrelations and Ni=N-N2. The matrix lag operator, r(L), can be partitioned conformably with Xinto F1(L) and F2(L) of dimensions (Nix N) and (N2xN) respectively. The (Nxi) error vector Titrepresents the set of structural disturbances from the theoretical model with covariance matrixdiagonal to reflect orthogonality of these disturbances. All dependent variables in this representation are stationary so that estimation of and inference from an associated reduced form is basedon standard asymptotic distribution theory.The structural MAR can be estimated, given knowledge of the cointegrating vectors, as areduced form VARB(L) [ (X2-a i)] [::] (25)with X1 and X2 defined as above. B(L) and t are the reduced form parameter and error vectorsrespectively and can be partitioned conformably with X. The reduced form has impact matrixB(O) = I and variance-covariance matrix E(eei) = E. Inversion yields the infinite order reducedform MAR[(X ] = C(L) [ ] (26)where C(L) = [B(L)]’ and C(O) = [B(O)]’ = I. From this reduced form the underlying structuralMAR can be identified given standard algebraic relations between the reduced form and structuralparameters and identifying restrictions imposed by theory.By assumption, C(L)Et = r(L). This implies that r(O) = et and that the structural MARpolynomial is given byI’(L) = C(L)F(O) (27)Therefore, both the structural parameters in F(L) and innovations 1It can be identified from thereduced form estimates if T(O) is known. In practice, the structural impact multiplier matrix isnot known and must be estimated. In the absence of additional information there are fewer knownreduced form coefficients than unknown structural parameters. This requires that P(O) be identifiedby imposing restrictions on the structural parameters to reduce the number of unknowns.Some information is available which can be used directly in the identification of I’(O). Fromabove there is a covariance condition to be satisfied which uses reduced form information:88= F(o)r(O)’ (28)where is assumed to be diagonal or, as here, normalized to be the identity matrix. This conditionprovides (N(N+1)/2) non-linear restrictions on the elements of I’(O). Since there are N2 unknownelements in I’(O), exact identification calls for another (N(N-1)/2) restrictions. 13I follow Blanchard and QuaJa (1989) by using zero restrictions implied by the Mundell-Flemingmodel on the matrix of long-run multipliers P(1)= >J I as the remaining identifying assumptions. Such restrictions are meaningful only in the presence of non-stationarity. If the vector, X,is stationary r(1) is a zero matrix since no shock can permanently affect the level of stationaryvariables. Unit roots in the variables of a MAR system, however, can always be decomposed intoa transitory and a permanent component (Quali (1992)), each of which can be viewed as havingmultiple structural sources. In multivariate systems that allow identification of multiple structuraldisturbances, this decomposition can be exploited and the two components isolated by imposingtheory-driven zero restrictions on I’(1). By using all of the zero-parameter long-run restrictions ofthe Mundell-Fleming model, in addition to three other (short-run) implications as linear restrictions on the elements of F(O) (see Section 2.5), the structural parameters and disturbances can bejust identified.’4 The resulting estimates of I’(L) and Tit describe the propagation mechanisms forgrowth rates, and I’(L)/(1— L) describes the dynamics and long-run properties for the levels ofvariables which are of most interest.2.3.3 Model Specffication TestsI can directly evaluate whether the data are consistent with the model’s implications in severalways using this empirical framework. First, I assess which of the model’s long-run equilibriumconstraints can be imposed on the triangular specification in the form of the ‘error-correction’terms with univariate and multivariate integration and cointegration tests. These inform on whetherindividual variables and their linear combinations are stationary, and on the number of independentstochastic trends in the data. The tests are commonly applied in empirical macroeconomics and13A number of alternative approaches have been employed to derive such restrictions. Sims (1980) identifiesr(0) by assuming that it is lower triangular (a Wold causal chain generates the system which is said to be resursive).Bernanke (1986), Fackler and Parker (1990) and others estimate ‘structural models’ of the contemporaneous relations;rather than arbitrarily assume recursivity in r(0) they impose identifying restrictions derived from economic theory.These approaches do not use long-run information implied by theory which implies restrictions on the long-runmultiplier matrix, as I do, although such restrictions are often less arbitrary and controversial than those placed oncontemporaneous relations.141 follow Cecchetti and Karras (1991), Gall (1992) and Ahmed at al (1993) in extending Blanchard and Quah’s(1989) bivariate decomposition of output fluctuations to the multivariate case.89are not discussed further here.’5Second, I evaluate consistency of the multivariate triangular reduced form selected by the nonstationarity tests with a decomposition for the non-stationary variables into transitory and permanent components using the Granger-priority test suggested by Quah (1992). This involves applyinga standard x2 block-exogeneity test to the lags of X2 — aX, in the equations for AX,. If theblock of lags for the error-correction terms have no predictive power for AX,, while the conversedoes not hold, the implied MAR with innovations orthogonalized by zero restrictions on F(1) hasno permanent/transitory decomposition for zXX,. Specifically, this structural MAR has zero coefficients at all lags for shocks to the transitory component for the integrated variables and zerorestrictions applied to elements of T’(l) to invoke a permanent/transitory decomposition cannot bejustified. 16Finally, consistency of the data with the model’s predictions for short-run dynamics and international transmission of disturbances is evaluated by inspecting the estimated dynamics of thestructural MAR. The information admitted by such inspection is conditional on the presence of‘overidentifying restrictions’ for the theoretical model. The model in Section 2.2 generates manylong-run and some short-run implications which can be imposed as zero and linear restrictions toidentify the structural MAR parameters and innovations with those of the economic model. However, there are more of these restrictions than are required to exactly-identify the N2 elementsof I’(0) in the empirical representation. I therefore select a subset of these economic restrictionsto identify the structural MAR and can assess the compatibifity of the estimated innovations, responses and variance decompositions with the remaining, non-imposed and testable implications ofthe model.’72.4 Data AnalysisI make the strong assumption that the U.S. data can represent the rest of the world relative toCanada. However, the arguments of Bordo and Redish (1990) that Canada fixed her currencyexchange rate against the $U.S. for most of the interwar era, and the large fraction of externaltrade in goods and assets for Canada accounted for by the U.S., suggest that this is a reasonablefirst approximation.I use monthly data, deterministically adjusted for seasonality, on six variables of interest forthe interwar subsample 1924:1-1939:12 : Canadian and U.S. industrial production, wholesale prices‘5See King, Plosser, Stock and Watson for data analysis that is motivated by the same concern with modelspecification.165ee Quah (1992) for details, theorem and proof.175ee Gall (1992) for use of overidentifying restriction tests as evaluation of a macreoconomic model.90and Ml money stocks, where the U.S. price and money stock variables are adjusted by the nominalCanada/U.S. exchange rate and all variables are expressed as natural logarithms (unless otherwisestated). The exchange rate adjustment is consistent with the model and does not alter the time-series properties of the data given Canada’s fixed exchange rate policy for much of the sampleperiod.’8 Since real and nominal interest rates are predicted to be purely endogenous, stationaryoutcomes of the model we do not incorporate them explicitly in my empirical representation inthe interests of parsimony. 19 The sample period 1925:1-1939:12 is used in all tests and regressions,with values for 1924:1-1924:12 used up as lags in pre-estimation data analysis and in VAR lags andlag length tests. Data sources, notation and definitions are given in Table 2.1. All notation in thetext now reflects use of U.S. and Canadian data to represent the rest of the world and the domesticsmall open economy respectively.2.4.1 The Interwar DataFigures 2.la-2.lf and Tables 2.2a, 2.2b and 2.2c present some informal (unconditional) evidence onthe behaviour of important Canadian and U.S. variables during the Great Depression. The figures,which plot the seasonally adjusted data normalized to the 1935-1939 average, show the very similarbehaviour of the Canadian and U.S. economies during the interwar period. Although each pairof series display some different short-run movements, they appear to ‘trend together’ and the dipin outputs, money supplies and prices during the 1929-1933 era is synchronized across the twocountries. Exchange rate adjustment of the U.S. data appears not to cause significant deviationsfrom common movements in the data. The similar bivariate trend behaviour of the series suggeststhe possibility of cointegrating relations between outputs, prices, money stocks and velocities whichis consistent with the model in Section 2.2 amended to allow for common stochastic output trends.Table 2.2a shows positive average monthly output growth for the period 1925:1 to 1928:12for both economies, and a high growth rate for Canada in particular, with ‘business cycle peaks’occuring in the first half of 1929. The Depression sample trough for industrial production in theU.S. occurs before that in Canada (July 1932 and February 1933 respectively). Mean outputgrowth rates are negative for both series during the Depression era (although positive in the othersubsamples), mean levels are lowest and variablility highest. Additionally, the sample correlation18Repeating the analysis of this paper using the unadjusted Ml and price series changes few results. Despite thedepreciation of the exchange rate due to Britain and the U.S. leaving the Gold Standard in 1931 and 1933, the timeseries properties of the data, non-stationarity, cointegration and estimated VAR results are qualititatively unchanged.Few qualitative changes arise in the innovation accounting exercises.19The responses of the remaining six variables to the disturbances that I identify will therefore reflect interest ratebehaviour.91of outputs is highest for this mid-sample period suggesting a peculiar strength of common factorsduring the Depression. Output in neither country recovers to its 1929 peak level by the end of 1939,nor does it fall to its 1934, recovery level during the recession of 1937-1938, reflecting the strongpersistence of the Depression. Overall, the output data suggest very similar properties and timingof business cycle peaks, troughs and persistence during the interwar era for the U.S. and Canada.Ml money stocks exhibit very similar patterns of behaviour in log levels and first differencesto those of production, although the U.S. series attains its trough only in 1933:11. The timing ofcollapse and recovery is otherwise similar. Money stocks are strongly contemporaneously correlated,implying that the small open economy, fixed exchange rate implication for external determination ofthe Canadian money stock may be valid. The behaviour of prices mimics that for outputs and moneystocks as expected; again, the two series exhibit strong similarities in their unconditional propertiesand in the timing of peaks and troughs. The Depression era is characterized by mean annualdeflation rates of 6% for both price series, and the full sample estimate of their contemporaneouscorrelation is remarkably high, 0.97. These statistics illustrate common nominal properties in thetwo economies which, in the context of the Mundell-Flerning model of Section 2.2, may indicatethat gold standard mechanisms functioned efficiently.While these statistics suggest close links between the two economies during the interwar eraand the Depression in particular, more formal analysis which studies conditional correlations in thedata is required to identify the nature of these relations. Preceding Sections argue that evaluationof the appropriate time-series representation for each series, and of the presence and number ofcommon stochastic trends in the data in particular, is an important pre-estimation specificationtest. I therefore apply standard tests for non-stationarity and cointegration which allow inferenceon whether the theoretical equilibrium constraints outlined in Section 2.2 are satisfied in the data.2.4.2 Tests For Non-stationarity And CointegrationTables 2.3a and 2.3b present evidence that each of the variables can be represented as a unit rootprocess; as containing a stochastic trend. Table 2.3a presents computed values for the Phillips(1987) Za and Z and the Dickey-Fuller (1976,1979 and 1981) t-statistics which test the null hypothesis of a unit root in the level of each series against the one-sided alternative that the seriesis stationary. The evidence is consistent with the null for all series examined. Table 2.3b presentsevidence against the null for the first difference of each series.20 I therefore treat each series in20The evidence conflicts with findings of non-stationarity in post-war inflation rates. Estimates of the autoregressivecoefficients for inflation rates in Canada and the U.S. in the ADF(4) test regression are 0.54 and 0.57 respectively.This suggests that inflation rates are stationary. Since there is also no evidence of non-stationarity in Ml or output92the vector [yc , , Yus, (m5 + e), (pus + e)] as a univariate unit root process which requires firstdifferencing to achieve stationarity.This implies that all series are subject to permanent shocks. In general, one cannot uncoverthe sources of these permanent shocks using univariate methods. However, cointegration testsinform on the data’s consistency with the model’s implications for structural long-run equilibriumrelations reflected in common sources of stochastic trends in the data. I use the same Phillips andDickey-Fuller statistics to test the null hypothesis that the residual series from each cointegratingregression is non-stationary or, equivalently, that there is no cointegration between variables in theregression. Table 2.4a presents results of univariate tests of cointegration applied to the residualsfrom the cointegrating regressions of the dependent variable on the regressor specified.Consistent with the long-run equffibrium conditions (16) and (18), I cannot reject the null ofnon-cointegration for money and prices for either country (rows 5 and 6 of Table 2.4a). This impliesthat prices in the rest of the world absorb permanent components additional to those reflected inthe money stock, and that while long-run PPP determines prices in the small open economy, thedomestic money stock will also reflect long-run asset market equilibrium conditions. The Phillips’test statistics in the first three rows of Table 2.4a provide strong evidence to favour bivariate cointegrating relations for Canadian and U.S. outputs, prices and money stocks. Weaker support issupplied by the Dickey-Fuller test results for these hypothesized equilibrium relations. Cointegration of outputs implies there is a common stochastic trend in outputs which, under the maintainedhypothesis that only aggregate supply shocks matter for production in the long run, reflects commonaggregate supply conditions. The common trend in prices reflects, under the maintained model,an unconstrained long-run PPP relation with common trend generated by aggregate supply shocksand money supply shocks in the U.S. economy. Finally, cointegrated nominal money stocks is animplication of the first two results and reflects the international monetary equilibrium condition,(20). The common trend in money stocks is generated by permanent money supply shocks in theU.S. and the common permanent real shock.There is no evidence to support cointegration of domestic real money balances with domesticoutput for either country; of long-run domestic money market equilibrium of the form (4). Notably,the addition of nominal interest rates to the money market equilibrium relations had no qualitativeeffect on this result, so the omission of interest rates is not important for this conclusion. Noncointegration of domestic money demand functions implies that both economies are subject topermanent money demand or ‘independent velocity’ shocks in asset markets.2’ Since nominalgrowth rates, this seems an appropriate ‘structural’ conclusion.21 In general, this result will reflect any misspecifIcation of the equilibrium conditions for asset markets. However,93money stocks and prices do cointegrate, these permanent velocity shocks must be common to the twoeconomies. If the money demand shocks are non-stationary processes and do not ‘disappear’ in long-run equilibrium, the long-run U.S. price level is given by Pus = m5 — ci6u8 — 71mdu8 and the long-runCanadian money stock by m = Pus + e + c1 0c + Given common 6’s, m = rn, + e + md —and so cointegration of nominal money stocks requires cointegration of the money demand processes;common money demand shocks. Long-run prices in both economies must contain a componentdue to this permanent asset market shock which provides additional rationalization for the noncointegration of money and prices in each economy.In Table 2.4b, I impose some coefficient constraints implied by theory. First, I assume that thecommon aggregate supply shock has an equal long-rim impact on the logarithms of output, or aproportional effect on the levels. Second, I assume that there is a constant, proportional relationshipbetween prices in the U.S. and Canadian economies in the long-run, or impose relative long-runPPP, as predicted by (17), and also impose the (1,-i) coefficient vector in the money stock (and realbalance and velocity) cointegrating regression implied by the condition for international monetaryequffibrium, (20). These restrictions allow application of simple non-stationarity tests to the log-differences of outputs, prices, and money stocks. Tests for non-stationarity of real balances confirmnon-cointegration of money and prices for each country in rows 5 and 6. The results documentstrong support for the coefficient restrictions at the 5% level for all but the long-run PPP relation,which is favoured at the 10% and 15% levels, as shown in the first three rows of Table 2.4b.In Table 2.4c, Johansen’s maximum-likelihood multivariate cointegration test statistics are applied to confirm inference drawn from the univariate results that there are three, independentcommon stochastic trends in the data. These multivariate tests use rank conditions to evaluate the dimension of a multivariate system. Specifically, they test the null of no more thanr-cointegrating vectors in a given system against the alternative of more than r cointegratingvectors, and provide unnormalized maximum-likelihood estimates of the space of cointegratingvectors. I evaluate the number of independent cointegrating vectors in the six variable system[yc, m , Pc, Vus, (m + e), (pus + e)]. Univariate tests imply that there are three such vectors in thesystem; one in the two output series, which reflects purely the common stochastic supply trend,one in the two money stock series, which additionally reflects the nominal money stock trend, andone in the two price series, which incorporates additional permanent components due to aggregatesupply and money demand shocks. The system should therefore be three-dimensional, have ‘rankthree’ or contain three independent unit roots.there is sufficient evidence from contemporary and historical data to support cointegration in such simple moneydemand specifications to warrant the labeling of this result an outcome of permanent velocity shocks.94The first line of Table 2.4c shows that although I firmly reject the null of no cointegration inthe system, I carmot reject the null of three independent cointegrating vectors. Tests of hypotheses about intermediate numbers of vectors suggest that there are no fewer than two independentcointegrating relations in the system which is also consistent with a three unit root specification.In addition, the Johansen procedure rejects the null of no cointegration for the bivariate systemsin outputs, money stocks and prices at least at the 15% level for all cases but cannot reject thenull of no cointegration between money and prices or real balances and output (no long-run moneydemand equilibrium) for either country’s data.The bivariate systems estimated in the Johansen tests imply normalized cointegrating vectorsgiven in Table 2.4d. These are consistent with theoretical priors in the output, money supply, realbalance and velocity equations and there appears to be a long-run PPP relation with a coefficientclose to but not equal to unity. Point estimates of the cointegrating vectors are also providedby the Phillips-Hansen Fully Modified procedure which shows some deviation from unit vectors.Subsequent sensitivity analysis showed that imposition of these alternative cointegrating vectorsgenerates no significant differences in the reduced form or structural model results compared toa system in which unit vectors are imposed for all three cointegrating relations. Consequently, Ireport results only for the model in which all three unit coefficient restrictions are imposed. 222.5 Identification Of The Empirical ModelThe preceding data analysis suggests the existence of three independent common stochastic trendsin this data set consistent with the following interpretations. First, there is a permanent output shock which is common to the two economies and interpretable as a world aggregate suppiyprocess. Second, there is a permanent nominal shock which is common to the two economies andinterpretable as a U.S. policy driven money supply process inherited by an endogenous money stockin the small open economy. Third, (and not predicted by the model), there is a permanent shockto real money demand, and so prices, which is common to the two economies and interpretableas a velocity or money demand process. While the money supply shock can be assumed importedfrom the U.S. through the fixed exchange rate regime, and the aggregate supply shock to eitheraffect both economies simultaneously or to be rapidly diffused across geographic and economicboundaries, interpretation of the commonality in money demand shocks is not unambiguous. Itmay represent permanent shocks to the demand for North American currency or assets relative to221 also find that real balances and velocities of the two economies cointegrate, in Table 2.4a, which is implied bybivariate cointegration of outputs, money stocks and prices. Further, they cointegrate strongly with unit coefficientrestrictions, supporting the coefficient restriction results for the underlying variables, in Table 2.4b. Johansen testssupport these univariate results, in Tables 2.4c and 2.4d.95those in Europe.In addition to the three permanent shocks I can identify three transitory disturbances in the sixvariable system. The class of Mundell-Fleming small open economy models ifiustrated in Section2.2 suggest the transitory component will incorporate a uniquely U.S. transitory demand shock, auniquely Canadian transitory demand shock and, under less than perfect capital market integration,possibly a uniquely Canadian transitory money supply shock. Since the current interest is primarilyin separately identifying international and idiosyncratic shocks, I attempt only to isolate the U.S.and Canadian elements of the transitory component and not to disentangle individual sources ofpurely transitory disturbances. Consequently, while I can exactly identify six disturbances in theempirical system, structural interpretation can be placed only on five; shocks to the three, commonstochastic trends, an aggregate U.S. transitory component and an aggregate Canadian transitorycomponent.I identify these disturbances with both long and short-run restrictions. Exact identificationrequires estimation of 36 elements in T’(O). The covariance condition, r(o)r(o)i = , provides21 of these. As noted in Section 2.3, theory often suggests more restrictions for the structuralempirical model than are needed for exact identification and, in fact, I select a subset that providesclose correspondence with the small open economy interpretations desired of the six disturbances.Other behavioural restrictions implied by the model (and by history) for the impulse responses andidentified disturbances are used to evaluate the model’s predictions (as overidentifying restrictions).Given the unit root and cointegration test results, and the shock interpretations implied byMundell-Fleming model, I specify and estimate the following empirical system which is the analogueto the triangular system of Section 2.3Iyct it8rn8’mdPCt= I’(L) (29)Yct— !JU8tJ Tit(m—— et) 71d(pct — PuBt — et) d2cSubscripts now denote country of origin and date, respectively, and superscripts denote shocktype and country of origin respectively. Where shocks are common to the two economies a singlesuperscript appears. This system is identified by applying the following restrictions.First, in the hypothetical long-run with no new disturbances, the variables are assumed to begenerated by the stochastic trend representation:96zXy F11(1) 0 0 0 0 0LIm F21(1) F22(1) 0 0 0 0 77rn81LsPc — r31(1) r32(l) F33(l) 0 0 0 30(yct—— r41(l) F42(l) r43(l) r44(l) F45(1) P46(l)(m— m8 — et) Ps1(l) I’52(l) [‘53(1) r54(l) F5s(1) F56(l) d1c(p—Pu8t — et) I’61(1) I’62(1) f63(1) F64(l) T65(l) P66(1) d2where the last three rows of (1) are all zeros by cointegration which imply stationarity of thethree log-differenced variables. The long-run zero constraints in the first three rows comprise12 of 15 restrictions that are imposed on the system. These uniquely identify three permanentdisturbances, by assuming that each has a unique iufiuence on the system, using only long-runrestrictions in a lower triangular long-run multiplier matrix. 23 These restrictions, in accordancewith the interpretations placed on the shocks by the model of Section 2.2, imply that only aggregatesupply shocks matter for Canadian and U.S. outputs in the long-run, that only aggregate supplyand money supply shocks matter for Canadian and U.S. money stocks in the long-run, and that allthree permanent disturbances are absorbed by prices in Canada and the U.S..In addition, I impose three short-run restrictions to just identify the empirical system. Thefirst two of these identify the aggregate of the last two disturbances as being of uniquely Canadianorigin. The third places an additional short-run restriction to identify the money supply shock asan ‘exogenous’ monetary policy disturbance in the U.S.. These are imposed as linear restrictionson the impact multiplier matrix, I’(O). The first two(Pi50) + I’16(0)) — (P450) +r46(o)) = 0 (31)(r25o) +r26(o)) — (r55o) +r56(o)) = 0 (32)impose a zero impact effect of the (aggregate) Canadian transitory disturbance for U.S. outputand money. There should be no significant feedback from the Canadian to any variable in the U.S.economy of shocks that originate in Canada at any lag, according to my traditional small openeconomy model. The short-run identifying restrictions impose no immediate feedback to outputand money. If these uncover the true Canadian component the theoretical restriction should alsohold.The final identifying assumption imposed is thatr24(o)— I’54(0) = 0 (33)This just identifies the system by imposing zero impact effect of domestic real demand disturbancesfor the domestic money stock in the U.S.. This is the most controversial of the identifying restric23See, for other lower triangular long-run identifying schemes, King, Plosser, Stock and Watson (1991) and Ahmedet al (1993).97tions, although entirely consistent with the theoretical model. There are other alternative plausiblerestrictions that could be used to help identify the second permanent disturbance as an exogenouspolicy shock to the money stock.24 These are used as overidentifying information (see Section 2.3)to evaluate the model.This empirical model forces the data to satisfy strong long-run constraints. In particular, thestructural specification implies that the Canadian economy is determined by international stochastic trends at the infinite horizon. However, it also admits a significant explanatory role for purelytransitory shocks of both Canadian and U.S. origin in generating short-run output fluctuationsduring the inter-war period. Quaia (1992) shows that my multivariate permanent/transitory decomposition of macroeconomic fluctuations has sufficient structure to generate meaningful measuresof the relative size of these two components. My short-run restrictions also allow identification ofa purely domestic transitory component. I can therefore assess the relative importance both ofpermanent and transitory and of domestic and international disturbances for Canadian outputfluctuations during the Great Depression.2.6 Estimation Results2.6.1 The Reduced Form Triangular VARI estimate the triangular cointegrated VAR. Standard criteria select a four lag specification anda constant term is included in each equation.25 Some selected statistics are shown in Table 2.5.F-tests of the hypothesis that given blocks of lags in an equation are zero reveal that Canadianmoney growth responds significantly to all variables in the model, suggesting that the small openeconomy assumption of money supply elasticity well represents the reduced form behaviour of thisvariable. Inflation in Canada, moreover, is not significantly predicted by domestic money growthwhich also implies endogeneity of the domestic money stock. Also notable is the significance ofsome block of lags of the error-correction terms, X2— cXi for all of the Canadian growth ratevariables.‘Quah’ tests applied to the reduced form VAR confirm the F-test results; the computed value ofthe X2(36) statistic for the null hypothesis that the set of error-correction terms [(yc — y), (m —m8 — e), (Pc PuA — e)] do not help predict [/.yc, IXm, p] is 103.02 which is significant at less than1%. Similarly, the integrated part of the system helps predict the error-correction component with24The U.S. money stock should not respond also to money demand disturbances (a zero short-run restriction couldbe imposed) at any lag, and the money supply shock should have an equal long-run impact on money and prices.25Time trends are insignificant in each equation of the VAR and make no significant difference to the reduced formor structural model results.98a test statistic computed value of 85.32. This system therefore does capture a permanent/transitorydecomposition for the integrated Canadian variables.262.6.2 Computation Of The Structural MARI invert the VAR, using 180 reduced form moving average coefficients as the cut off point forthe reduced form moving average, and identify the structural MAR as described above using theestimated reduced form coefficients and identifying restrictions. 27 derive the structural movingaverage for the levels of the Canadian variables by inverting the difference operator in the difference-stationary component, X1, of the MAR. I then generate impulse responses for each of the U.S.variables by taking linear combinations of the estimated parameters of the system [Yc, m , J, (Yc —Yus), (m — m3 — e), (Pc — Pu8 — e)].I calculate confidence intervals for the point estimates of the structural moving average parameters and structural innovations, and so the impulse responses, forecast error variance decompositions and historical decompositions, using Monte Carlo integration to compute the empiricaldistributions of these statistics. These one-standard error bands are based on specific distributionalassumptions about the parameter estimates of the reduced form.28 I report bias adjusted estimateswhen the bias, measured as the difference between the mean of the Monte Carlo draws and thepoint estimate, is large and significantly alters the results. All standard errors and biases reportedare generated from 2500 Monte Carlo draws.2.6.3 The Identified InnovationsThe shocks that I identify, and their one standard error bands, are shown in Figures 2.2a-2.2e. Ican infer nothing about the relative importance of each in the Depression without also accountingfor the estimated values and significance of the impulse response functions, however, investigatingthese plots helps evaluate my interpretation of the structural innovations. In particular, I can judgewhether remarkable values of the point estimates are consistent with known historical events thatcan be associated with specific macroeconomic disturbances. In general, the identified disturbancesare at least consistent with interpretations implied by the structural model.26This result is invariant to the presence of a time-trend in the VAR equations and to the use of the non-exchangerate adjusted U.S. money supply and price variables.27The solution to r(O) is derived using a non-linear system solution a’gorithm available in GAUSS386 (with thedefault program settings.Specifically, I assume that the OLS estimate of the VAR variance-covariance matrix, , is generated by aninverted-Wishart distribution, and construct a sequence of E ‘s from which I generate a sequence of the VAR parameter vector in B(L). These two sequences are then used to compute the structural model parameters using the usualidentification techniques for each draw in the sequence.99The 1929 recession which precipitated the Depression is preceded by and coincident with severalsignificant events. First, there is a run of significant and negative common supply shocks to output,the i, from 1929:7 onwards culminating in a large negative supply shock in November of 1929,the month following the Stock Market Crash. These are consistent with Fisher’s (1933) hypothesisthat negative actual and expected productivity shocks drove the U.S. economy to financial marketdisaster and into Depression. Second, there is a run of significant, negative autonomous moneysupply shocks, the in late 1928 and early 1929 with a large negative realization in December1929 which may represent the monetary base contraction initiated by the Federal Reserve stressedby Hamilton (1987) and Friedman and Schwartz (1963). Third, there is a significant negative runof ‘velocity’ shocks, the nd, during late 1928 which represent positive money demand disturbancesand could reflect the rising demand for transactions balances in U.S. stock markets.29 Finally, Iidentify a series of negative U.S. transitory demand shocks, the during 1929, which can beassociated with Temin’s (1976) autonomous demand shocks. The Canadian transitory component,captured by the aggregate if’ +2c, is too imprecisely estimated for us to draw inference aboutits behaviour during 1928 and 1929.The persistence of the Depression from 1930 to early 1933 is associated with a series of significant, negative aggregate supply shocks over that period, with some large negative autonomousmoney shocks in early 1930 and in early and late 1932, and with large positive velocity shocksof late 1931 and early 1933. The supply shocks are consistent with Bernanke’s hypothesis aboutthe supply effects of financial crises during this period. Similarly, the money shocks in 1930 areconsistent with Hamilton’s (1987) and Friedman and Schwartz’s (1963) assertions that the FederalReserve pursued contractionary policy during this period. I interpret the velocity shocks as speculative runs against the U.S. dollar during periods of withdrawal from the Gold Standard of keyparticipants.I also note the identification of significant positive supply, money supply and velocity shocksin September 1939 with the onset of World War IL These are consistent with priors about NorthAmerican output, monetary policy and money demand responses to the announcement of theoutbreak of war in Europe.29While this is a permanent money demand disturbance I identify it only with the long-run restriction that it canpermanently affect prices but not the money stock or output. Consequently, it has a long-run positive price effectand behaves like a ‘negative’ money demand disturbance the structural covariance Choleski decomposition is uniqueup to sign changes.1002.6.4 Impulse Response FunctionsFigures 2.3-2.8 show the response of each variable to a one standard deviation innovation to aggregate supply, money supply, and velocity, and to one standard deviation transitory shocks in theU.S. and Canada respectively. One-standard error bands are also plotted.The response of Canadian output to the supply shock is somewhat unstable during the firstfew months following the innovation in contrast to the smooth response of U.S. output which risessteadily to its new permanent level. This may be attributable to different dynamic responses ofCanadian and U.S. output and prices to the common shock and the consequent impact for exportdemand and the terms of trade. The overall response for both variables is as anticipated; large,positive, significant and increasing over a one-year period. The initially negative response of production to the money supply shock disappears rapidly.3°Production in both countries subsequentlyrises within four months of the money supply shock. However, the responses are insignificant atall lags for both countries except for the very small, significant response at the very first lag forthe U.S. economy. A positive velocity shock has a very small, barely significant negative effect forCanadian output at the first lag but otherwise has no significant effect on either output series at anylag. Despite large point estimates, the output responses to the transitory shocks are insignificant.These results suggest that the data exhibit some, but not all of the dynamic implications of mystructural model. For outputs, there are two (sets of) overidentifying restrictions. The first is thatthere should be no significant response at any lag of U.S. output to the uniquely Canadian shock,and this is (essentially) satisfied. Second, the model predicts that impact, and short-run dynamic,responses should significantly differ for all shocks in the two economies. This is also satisfied forthe three permanent shocks in the model but not for the transitory shocks, for which short-runresponses are zero.31The effect of all shocks on the Canadian money stock is quite unstable at short lags whichcontrasts with the U.S. responses (Figures 2.5 and 2.6). The supply shock has a small, significantand positive permanent effect on both money stocks. The money supply shock has an immediate,significant positive effect on the money stocks, the permanent effects of which are almost fullyrealized within six months. The U.S. money stock responds insignificantly to all other shocks at allhorizons. There is a very small, barely significant negative response of the money stock in Canadato the velocity shock and a positive response to the U.S. transitory shock.30This negative output response is rationalized by transitory expected inflation effects dominating liquidity effectsin nominal interest rates in some models with temporary monetary non-neutralities.31 overidentifying restriction that Canadian output does not respond to domestic asset market shocks is eliminated by the finding of permanent, common money demand disturbances which affect Canadian output throughrelative price movements.101The structural model’s testable predictions for money stock behaviour are largely satisfied inthe data. The U.S. money stock responds insignificantly to all but the domestic money supplyand common real supply shocks at all lags, suggesting that I have successfully identified a policydriven, exogenous money supply shock. In particular, its impact response to the velocity shock iszero though unrestricted. This satisfies one set of overidentifying restrictions for U.S. money stockbehaviour. Moreover, the estimated impact responses for the Canadian and U.S. money stocksdo significantly differ in at least three cases, implying satisfaction of a second subset of testablerestrictions that impact (and short-run) responses should differ across the two economies. TheCanadian money stock exhibits significant short-run responses to two of the three disturbanceswhich do not affect the U.S. money stock at any lag. Furthermore, the signs of the money stockimpact responses are consistent with those indicated by the model. These results imply that thepredicted short-run adjustment of the Canadian money stock to all disturbances holds in the data atleast for external and asset market disturbances. The model successfully replicates this implicationof the small open economy model.The price responses are ifiustrated in Figures 2.7a-2.7e and 2.8a-2.8e for Canada and the U.S.respectively. Prices in both economies respond positively and significantly to aggregate supplyshocks at all but the first lag, and positively and significantly to the autonomous money supply andvelocity shocks at all lags, but not to the transitory disturbances. The positive impact of the supplyshock on the price levels is, perhaps, counterintuitive but consistent with the Mundell-Flemingmodel presented in which the sign of the long-run price response to permanent output shocksdepends on the relative size of money supply and money demand responses to the disturbance.The price responses to money supply shocks have the expected sign and significance. The positiveimpact effect of the ‘velocity’ shock on price levels identifies this as a negative money demandshock; the long-run effect is significant and positive, driving the wedge between money and pricesidentified in the data analysis. Prices in neither economy respond significantly to the two transitorydemand disturbances.Recall that both the model and the data imply a positive, significant long-run money stock response to the supply shock, which should induce an equal long-run price effect. Here, while estimatedshort-run price effects are barely significant, the long-run price impact is positive and insignificantlydifferent from the long-run money stock response. Moreover, accounting for confidence intervals,the long-run neutrality restriction (16) for autonomous money shocks holds. Consequently, priceresponses satisfy the overidentifying restrictions that shocks to money stocks have equal long-run102effects for prices and, further, this neutrality result is attained well within a twelve month period.32U.S. prices satisfy the overidentifying restriction that there is no significant reponse of any U.S.variable to the transitory Canadian shock at any lag, with the exception of a small, significantresponse at lag 3.Overall, the data fail to indicate significant short-run non-neutralities of outputs in response toeach shock. The largest significant output movements derive from aggregate supply shocks implyinga more classical representation than anticipated. In fact, many of these estimated impulses implyreal effects for outputs, the output ratio, the terms of trade and real money balances which arequantitively limited and short-lived.The economic model implies that one of the most important sources of transitory deviationsfrom trend in domestic output is shifts in the terms of trade. The economic history of the globalDepression has recently posed terms of trade movements as a primary mechanism for transmissionof disturbances from the U.S. economy under the Gold Standard. Figure 2.9 plots impulse responsefunctions and standard error bands for the terms of trade to each disturbance and shows that onlypermanent velocity disturbances generate significant short-run deviations of the terms of trade fromits (zero-mean) equilibrium value. This reflects both the failure of prices to respond siguficantly tothe two transitory shocks and remarkable symmetry in the price responses across the two economiesat all leads and lags to permanent U.S. and common shocks. The impulses imply insignificance ofthis mechanism for transmission of all but common velocity shocks, and such rapidity and completeness of price transmission for permanent monetary and real shocks across national boundariesthat there is little support in this empirical representation for the idea the Gold Standard promotedreal transmission of these shocks.2.6.5 Forecast Error Variance DecompositionsThe relative effects of standardized shocks on the endogenous variables can be gauged from theforecast error variance decompositions which present the percentage of the total forecast errorvariance at each horizon attributable to each shock for a given variable. Again, some of themodel’s testable implications are unconstrained in identification and allow evaluation of the data’sconsistency with the model.Table 2.6a shows that a high proportion of the variance in Canadian output can be accountedfor by the two country-specific transitory shocks at short horizons, and by the supply shock. As the32Notably, the price response to supply shocks implies that the long-run money demand response, Cl, to permanentoutput shocks is insignificantly different from zero. This suggests that the standard money demand function doesnot capture well properties of interwar data.103horizon increases, a rising fraction of the variance is attributable to supply, although the standarderrors are large and the point estimates may overstate the rapidity of this rise. The money supplyand velocity shocks play no significant role at any forecast horizon. The results are somewhatdifferent in the U.S. case, where the two transitory shocks do not account for a significant fractionof the forecast error variance at any horizon, but the money supply shock accounts for a significantpercentage at the one month horizon. These decompositions reassure that the model’s implicationsfor exogeneity of the U.S. economy are satisfied. There is no feedback from the Canadian shock tothe U.S. economy by this measure but there is a significant role for U.S. originating (transitory)shocks in Canadian output fluctuations. Additionally, by this criterion the two economies exhibitsignificant differences in output dynamics in response to all shocks.The money stocks in the two countries also behave quite differently at short horizons, as shownin Tables 2.6c and 2.6d. The supply shock accounts for almost none of the Canadian moneystock variance at short horizons, but a significant fraction of the U.S. money stock variance at allhorizons. Its importance for Canadian money grows gradually over time, while its importance forthe U.S. money stock is unambiguous at all horizons, despite large standard errors for both moneystock decompositions. The standard errors do not hide the importance of autonomous moneysupply shocks at all horizons for both the U.S. and Canadian money stocks. Until the six monthhorizon a significant percentage of forecast error variance for the Canadian money stock derivesfrom transitory Canadian shocks, suggesting that some Canadian monetary disturbances may havebeen captured in this component. All of the short-run forecast error variance of the U.S. moneystock derives from the money supply and aggregate supply shocks.The data therefore satisfy the short-run implication of the model that money stock behaviourdiffers across the two economies. They are consistent with the view that Canada is a small openeconomy in which the money stock adjusts endogenously to both domestic and foreign disturbances.The U.S. money stock responds only to domestic monetary policy shocks and ‘endogenously’ topermanent domestic output shocks. This latter characteristic of the U.S. money stock is notstrongly reflected in Canadian money stock behaviour for several months suggesting there is shortrun divergence between the variance of Canadian Ml and its long-run external determinants.Tables 2.6e and 2.6f present the forecast error variance decompositions for Canadian and U.S.prices. At long forecast horizons the variance of prices in both countries is explained primarily bythe velocity and money supply shocks respectively, with little signficant role for the supply shock.At short horizons the Canadian price level is also significantly influenced by the domestic transitoryshock, although there is no significant role for the transitory U.S. shock, while the U.S. price forecast104error variance is dominated by velocity shocks. The money supply shock plays a surprisingly smallrole for both variables at short horizons, however its share in price forecast error variance growssteadily as the forecast horizon is extended. In general, the price decomposition results reflect thesame failure of prices to respond significantly to demand components as the impulse responses do.Overall, these results confirm that the identifying assumptions applied have isolated a uniquelyCanadian component which does not significantly impinge on fluctuations in the U.S. economy,and that the monetary implications of the small open economy model of Section 2.2 are satisfied.There is no significant component of any of the U.S. variables’ forecast error variance attributableto the Canadian transitory shock at any forecast horizon although the forecast error varianceof the Canadian output is significantly accounted for by both the Canadian and U.S. transitorydisturbances. This suggests that while it has comparatively small importance for U.S. fluctuations,the U.S. disturbance can significantly affect the smaller, Canadian economy through export demand.2.6.6 Historical DecompositionsThe preceding data analysis, estimated innovations, impulse responses and forecast error variancedecompositions all reflect an empirical representation for the interwar data from Canada and theU.S. that reasonably captures the dynamics and long-run properties of a small open economy anda large external economy implied by standard Mundell-Fleming open economy models. The leastsatisfactory assumptions of the structural model for this data are that there will be significant non-neutralities for outputs in both economies from a wide variety of real and nominal disturbances andthat terms of trade movements are a primary source of short-term transmitted output shocks for thesmall open economy. However, most importantly, the estimated innovations and responses appearto reflect quite well standard interpretations of the shocks identified. I therefore turn to evidenceprovided by the historical decompositions on the ‘causes’ of the Great Depression in Canada (andthe U.S.) using these interpretations.The historical decompositions shown in Figures 2.10-2.15 combine the information in the impulseresponse functions with the realized values of the shocks at each point in time. In particular, Idepict the 12-month ahead total forecast error for the level of each variable, the forecast error dueto each shock and the computed standard errors of the individual forecast error series.In both Canada and the U.S. the total forecast error for industrial production is negative fromearly 1930 to early 1933, and again throughout 1938. In addition, the total forecast error for U.S.industrial production is negative in late 1927 and early 1928. In each of these cases, virtually allof the forecast error can be explained by the permanent output (supply) shock (Figures 2.lla and1052.12a). With few exceptions, the other identified shocks have a relatively small and insignificantrole in generating unpredictable output fluctuations. The transitory Canadian shocks appear topredict short-run domestic output dynamics well, but have no significant influence for the outputcollapse or recovery. However, in 1938 positive realizations of Canadian transitory shocks offsetpermanent output shocks, making the downturn of 1937/8 less severe in Canada than in the U.S.Figures 2.16 and 2.17 show the decomposition results for output most starkly. These permanent/transitory decompositions plot the permanent and total transitory components of output ateach date which are generated by the cumulative effects of aggregate supply shocks and the sum ofmoney supply, velocity, and idiosyncratic shocks respectively. The time path of the total stochasticcomponent of output is almost completely governed by the cumulative effects of aggregate supplydisturbances for both countries for the sample period 1929:1-1936:12. Although transitory shockscan account for short-run fluctuations in Canada in the early part of the sample, and money supplyshocks generate some pre-Depression fluctuations in the U.S., only permanent output shocks matterfor output in both countries from the beginning of 1929.The fall in output appears to be virtually monocausal, but the behaviour of money and prices ismore complex. The total forecast error for money stocks in both countries is comparatively small,but is significantly negative in early 1929 and from early 1930 to early 1934 and especially largein late 1930 and late 1932. The U.S. forecast errors are entirely attributable to a combinationof the permanent output and money supply shocks, while in Canada the effect of the transitoryCanadian shock (which is an amalgam of both monetary and real idiosyncratic transitory shocks)is correlated with the total forecast error, although rarely significant. The unanticipated decline inmoney stocks reflects in part an endogenous response to the aggregate supply shocks that causedthe output collapse, and in part an exogenous monetary contraction especially in the unanticipatedmonetary ‘trough’ of 1930-1931. However, as argued above, autonomous money shock effects hadno feed back into output fluctuations.In Canada there were bouts of unanticipated deflation in early 1930 to mid-1932 and againin early 1933. On each occasion, unanticipated deflation began a few months earlier in the U.S.and, in addition, the U.S. experienced unanticipated deflation in 1938 which does not reflect inCanada. lii the U.S., the monetary velocity and aggregate supply shocks contributed in roughlyequal measure to the deflation of the early 30s while the hiatus from late 1931 to the end of 1932reflected the effects of the positive velocity shock of late 1931. The story is similar for Canada witha greater, but insignificant, role for Canadian shocks.1062.6.7 A Note On RobustnessThe empirical results proved robust to several changes in specification; most notably, inclusion ofthe non-exchange rate adjusted U.S. money supply and price series, of the estimated (PhillipsHansen) error-correction terms rather than the unit valued error-correction vectors, and to theuse of different price, output and money stock series for the U.S.. While small quantitative andqualitative changes do arise in the structural estimation results, the main result does not change;common, permanent shocks to output explain the onset, depth and duration of the Great Depressionin Canada and the U.S..332.7 ConclusionsAn extensive U.S. literature assumes that the global Depression of the 1930’s reflected international transmission of the U.S. output collapse, initiated perhaps by Federal Reserve policy. Totest this hypothesis I have estimated a small open economy model for Canada in which the U.S.represents the rest of the world. I exploit common stochastic trends in the U.S. and Canadianmacroeconomies to identify international and domestically originating disturbances with standardmacroeconomic interpretations and assess their relative contributions to interwar output fluctuations in both economies. I find that the onset, depth and duration of output collapse in bothCanada and the U.S. are attributable to a common, permanent output shock leaving no significantrole for idiosyncratic disturbances originating in either economy. I conclude by contrasting theseresults with the hypotheses and empirical results reviewed in Section 2.1.I do identify the U.S. monetary contraction in late 1928 that Hamilton (1987) emphasized, andthe attendant rise in transactions money demand, but these shocks are absorbed by prices andhave an insignificant effect on output in both the U.S. and Canada. Similarly, while I find evidenceof deflationary monetary policy in 1930 and a significant monetary contraction in 1931 and 1932to which Friedman and Schwartz (1963) attribute the severity and persistence of the Depression,the former has no significant output effects and the latter I find to be primarily an endogenousmonetary contraction as Temin (1976) argued. Idiosyncratic U.S. demand shocks are significantduring 1929, as Ternin and Romer (1990) asserted, but equally have no output effects in eithereconomy. Consequently, my results reject explanations of the global Depression which emphasizeinternational transmission of autonomous monetary and real disturbances originating in the U.S.My results also are not supportive of the more general hypothesis that Canada imported theDepression through the collapse of export demand or of export prices. The symmetry of output33Results available from the author upon request.107behaviour in Canada and the U.S. and the insignificance of terms of trade movements in response toall but common asset market disturbances suggest that the Depression in Canada derived from thesame sources as that in the U.S. economy rather than being transmitted through export demand.These same symmetry results challenge the views of Temin (1991) and Eichengreen (1992) thatthe Depression was propagated worldwide from the U.S. through the Gold Standard. However, Icannot separately identify the purely domestic short-run effects of common disturbances from theeffects due to transmission of short-run U.S. responses to the same disturbances. Consequently,while my results do not support it, I cannot rule out a siguficant role for a Gold Standard or exportdemand transmitted contraction originating in the aggregate supply collapse.The implications of my results for Bernanlce’s (1983) hypothesis are unclear. Bernanke argued that bank failures, and financial crises more generally, caused a protracted cmonet&y non-neutrality due to the investment and consequent supply-side effects of the decline in efficient creditintermediation arrangements. Since I cannot isolate different sources of supply disturbances withmy empirical model, any permanent output effects of credit market disruptions during the 1931-1933 era wifi be captured by the identified supply shocks. My finding that there was significantunanticipated deflation in 1930-1931 which could engender bankruptcies and financial crises, asboth Bernanke (1983) and Fisher (1933) have argued lends support to this interpretation. Thesymmetry in output collapse across the two economies must then, however, be accounted for bysimilarity in credit market disturbances for Canada and the U.S., a hypothesis which Haubrichrejects.My results provide dramatic support for hypotheses, such as those of Fisher (1933), Bernstein(1987) and Safarian (1959) that emphasize secular factors in explaining the Depression. Moreover,they indicate that these factors were continent-wide, and potentially global, providing a rationalization for the synchronicity of the international output collapse. This suggests a promising alternativeto traditional views that the worldwide Depression simply reflected transmission of idiosyncraticU.S. disturbances to the rest of the world.While the exceptionally close geographic and economic ties between Canada and the U.S. implythat my results may not extend to the European Depression experience, they do challenge futureresearch to account more fully for common, secular factors in the global output collapse.108Table 2.1 : Data Sources and NotationAll series are monthly, and deterministically seasonally adjusted except the nominalexchange rate series which has no significant seasonal component. Logarithms are usedthroughout the analysis except in the data plots presented in Figures 2.la-2.lf whichemploy an index number of the level of each series, setting 1935-1939=100. All serieswhich are expressed as indexes in raw form (industrial production and price variables)are re-indexed to a 1935-1939 =100 base prior to application of the logarithmic transformation.• Yc is the log of industrial production index, Canada, (1935-1939=100) from the Monthly Review of Business Statistics, published in various issues by the Dominion Bureau of Statistics,Canada• Yus is the log of industrial production index, U.S., (1935-1939=100) from the Federal ReserveBoard of Governors, U.S.• m is the log of Ml money stock, Canada, from Metcalfe, Redish and Shearer (1993)• mus is the log of Ml money stock, U.S., from Friedman and Schwartz (1970), Table 1• Pc is the log of wholesale price index, Canada, (1935-1939=100), published in various issuesof Prices and Price Indexes by the Dominion Bureau of Statistics• Pus 15 the log of wholesale price index, U.S., (1935-1939=100), from various issues of StatisticalAbstract of the U.S., published by the U.S. Department of Commerce• e is the log of (noon) nominal spot exchange rate in $C / $U.S., from various issues of Pricesand Price Indexes, published by the Dominion Bureau of Statistics. Specifically, the monthlyaverage of closing rates in Montreal.• v is the log of velocity in Canada, computed as yc+pc-mc with data sources as above• v is the log of velocity in Canada, computed as y+pus-mus with data sources as above109Table 2.2 : Descriptive StatisticsTable 2.2a : Descriptive Statistics (Log Levels)Series Sample Date of Date of Standard Mean CorrelationMinimum Maximum Deviation with YcValue ValueYc 25:01-39:12 33:02 29:01 0.182 4.479 1.00025:01-28:12 25:04 28:05 0.132 4.452 1.00029:01-33:12 33:02 29:01 0.233 4.395 1.00034:01-39:12 34:02 39:12 0.122 4.566 1.000Yus 25:01-39:12 32:07 39:12 0.192 4.484 0.85725:01-28:12 25:06 28:10 0.044 4.542 0.79229:01-33:12 32:07 29:05 0.235 4.357 0.94734:01-39:12 34:11 39:12 0.160 4.550 0.865m 25:01-39:12 33:01 39:12 0.139 6.535 0.84325:01-28:12 25:07 28:06 0.082 6.493 0.85729:01-33:12 33:01 29:12 0.144 6.468 0.90734:01-39:12 34:01 39:12 0.146 6.620 0.894(mus +e) 25:01-39:12 33:11 39:12 0.134 7.887 0.66125:01-28:12 28:04 25:01 0.017 7.868 0.61129:01-33:12 33:11 29:10 0.085 7.807 0.61034:01-39:12 34:01 39:12 0.164 7.966 0.899Pc 25:01-39:12 33:02 25:02 0.150 4.669 0.35225:01-28:12 28:12 25:01 0.028 4.861 -0.74129:01-33:12 33:02 29:08 0.150 4.606 0.94134:01-39:12 34:01 37:07 0.055 4.592 0.730(Pus +e) 25:01-39:12 33:01 25:03 0.121 4.656 0.32525:01-28:12 27:04 25:03 0.035 4.811 -0.77129:01-33:12 33:01 29:07 0.115 4.601 0.88834:01-39:12 34:03 39:12 0.055 4.600 0.720Table 2.2b Cross-Correlation Matrix (Log Levels)Series Yc Yus m (mus +e) Pc (pus+e)Yc 1.00 * * * * *Yus 0.86 1.00 * * * *mc 0.84 0.74 1.00 * * *(mus +e) 0.66 0.67 0.88 1.00 * *Pc 0.35 0.56 0.18 0.16 1.00 *(pus +e) 0.32 0.57 0.17 0.22 0.97 1.00110Table 2.2c : Descriptive Statistics (Log Differences)Series Sample Date of Date of Standard MeanMinimum Maximum DeviationValue Value‘ Yc 25:02-39:12 31:06 29:01 0.060 0.00325:02-29:01 26:12 29:01 0.072 0.01229:02-34:01 31:06 30:01 0.066 -0.00834:02-39:12 35:03 34:05 0.042 0.007IX Yus 25:02-39:12 29:12 33:05 0.045 0.02125:02-29:01 27:11 29:01 0.025 0.00429:02-34:01 29:12 33:05 0.058 -0.00734:02-39:12 37:11 34:12 0.041 0.008Lk mc 25:02-39:12 30:01 25:12 0.035 0.00325:02-29:01 28:01 25:12 0.036 0.00429:02-34:01 30:01 33:12 0.034 -0.00434:02-39:12 39:04 35:03 0.033 0.008(m +e) 25:02-39:12 29:11 39:09 0.022 0.00325:02-29:01 28:06 28:12 0.011 0.00129:02-34:01 29:11 33:12 0.029 -0.00434:02-39:12 35:09 39:09 0.019 0.010Pc 25:02-39:12 30:12 39:09 0.013 -0.00125:02-29:01 25:04 25:11 0.010 -0.00229:02-34:01 30:12 33:07 0.015 -0.00534:02-39:12 38:08 39:09 0.014 0.0021 (Pus +e) 25:02-39:12 32:01 39:09 0.018 -0.00125:02-29:01 25:04 25:07 0.008 -0.00229:02-34:01 32:01 31:10 0.020 -0.00534:02-39:12 37:11 39:09 0.019 0.003NotesAll series in logarithms and deterministically seasonally adjusted except the nominalexchange rate which has no significant seasonal component. Data analysis for the U.S.price level and Ml money stock shows that these variables have properties qualitativelysimilar to their exchange rate adjusted counterparts, and so only the latter results arereported in the interest of clarity.111Table 2.3 : Non-Stationarity Test ResultsTable 2.3a : Tests For Non-stationarity (Log Levels)Series Z 1) TT(4) i (6)Yc -6.21 -1.72 4.57 -1.53 -1.70Yus 5.53 -1.45 -1.66 -1.54 -1.13m -2.29 -0.72 -0.92 -0.36 -0.40(m3+e) 1.05 0.39 0.70 -0.06 -0.10Pc 4.28 -0.59 -0.73 -0.10 -1.25(pu8+e) -2.52 0.79 -0.97 -0.91 -1.02v -9.45 -2.23 -2.10 -1.69 -1.89v -8.23 -1.97 -2.13 -2.13 -1.57Table 2.3b Tests For Non-Stationarity (Log Differences)Series Z Z,. TT(1) ‘t7(4) ‘t (6)A Yc 224.63*** 48.50*** 41.78*** 5.98*** 4.70***A Yus 423.97*** 9.780*** 8.18*** 6.56*** 497***A mc 47779*** 45.46*** 42.27*** ..594*** 4.63***A (rnu+e) 203.51*** 13.72*** 7.270*** 5.61*** 4.13***A Pc 417.53*** 9.350*** 7.20*** 3.85** 3.27*A (pus+e) 138.74*** 10.67*** 8.20*** 555*** 394**A Vt 206.31*** 18.64*** 13.24*** 6.48*** 5.23***A 129.87***-7.990’’ 6.32*** 4.83***Notes* denotes significance at the 15% level, ** denotes significance at the 5% level, anddenotes significance at the 1% level. Z and Zt are computed values of the Phillips(1987) statistics for the null hypothesis that the series is non-stationary around a firstorder polynomial time trend and constant term. Four autocovariance terms are usedto compute the spectrum at frequency zero. TT(k) is the computed value of the Saidand Dickey (1984) (Augmented Dickey-Fuller (1979, 1981)) statistic for the same nullhypothesis, where k is the number of lagged first difference terms included in the testregression. Critical values tabulated in Phillips and Ouliaris (1990), Fuller (1976) andfrom Ouliaris (1991). The time series properties of the U.S. money supply and price levelseries are qualitatively the same as those for their exchange rate adjusted counterpartsand so only the latter are reported.112—‘,—‘V‘.‘.—‘at’aca‘—aa ‘-CDaa‘—acC,,a c‘—+ CD % t a C,, + CDC.3—.-_‘—‘‘,-.‘CD(999.IC,IIaaarr‘T-a‘—s--•r—C.zi4-i—c.zc,9bo00èb-’c,z--o*************003C1C)1O0000*****************__*******0DboàoD00cD*********..__**C2CZD00CD01-1:’C-*****s__******Uw!4•CDr‘—--‘—.‘‘‘,—‘,—‘I—I:aaC,,CU6 aCDCi,‘—‘—CD -03010003 **********obiC-01©C101C*********-1-’a-oo********bb’-’cL,0300***I4.* *eg.øO—030000***a* *$àobo©D00C3100.,3cDcL’3c5DcD**********‘__**-01C.49°9cC3DC100******—.s****©**‘__--—‘.00 —% Ci3I-,c_Ip,‘““I’.,—CD0E. ,.t.Ct’I-c C I—.0CD cjQCDI-e CD — Cl)Table 2.4 cont.Table 2.4d : Multivariate Cointegrating Vector EstimatesSeries FM Estimate SJ EstimateYc, Yus (1, -0.85) (1, -0.96)m, (mus+e) (1, -0.95) (1, -1.06)Pc, (pus+e) (1, -1.21) (1, -1.26)v, (1, -0.85) (1, -0.93)(mc-pc), (mus-pus) (1, -1.11) (1, -1.11)NotesNotes for Tables 2.4a and 2.4b as for Tables 2.3a and 2.3b. The test statistics forthe unconstrained coefficient tests are applied to the residuals from the comtegratmgregressions of the Dependent Variable on the Independent Variable in Table 2.4a, as innon-stationarity tests in Table 2.4b. I report results for the case in which a constantterm, t, is included in the test regressions. The cointegration results for the U.S. moneysupply and price level series are qualitatively similar to those for their exchange rateadjusted counterparts and so only the latter are reported. In Table 2.4c, J,(K) andm1 (K) are computed values of the Johansen and Juselius (1990) trace and maximumeigenvalue test statistics for the null hypothesis that there are K cointegrating vectorsin the specified system. Critical values from Johansen and Juselius (1990) and Ouliaris(1991). Column 2 in Table 2.4d gives the Phillips-Hansen Fully Modified estimatesof the cointegrating vectors. Column 3 gives normalized estimates derived from thosegenerated from the Johansen tests for Table 2.4c.114Table 2.5 : VAR Results (1925:1-1939:12)Table 2.5a: VAR F-statisticsVariable /Equation A Yc mc A Pc (ycyus) (mc-mus-e) (pc-pus-e) R2A Yc 2.68** 2.35** 0.03 6.09*** 2.98** 1.16 0.27A mc 347*** 2.52** 2.91** 5.05*** 10.37*** 5.72*** 0.35A Pc 1.80* 2.00* 394*** 1.63* 0.63 2.77** 0.22(ycYus) 8.15*** 1.92* 0.83 4997*** 1.98* 0.62 0.75(mc-mus-e) 2.17* 2.26* 2.04* 4.69*** 49.76*** 4.80*** 0.74(pcpuse) 1.07 0.77 0.34 1.59* 1.26 180.34*** 0.89NotesThe rows give value of F-statistics for each equation in the VAR system. This statisticevaluates the null hypothesis that the block of lags pertaining to the variable in eachcolumn is zero. * denotes rejection of the null at 20%, ** at 5% and at 1% . Finalcolumn gives adjusted 1?2 for the equation.115Table 2.6 : Structural Model (1925:1-1939:12)Table 2.6a Forecast Error Variance Decomposition For Canadian Output (Yc)Forecast Supply Money Velocity U.S. CanadianHorizon Shock Shock Shock Transitory TransitoryShock Shock1 month 28.7 7.3 2.3 33.1 28.7(18.4) (13.3) (10.5) (19.5) (26.7)3 months 49.0 5.4 2.2 23.3 24.1(20.5) (11.7) (10.0) (15.0) (20.9)6 months 71.1 3.0 1.5 12.0 12.4(22.3) (10.2) (9.3) (12.6) (15.2)12 months 86.6 1.4 0.8 5.4 5.8(22.3) (10.5) (8.9) (10.8) (10.6)24 months 93.9 0.6 0.4 2.5 2.6(18.7) (10.1) (7.6) (7.2) (6.6)36 months 96.0 0.4 0.2 1.6 1.7(15.7) (9.2) (6.3) (5.2) (4.8)120 months 98.9 0.1 0.1 0.5 0.5(6.0) (4.3) (2.2) (1.2) (1.4)Table 2.6b : Forecast Error Variance Decomposition For U.S. Output (yus)Forecast Supply Money Velocity U.S. CanadianHorizon Shock Shock Shock Transitory TransitoryShock Shock1 month 62.9 20.0 0.3 16.8 0.0(25.0) (18.3) (10.9) (19.2) (0.0)3 months 77.4 7.4 0.2 13.4 1.6(24.0) (13.4) (10.2) (17.8) (3.6)6 months 87.9 3.2 0.2 7.8 0.9(23.1) (11.7) (9.7) (14.9) (4.3)12 months 92.4 1.6 0.2 5.4 0.4(21.4) (11.2) (9.1) (10.9) (3.3)24 months 95.3 0.9 0.1 3.4 0.2(18.6) (10.4) (8.0) (7.3) (2.7)36 months 96.6 0.6 0.1 2.4 0.2(16.2) (9.6) (7.0) (5.5) (2.2)120 months 98.8 0.2 0.0 0.8 0.1(7.8) (5.7) (2.8) (1.8) (0.8)116Table 2.6 cont.Table 2.6c : Forecast Error Variance Decomposition For Canadian Money (mc)Forecast Supply Money Velocity U.S. CanadianHorizon Shock Shock Shock Transitory TransitoryShock Shock1 month 11.3 31.7 3.8 5.4 47.9(14.5) (18.9) (12.5) (18.1) (24.9)3 months 12.3 59.6 1.8 3.8 22.5(12.9) (19.9) (9.1) (12.3) (16.2)6 months 22.1 61.9 1.2 2.4 12.4(15.1) (20.1) (7.9) (10.4) (13.2)12 months 26.7 65.3 0.6 1.2 6.2(16.8) (20.6) (7.5) (7.8) (9.9)24 months 29.2 66.8 0.3 0.6 3.1(18.9) (21.4) (6.5) (5.3) (6.5)36 months 29.8 67.5 0.2 0.4 2.1(20.2) (21.9) (5.5) (3.9) (4.8)120 months 30.6 68.6 0.1 0.1 0.6(23.7) (23.8) (2.2) (1.0) (1.5)Table 2.6d : Forecast Error Variance Decomposition For U.S. Money (mus+e)Forecast Supply Money Velocity U.S. CanadianHorizon Shock Shock Shock Transitory TransitoryShock Shock1 month 56.7 40.4 2.9 0.0 0.0(26.3) (25.7) (18.6) (0.0) (0.0)3 months 48.0 47.7 3.3 0.8 0.1(23.7) (24.4) (17.1) (1.8) (3.1)6 months 45.9 51.0 1.7 1.1 0.2(22.6) (24.0) (15.4) (2.7) (4.5)12 months 42.7 55.3 0.8 0.8 0.3(21.8) (23.5) (13.0) (2.9) (4.9)24 months 38.4 60.5 0.4 0.5 0.2(20.9) (22.4) (9.3) (2.9) (3.9)36 months 36.3 62.9 0.3 0.4 0.1(21.1) (22.3) (7.2) (2.5) (3.2)120 months 32.8 67.0 0.1 0.1 0.0(23.8) (23.9) (2.3) (0.8) (1.0)117Table 2.6 cont.Table 2.6e Forecast Error Variance Decomposition For Canadian Prices (Pc)Forecast Supply Money Velocity U.S. CanadianHorizon Shock Shock Shock Transitory TransitoryShock Shock1 month 1.4 16.5 34.3 9.8 38.0(7.8) (11.2) (20.9) (18.1) (23.5)3 months 11.2 20.5 32.2 9.3 26.9(12.2) (12.9) (20.0) (17.6) (20.6)6 months 20.1 26.7 23.6 10.6 18.3(14.9) (15.0) (17.8) (16.5) (17.6)12 months 31.4 26.6 23.6 10.3 8.0(17.3) (15.6) (17.4) (10.8) (12.0)24 months 35.7 25.9 28.1 7.1 3.2(20.1) (16.3) (17.8) (7.5) (7.0)36 months 35.1 26.5 31.3 5.1 2.0(21.6) (17.0) (18.2) (5.1) (5.0)120 months 29.9 29.2 38.9 1.4 0.5(24.7) (19.1) (19.5) (1.2) (1.4)Table 2.6f: Forecast Error Variance Decomposition For U.S. Prices (pus+e)Forecast Supply Money Velocity U.S. CanadianHorizon Shock Shock Shock Transitory TransitoryShock Shock1 month 17.6 4.5 75.1 0.4 2.3(19.6) (11.2) (22.3) (9.1) (12.4)3 months 21.9 13.4 63.2 0.7 0.8(19.2) (13.3) (21.6) (8.3) (10.3)6 months 28.0 19.8 50.1 1.6 0.4(19.7) (15.0) (20.8) (8.0) (8.8)12 months 30.9 24.3 43.0 1.5 0.3(21.2) (16.7) (20.8) (6.2) (6.7)24 months 31.2 26.7 41.0 1.0 0.1(22.7) (17.7) (20.7) (4.2) (4.8)36 months 30.5 27.7 40.9 0.8 0.1(23.3) (18.2) (20.6) (3.1) (3.7)120 months 28.1 29.8 41.9 0.2 0.0(25.1) (19.6) (20.5) (0.9) (1.2)NotesTable 2.7 presents the % forecast error variance attributable to each shock at the forecast horizons indicated. A 0.0 indicates a measured value of less than 0.05%. Standarderrors are in parentheses, calculated by Monte Carlo procedures (described in Section1182.5) with results based on 2500 draws. Sensitivity analysis, involving the use of theFully-Modified cointegrating vector estimates (see Table 2.5b) rather than the unitcointegrating vectors and of the non-exchange rate adjusted U.S. money supply andprice series, indicates robustness of the model to minor specification changes and we report only structural results for the baseline model. Other results available upon requestfrom the author.119FIgure.1a:IndustrialProductionIndicesFigurezib:)1VelocityIndices‘K) 1-•o282728293031323334353637383940o262728293031323334353637383940Figure2ic:WholesalePriceIndicesFlgure2.ld:MlMoneyStockIndices‘K)in4.xL[Canad:Ed.wó262728293031323334353837383940a262728293031323334353637383940Flgurea•le:CommonCurrencyPriceIndicesFIgure21f:CommonCurrencyMlIndices‘K)U)F -4ICanadlinInd.xICan.dtanIndex1282728293031323334383837383940282728293031.323334353637383940Figure22a:PermanentSupplyShockC.,C1):Figure22c:PermanentVelocityShockiA11AiALAiAA.I-.. 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I*.*?*82*303102335435360?3839402.15c:PusHistoricalDecomposition(Velocity)-126272829303*3*3334313537353940T56275**02021225334063637353940Fre.t4d:PeHistoricelDecompo.Uon(USTren.ttory)Z.16d:Pu.HI.LorlcnlDecompoaltion(UsTran.Itory):\liSOIStSO3433SI3?333340?EO37£3030St333334333337333040Fovcq.t4e:PcHistoricalDecomposition(Cdn.Transitory)i.15e:PusHistoricalDecomposition(Cdn.Transitory)d3?UU363432U34053527DI3040tI3725203031323334333331333040Flgure2•16a:YcPermanentComponentFlgureZ.17a:YusPermanentComponent0 -4 0 0 0 0 0 0 U,0 0 0•28303234363840726Figure216b:YcTotalTransitoryComponent28303234363840Figure2.17bYusTotalTransitoryComponent0 0I———YusPermanentDetrendedYusComponent0 -426U, d/3U,03 d———YcTotalTransitoryComponentDet.rendedYc—% iiU,0YusTotalTransitoryComponentDetrendedYusU,1’-0 U,03 a ‘K, 0 (.-. 0262830323436384026283032343638403 CHAPTER 3: Money, Banking And The Determination OfReal And Nominal Exchange Rates3.1 IntroductionA substantial body of evidence indicates that national price indices and foreign exchange ratesdisplay large- and permanent - departures from purchasing power parity. Moreover, a strilcingempirical regularity is that, under regimes where exchange rates are flexible, movements in realexchange rates largely mirror movements in nominal exchange rates, with the magnitude of movements in both dwarfing changes in relative price levels. In addition, recent empirical evidencesuggests that monetary disturbances are an important source of real exchange rate fluctuations,and it is also well established that the volatility of the real exchange rate is substantially lessunder fixed than under flexible exchange rate regimes despite the fact that ‘fundamentals’ havebeen approximately equally volatile under the two regimes in the last thirty years. And finally,another manifestation of observed deviations from purchasing power parity is that there are sizablecross-country differences in real interest rates.’This paper produces a theoretical model that is consistent with these observations, and in whichthe importance of monetary factors is brought into the foreground. Permanent violations of purchasing power parity are made possible by the presence of non-traded goods. Spatial separation(within and across’ countries) and stochastic shocks to agents’ desired portfolios give rise to animportant allocative role for both money and banks.2 Within this context I consider the determination of real and nominal exchange rates and, by implication, national price levels under regimesof flexible and fixed exchange rates, as well as under regimes that differ with respect to the presenceor absence of reserve requirements and exchange controls. All prices in the model are fully flexible,there is continuous market clearing, and all agents have equal access to all asset markets at each1lsard (1977), Roil (1979), Frenkel (1981) and Huizinga (1987) document the existence of large and persistentviolations of purchasing power parity. Betts (1993) finds that these violations occur at all horizons. Indeed, Jsard(1977) and Lapham (1992) suggest that the law of one price is violated, both within and across countries, which isconsistent with the theoretical formulation in the sequal.Betts (1993) documents that a large fraction of the movement in the real exchange rate is accounted for by nominalexchange rate movements. Clarida and Gall (1994) find that shocks to both the supply of and demand for moneyexplain a substantial amount of the variance of the real exchange rates, and Rogers (1993) reports that about onehalf of the forecast error vaiiance of real exchange rates can be accounted for by monetary disturbances at shortforecast horizons.That real exchange rates are more volatile under flexible than under fixed exchange rate regimes is shown by Mussa(1986). This is true despite the fact that - since 1960 - ‘fundamentals’ have been approximately equally volatile underthe two regimes (Flood and Rose (1993)). Finally, Isard (1983), Cumby and Obstfeld (1984), and Mark (1985)document the existence of sizable cross- country differences in real interest rates. These are related to violations ofpurchasing power parity by Isard (1983), Dornbusch (1983), Stulz (1987) and Devereux (1988).2The potential importance of spatial separation of agents in accounting for the observations described above wassuggested by Backus and Smith (1992).137date.In this context, I consider the equilibrium consequences of changes in both monetary and realfactors. Under flexible exchange rates, an increase in the money growth rate of any country causesboth a real and nominal depreciation of that country’s currency. Moreover, the initial magnitudesof these real and nominal exchange rate movements are equal in size, at least in equilibria whereexchange rates and prices are determined only by fundamentals. In such equilibria, national pricelevels then rise at the relevant rate of money growth, while the real exchange rate remains constant.Thus permanent effects on the nominal and real exchange rate occur as a result of a permanentchange in the rate of money growth. It bears emphasis that variations in the rate of money growthhave large impacts on the nominal exchange rate compared with their impacts on relative pricelevels. This is true despite the full flexibility of prices.When exchange rates are fixed, independent variations in national money growth rates are notpossible. Indeed, in steady state equilibria, money growth rates across countries must be keptequal in order to maintain the fixed nominal exchange rate. Under such a regime, increases inthe conunon rate of money growth have ambiguous effects on real exchange rates. However, it ispossible to show that - in a particular sense - the effect on the real exchange rate will be smallerthan would be the case under a regime of flexible rates.For changes in real factors, which here means exogenous relative income levels, matters aresubstantially different. Changes in relative income levels induce the same effects on real exchangerates whether nominal exchange rates are fixed or flexible. And, when nominal rates are flexible,changes in relative income levels induce equal proportional changes in initial relative prices and, asa consequence, have no impact on the initial nominal exchange rate.I also examine, under flexible or fixed exchange rates, the consequences of the imposition ofreserve requirements or exchange controls. The imposition (or tightening) of exchange controlscauses a real (and, under flexible rates, nominal) appreciation of the currency of the countryimposing the controls. Reserve requirements can also be used to manipulate exchange rates, but -in a sense I describe - these are less effective devices than exchange controls for accomplishing thisobjective. In addition, both reserve requirements and foreign currency controls affect the ability ofnational monetary policy to manipulate real and nominal exchange rates.The statements just made apply to equilibria where all variables are determined by fundamentals. Notably, the steady state fundamental’ equilibrium is unique under both fixed and flexibleexchange rates and, for identical money growth rates, is invariant to the choice of these two regimes.In addition, the fundamental equilibrium which obtains under fixed exchange rates has an interest-138ing property: the choice of fixed nominal exchange rate value has no ailocative consequences, andno effect on the real exchange rate at any date. This suggests that many discussions concerningthe alignment of fixed exchange rates - for example, within the EMS - are misguided. Here suchalignments are irrelevant for allocations, and they cannot aid in the attainment of a situation of(near) purchasing power parity.Finally, I also consider the scope for multiplicity of equilibria under flexible exchange rateregimes. This is an important topic which has been considered elsewhere by Kareken and Wallace(1981), Manuelli and Peck (1990), King, Wallace and Weber (1992) and Barnett (1992). The firstthree of these papers show that the nominal exchange rate is indeterminate when there is sufficientsubstitutabifity between different currencies. The fourth shows that the real exchange rate canalso be indeterminate when not all agents can participate in all asset markets. I show, on theother hand, that both the real and the nominal exchange rate are necessarily indeterminate undera regime of flexible exchange rates, despite the fact that all agents view all currencies as imperfectsubstitutes, and despite the fact that all agents have equal access to all asset markets. Indeed, themodel possesses a continuum of non-stationary, perfect foresight equilibria that are indexed by theinitial value of the real (or equivalently, as it turns out, the nominal) exchange rate. Here, all suchequilibria are ‘non-fundamental’, and they have the property that countries whose real exchangerate is rising (falling) over time have inflation rates that are permanently below (above) their rate ofmoney growth. In addition, in such equilibria, countries whose real exchange rate is rising (falling)over time will (under a weak restriction on parameters) have their nominal exchange rate rise at arate exceeding (below) their relative rate of money growth. This gives an additional sense in whichthe effects of monetary factors can be magnified in terms of their implications for exchange ratemovements. Finally, non-stationary equilibria have the property that cross-country differences inreal interest rates will exist at all dates, although these will tend to disappear asymptotically.The vehicle I use for considering these issues is a two-country, single good3 pure exchange overlapping generations model. In each country there is a government that issues both flat currencyand interest-bearing debt. While international trade in goods is limited, allowing permanent deviations from purchasing power parity to be observed, international trade in all assets is unrestricted.All agents have identical access to all asset markets, all goods and asset markets are perfectlycompetitive and all markets clear at each date.Within each country there are two spatially distinct locations. Agents move between loctaions3This good is not traded across countries. It is conceptually straightforward to have more than one good in themodel and to have some traded and others non-traded goods. However, such a formulation adds complexity withoutchanging the substantive issues under consideration.139in a stochastic manner, both domestically and internationally. Only currency is transportablebetween locations, and inter- location exchange requires the currency of the country in which theseller is located. As a result, agents seek to diversify their portfolios, holding the currencies ofboth countries as well as interest-bearing assets that dominate money in rate of return.4 Agents’demands for these assets, and their supply as determined by national monetary policies, are thenfundamentals for the real (and nominal) exchange rate.The possibility of stochastic relocation, coupled with the role of currency in inter-locationexchange, plays the role of a ‘liquidity preference shock’ in the Dia.rnond-Dybvig (1983) model.Banks, therefore, arise to insure agents against their random, currency-specific liquidity needs. Inorder to provide this insurance, banks in each country hold reserves of both the foreign and domesticcurrency, and in addition they invest in interest-bearing government bonds. The optimal portfolioweights for these banks impinge on real exchange rate determination in a manner that reflects howthe liquidity preference shocks generate aggregate demands for the currencies of each country.Although the model is one with two-period lived overlapping generations, the fact that inter-location exchange must be accomplished using the seller’s currency causes it to resemble a hybridcash-in-advance, overlapping generations model. In addition, the existence of spatial separationrenders significance to the timing of transactions; in this sense the model resembles the liquidityeffects models of Grilli and Roubini (1992,1993) and Schiagenhauf and Wrase (1992a).The remainder of this paper is organized as follows. Section 3.2 describes the economic environment, while Section 3.3 outlines the nature of trade and the role for banks. Sections 3.4 and3.5 consider the properties of a fall general equilibrium under flexible exchange rates, and Section3.6 examines the issue of multiple equilibria under this policy regime. Section 3.7 considers fixedexchange rate regimes, while Section 3.8 analyzes the consequences of reserve requirements andforeign currency controls. Section 3.9 concludes.3.2 The EnvironmentI consider a two-country, single good, pure exchange model. Within each country there are twolocations; at the beginning of a period agents in each country are assigned to one of these, andwithin a country locations are symmetric.Each country is populated by an infinite sequence of two-period lived, overlapping generations.Time, then, is obviously discrete, and is indexed by t=1,2.... Within each location at each datethere is a continuum of (ex ante) identical young agents with unit mass. Also, all residents of a4This formulation resembles that in Champ, Smith and Williamson (1992), which has many of these features in asingle country context.140given country are identical ex ante, although I allow for heterogeneity of agents across countries.Each agent in the domestic (foreign) country is endowed with d (yf) units of the single,perishable commodity, and for simplicity I assume that agents have a zero endowment when old.I also assume, again for simplicity, that all agents care only about old age consumption, which isdenoted simply by c, and that agents have the utility function u(c)=ln c, which is common acrosscountries.5I assume that goods are immobile between countries or locations; that is, transportation costsfor the good are prohibitive. Agents, however, do move between locations- either domestically orinternationally- in a manner I now describe.At the beginning of a period, young agents are assigned to a specific location in either thedomestic or foreign country. These agents have a positive probabffity of being relocated before theend of the period; relocations can occur either within a country or across countries. Let (4) bethe probability that a resident of the domestic (foreign) country is relocated within his own country,and ir (r) be the probability that a resident of the domestic (foreign) country is relocated to theforeign (domestic) country. The probability of relocation is constant across periods, known by allagents, and is lid across agents in a given country. Thus there is no aggregate randomness, andnet domestic relocations are always zero. This need not be the case for relocations of agents acrosscountries. Finally, to keep the locations within a country symmetric, I adopt the convention thatif residents of location 1 (2) of either country are relocated internationally, they are relocated tolocation 1 (2) of the other country.Since goods are not transported between locations, agents who are relocated must carry withthem some assets. I allow for two types of primary assets; each country issues its own flat currency and its own interest-bearing bonds. Let M (Mi) be the per capita money supply of thedomestic (foreign) country at t, and let B (Br) be the nominal outstanding per capita quantityof domestically (foreign) issued bonds at t. The liabilities of the domestic (foreign) governmentare each denominated in units of its own currency. Let p (pr) denote the domestic (foreign) pricelevel at t, and et denote the domestic currency price of one unit of foreign currency, so that e isthe nominal exchange rate. Thus, ep( /p is the real exchange rate of the domestic country,and let m M/p and b B/p (m( i4 /p( and b( B( /p() denote the supplies of realbalances and real bonds by the domestic (foreign) government at t.5A11 of these assumptions can be relaxed at the expense of considerable added complexity. In particular, I can allowfor multiple goods, some of which are traded internationally, and can allow agents to make a non-trivial consumptionsavings decision when young. These additions substantially complicate the analysis, without substantively affectingthe issues of interest here.141I assume that currency is transportable between locations (and that it is not counterfeitable)whereas the same is not true of bonds or other, privately issued liabilities. In addition, a country’sown currency is used for inter-location exchange within that country, whereas the foreign countrycurrency is used for inter-location exchange between countries. This amounts to imposing a cash-in-advance constraint on all inter-location exchange; a buyer in these kinds of transactions must payfor purchases using the currency of the seller. This convention is an extension to a multi-countrycontext of the formulation used in Champ, Smith and Williamson (1992). 6I assume that bonds issued by the domestic (foreign) government at t pay the gross nominalrate of interest I (If) between t and t+1. Thus R #/1+i and = ifp(/p(1 are thegross real rates of interest received by the holders of these instruments within the relevant country.Clearly, when both I’ and if >1 so that currency is dominated in rate of return the assumptionsof the preceding paragraph imply that all agents will, ex ante, wish to hold diversified portfolioscomprising both types of currency and bonds.The fact that currency is required for inter-location exchange means that the possibility ofstochastic relocation plays the role of a liquidity preference shock in the Diamond-Dybvig (1983)model. Agents who are relocated within (across) countries wifi wish to liquidate other asset holdingsand use the proceeds to acquire the currency of the relevant country. It is natural for banks toarise in order to insure agents against the associated risks of premature asset liquidation. Doingso will involve them holding reserves of both currencies, as well as bonds. The behaviour of thesebanks is described in the next section.3.3 Trading, And The Role Of Banks3.3.1 The Timing Of TradeSince agents do not consume when young, all trade takes the following form. At the beginning ofperiod t in each location there are some old agents who have arrived there from elsewhere. Theseagents are carrying the currency of the location they arrive in, since currency is the only assetthat can be transported between locations. This currency is then used to buy goods from youngagents. In addition, there are old agents in each location who have remained there from the previous6By inter-location exchange I refer, of course, to situations where a buyer who has beeen relocated purchasesgoods in the new location. The assumption that only currency is useful in inter-location exchange also appears inTownsend (1987), Mitsui and Watanabe (1989) and Hornstein and Krusell (1993). This assumption can be motivated- as in Townsend (1987) - by appealing to limitations on the degree of conununication between locations. See Champ,Smith and Williamson (1992) for a further discussion of this issue. The notion that government bonds are not usefulin inter-location exchange could also be motivated by the possibility- which is common in most countries- that theyare issued in denominations too large to be useful in transactions.142period; these agents consume the income generated by any assets that they hold - either directlyor indirectly- and they do not require currency in order to do so.An essential ingredient in any model with spatial separation and inter-location mobility is thetiming of transactions. My timing assumptions are as follows. At the beginning of period t oldagents who hold bonds - either directly or indirectly- are paid in units of goods in the relevantlocation, which they consume. Old agents who hold currency use it to purchase goods from youngagents; goods purchases by assumption occur in the seller’s currency.Once goods trade is completed, asset trading begins. Young agents can either hold assets directly, or they can make a bank deposit and holds assets indirectly. After asset trading is completedat t, young agents find out whether or not they are to be relocated, and their ultimate destination.If young agents are to be relocated, only the currency of the country of their destination is of useto them; any other assets that they hold directly become valueless to them.7 If young agents holdbank deposits, then they go to their banks, and make a withdrawal in the relevant currency beforebeing relocated. This timing of transactions is depicted in Figure 3.1.The risk of relocation implies that agents will not wish to hold primary assets directly. Rather,they wifi prefer to have their savings intermediated by banks which take their deposits, hold theprimary assets in the model directly, and promise state contingent payments to depositors dependingon their relocation status and ultimate destination. I now turn to a description of these banks.3.3.2 Bank BehaviourI assume that, in each location, there are some banks that behave competitively in the sense thatthey view themselves as being unable to influence the equilibrium returns on assets. On the depositside these intermediaries behave as Nash competitors; that is, they announce state contingentreturns to depositors as a function of relocation status and ultimate destination. In addition, thereis assumed to be free entry into intermediation. Thus competition among potential intermediariesfor deposits means that- in a Nash equilibrium- deposit returns must be chosen to maximize theexpected utility of a representative depositor, subject to bank balance sheet constraints which Inow describe.I focus throughout on the situation where nominal interest rates in each country are strictlypositive at each date; that is, in which I > 1 and if > 1 hold for all t. In equilibria with thisproperty, banks will hold (either) currency only in order to accomodate the liquidity needs of agentswho are relocated. Any excess holdings of currency are sub-optimal, as bonds dominate money in7Recafl that at this point asset trading has been concluded in period t.143rate of return.Let denote the per depositor holdings of domestic real balances by domestic banks at t,and let denote the time t quantity of foreign real balances held by domestic banks (again,per depositor). The former, of course, are measured in units of domestic goods, while the latterare measured in foreign goods. Similarly, let (b) denote the per depositor real holdings ofdomestically (foreign) issued bonds at t. The same comment about units applies. Then the value,in domestic goods, of units of foreign real balances at time t is given by mt(etp(/p) E mXt,and similarly, the domestic goods value of units of bonds denominated in foreign goods isat t. Since all savings are intermediated, a representative domestic bank will receive a real depositof yd per depositor at each date. Thus the bank’s balance sheet constraint is> m + + xt(mt + bt);t >1. (1)I assume that each bank offers a set of state contingent real gross returns on deposits. Theseare denoted as follows. is the return delivered to domestic depositors at t who are relocateddomestically, while 4 is the real return paid to domestic depositors who are relocated abroad. ris the real return paid to domestic depositors who are not relocated.8 The returns the bank canoffer are, of course, constrained by its portfolio composition and the returns on assets that it faces.These constraints are as follows.At time t, a fraction ir of the bank’s depositors are relocated domestically. These agents havebeen promised a payment of per unit deposited, and each of them has deposited d. Thusthe per depositor obligation to these individuals is These agents must be given domesticcurrency to accomplish their transactions. This will be done using the bank’s holdings of domesticreal balances: all of these holdings will be paid out to domestically relocated depositors at t whocarry them into t+l. The real return between periods on these real balances is /+1;thus thebank faces the budget constraintdd d did,d .drdty < mftp fPt+i), t 1. 2For domestic agents who are relocated abroad (of whom there are per depositor), the bankhas promised a payment of 4yd. These agents must be paid in foreign currency in order to maketheir purchases; thus payments are constrained by the bank’s foreign currency holdings Theseholdings have a domestic goods value of mxt. In addition, domestic agents who are relocated81t bears emphasis that the assumptions on timing and communication between locations imply that domestic(foreign) residents make deposits only in domestic (foreign) banks.144abroad carry these real balances with them between t and t+1, earning a gross real return ofidid \f I 9 miPt /Pt+l)et+1,et). . LILUSi44yd < m t(p/p1)(et+i/et);t> 1, (3)must hold.For domestic agents who are not relocated - who comprise a fraction 1-ir-i4 of depositors- the bank promises a total repayment of (1 — ir — i4)ryd. This must be financed out of thebank’s earnings on its bonds, since all currency holdings are liquidated to pay off agents who arerelocated.’0 Foreign issued bonds held by domestic banks yield a real return- in units of domesticgoods - of I((p/p,)(et+,/et) The return constraint relevant to the choice of 4 is, inunits of domestic goods,(1 — .d .d )rdyd b + R; t 1. (4)Competition among banks for deposits implies that - in a Nash equilibrium - deposit returnschedules and bank portfolio allocations must be chosen to maximize the expected utility of a representative depositor, subject to constraints (1)-(4). In other words, in equilibrium domestic banksmust choose r,4 , r, and to solve the problem(P.1) max irln(rtyd) + ln(ry”) + (1 — ir — ir)ln(ryd)subject to (1) to (4) and non-negativity.This problem can be transformed as follows. Let ‘y (-4) denote a domestic batik’s ratio ofdomestic (foreign) currency real holdings to deposits at t; that is7t E mt/yd, (5)‘4t mx/y. (6)Similarly, let /3 (1—-y—— /3) denote a domestic bank’s ratio of real domestically (foreign)issued bonds to deposits at t, so that— &did 791n particular, e /p’ units of domestic goods are requires to obtain at t one unit of foreign currency (in nominalterms). At t+1, this unit of currency has a domestic goods value of e+1/p+l. Hence the real return, to a domesticresident, of holding foreign real balances is (et+j/pi)(p/et)‘°Recall that the bank does not wish to carry currency between periods, since money is dominated in rate of return.“To see this, note that e /p units of domestic goods are required to buy one unit of (nominally denominated)foreign bonds at t. This bond unit repays if units of the foreign currency at t+1, which has a domestic goodsvalue of if (et+j/p+,) at that date. Thus the real return, to domestic residents, of holding a foreign bond isIf (e +i /p+i )(pf/e.145(1———b/yd. (8)Then constraints (2) to (4) can be re-written asft (P /P+i ) /1r, (9)4 4t(p/p+i)(et+i/et)/4, (10)4 [4 + (1 ——— 8t ) R] / (1 — ir— 4), (11)which must hold V t> 1.The bank then seeks at each date to solve the problem(P.1 1) max 7rlnr + rln4 + (1 — — i4’)1n4subject to (9) to (11) and non-negativity. The solution to this problem setsd — d7dt —= 4. (12)In addition, an absence of arbitrage opportunities in bond markets requires that= Thiscondition is equivalent to the uncovered interest parity condition= if (et+i/et); t 1. (13)For ftiture reference it wifi be convenient to note an alternate form of (13):= Rt(at+i/xt);t 1. (131)The problem of banks located in the foreign country is completely symmetric. In order todescribe it, I proceed as before and define (y) to be the ratio of foreign (domestic) countrycurrency to deposits in foreign banks; thusm//, (14)and‘Yd’t mt/y’xt, (15)hold, where (m) is the per depositor holding of foreign (domestic) country real balances by arepresentative foreign bank at t. Similarly, f3 (1—7c—— /5) is the ratio of foreign (domestic)146real bond holdings to deposits of a foreign bank. Then we have(16)(1—7——/3.) E (17)where (b) is the (per-depositor) holding of foreign (domestic) real bonds by a foreign bank atdate t.The budget constraints facing a foreign bank are as follows:7t(p/p(+i)/4;t> 1, (18)r t(pi/pt+i)(et/et+i)/;t 1, (19)r( [,3cR + (1— —— I3c)R]/(1— 4 — irs); t 1, (20)where (rt) is the gross real return on deposits promised to foreign agents who are relocatedwithin (across) countries, rt is the return promised to foreign agents who are not relocated, andis the gross real return to foreign holders of domestically issued bonds.holds. 12Competition among foreign banks for depositors then forces these banks - in equilibrium- tochoose return schedules and portfolio weights solving the problem(P.2) max irçin4 + Ird’ lmr + (1— 4 — r)lnr(subject to (18) to (20) and non-negativity. The solution to this problem sets— f— 1r,= irs. (21)In addition, equation (13) or (13) must hold in order for agents to perceive no arbitrage opportunities in bond markets.3.4 General Equilibrium: Flexible Exchange RatesI now describe the determination of a full general equilibrium of the model under a regime offlexible exchange rates. Central to this determination is a complete description of the behaviour ofthe government of each country, which I now provide.In particular, 1/ep units of the foreign good are required to purchase one (nominal) unit of domestically issuedbonds at t. These bonds return I units of domestic country currency at t+1. This currency has a foreign goods valueof 1/et+1p+i per unit at t+i. Hence the gross real return to foreign residents of holding domestic country bondsfrom t to t+1 is I(p/p÷) et/eti). The same reasoning yields the real return on foreign holdings of domesticcurrency in equation (19), except that currency bears no interest.1473.4.1 Government ActivityAt each date t>1, the domestic (foreign) goveriirnent has an outstanding money stock (per capita)of M (Mi) held by private agents, and a quantity of nominal, interest-bearing bonds outstandingof B (B() per capita. In addition, the domestic (foreign) government holds reserves of the foreign(domestic) currency in the amount of Z (Z) per capita at t. I assume (in this section) thatneither government levies taxes nor has direct expenditures. Thus, at each date, the governmentof each country must generate enough seignorage revenue to service its debt, and to finance anychanges in its net reserve position. In other words, the domestic country government faces thefollowing budget constraint for t>1:#_iB_i =Md_ M_1+B— et(Z— Z_1)+Z — Z_1. (22)For t1, the foreign government’s budget constraint isI(_1B( = M/ — + — (l/et)(Z — Z_1)+— Z_1. (23)I consider the following choice of government policies. For t 1, each country is free to set (onceand for all) a constant rate of growth for its money supply; that isM1/ c,.d;t> 1, (24)I41/M/ o4;t 1, (25)where 4 > 1 and o > 1. The quantities of money held by initial old agents in the domestic(foreign) economy are also given and equal Mg > 0 (M > 0). For reasons that will becomeapparent, M and M must be determined endogenously. Further, initial foreign exchange reserveholdings are given as Z0 = Z = 0. I allow each government to assume an endogenously determinedreserve position Z1 (Z1) at t=l, which it then maintains forever. Thus= Z_1;t 2, (26)= Z_1;t2. (27)Finally, Bg = B = 0 is the last initial condition; from t=l onwards the values B and B( areendogenously determined.Under this specification of government policies, it is possible to rewrite the government budgetconstraints in the following, more convenient, form:= m—m_1(j4_/p)+b’;t 2, (28)m( — mf_1(p(/ ) + b(;t> 2. (29)148Observing that, by definition, p_1/p’ E (m/M)(M_1/ _) m/’m_1[p_1/(mt/M’)(Mf_1/ f_) m(/o.fm(_1]for t>1, (28) and (29) may be farther simplified:= m’(o4 — 1)/a4 + b;t 2, (30)= m((a — l)/a + b(;t> 2, (31)where I have used (131) to eliminate R4_1 from (31). At t=iMg = M + B — e1Z + 4’, (32)M = M(+Bf—(1/ei)4,+Z,, (33)are the government budget constraints.3.4.2 Asset MarketsIn order for asset markets to clear, it is necessary that the per capita supply of real balances by thedomestic (foreign) government at t - m (mi) - equal the per capita demand for domestic (foreign)real balances by the residents of each country at that date. The (per capita) demand for domestic(foreign) real balances at t is just + E 7d + = dd + yiJt[mt ++ 4y’t/xt = + 4y’/xt]. Thus money market clearing requires thatm = irdy+irfyfat> 1, (34)m( = irçy’+4y’/t;t1. (35)In order for bond markets to clear, an absence of arbitrage opportunities requires that theuncovered interest parity condition (13) or (131) hold at each date. In addition, the total per capitasupply of bonds - measured in a common unit - must equal the total per capita demand for bondsat each date. The former quantity is b + b(zt - measured in units of domestic goods - while thelatter is (1 — ir — i4)y’ + (1— 4 — ir)yfxt at t. Thus bond market clearing requires that(36)For future reference I note that (34)-(36) imply that the total value of assets at each date - measuredin a common unit - must equal the total demand for assets; that is,m+b+xt(m(+b()=yd+yfxt;t 1. (37)1493.4.3 Goods Market ClearingIn order for the domestic (foreign) goods market to clear at each date it is necessary that theper capita supply of domestic (foreign) goods - yC (yf)- equal the per capita demand for domestic(foreign) goods. But per person goods demand in (either location in) the domestic (foreign) countryat t is simply the real income of domestic (foreign) residents who were not relocated at t-1, plus thevalue of real balances carried by agents who were relocated at t-1. The income of agents who werenot relocated is simpiy the interest income generated by their (intermediated) holding of bonds,which in the domestic (foreign) country is R_1(1—— .4t_1)yd= R_1(1 — —[R_1(1—— -y_1) = R_1(1 — — ir)yf] at t. For agents who were relocated at t-1,they have arrived in their current location carrying the entire t-1 per capita supply of domestic(foreign) real balances- m1 (mf_1)- which at t has a real value ofm_(p/ )[m(1(p_/pf)].Thus the domestic goods market clears at t ifm_1(p/ )+ (1— ir— 4)y”Rt_i;t > 2, (38)while the foreign goods market clears ifmf_1(p(/ ) + (1— irç— ir)yR_1;t 2. (39)By using the relations p_1/j4 m/m_i, p(_1/p( mt/a’m(_1 and (131), these conditionscan be simplified to2, (40)(4f + 4yd/t)/oJ + (1— 4 — ir yfRt_i(x_1/x);t> 2.13 (41)For t2, equation (13) or (131), equations (34)-(36), equations (40) and (41), and the two goveminent budget constraints (30) and (31) constitute the complete set of equilibrium conditions forthis econony. Wairas’ Law implies (and it is straightforward to show) that only seven of theseconditions are linearly independent. However, I display all nine since all of them will be useful atsome point in the analysis.3.4.4 The Initial PeriodThe asset market clearing conditions at t= 1 have the same form as the asset market clearingconditions that are relevant at other dates, as indicated by (13) and (34)-(36). This is not true,however, for the goods market clearing conditions at t=1, since old agents have no bond incomein the initial period. Rather, at t=1, old agents have arrived in their present location by whatever150means, and in the domestic (foreign) country hold the initial domestic (foreign) supply of moneyto private agents M (Ms). All of this is spent on consumption, yielding the time 1 market clearingconditionsMg/p = d, (42)= y1. (43)Thus, the initial price levels are predetermined. This is why the time 1 period money supplies,nominal bond supplies and foreign exchange positions of each government must be endogenouslydetermined. In particular, in the intial period each goverument must adapt to the predeterminedprice level that it confronts.3.5 Characterization Of Equilibrium: Flexible Exchange RatesI now turn attention to a characterization of the equilibria described in Section 3.4. I begin byanalyzing steady state equilibria.3.5.1 Steady State EquilibriaWhen Xt and are constant (at x and R), equations (40) and (41) reduce to two equations inthose two unknowns. They therefore jointly determine the steady state values of the real exchangerate and the real interest rate. The remainder of the steady state equilibrium values can then bedetermined recursively: equations (34) and (35) give the steady state values of md and m’, while(30) and (31) givebd = (c,.d— 1)md/o(R— 1), (44)b1 = (0.f— 1)m/o(R— 1). (45)Moreover, clearly 74÷ = and 4i/p( = o1 hold, whIle p and p are given by equations(43) and (44). 1d = RU gives a Fisherian determination of the nominal interest rate in thedomestic country, while (13) and et+i/et (x+1/x)(p(/pf)(p/74+ o.d/uf imply that theforeign nominal interest rate is # = Id(,.f/ud) = Ro = Ro (in the steady state).It is possible for this economy to reach its steady state equilibrium at t=1, so that x1 = x. Inorder to support the predetermined price levels as a part of this equilibrium, M and M must beset so that(M/Mg)yd = = + (46)Mj/p (Mj/M)y’ = m1 = iry’ +i4yd/z, (47)151where the first equalities follow from (42) and (43). From the government budget constraints (30)and (31), and the bond market clearing condition (36), B and B must likewise be set to satisfy= bd and B/j4 =b1.It remains to show that the endogenously determined initial levels of foreign exchange reservesconstitute an equilibrium. To do so I must show that the net foreign reserve positions of thetwo governments sum to zero at each date. Clearly, since I have imposed that the initial foreignexchange positions are preserved for t2, it suffices to show that the governments’ net reservepositions sum to zero at t=1. From (32),(eiZ1 — Z1)/p = md + b’1 — = md + bd — d, (48)while from (33)(Z1 —e1Z)/ep= m + — = m +—(49)Multiplying both sides of (49) by x and summing (48) and (49) yields(50)which is satisfied by (37). Thus the net foreign exchange positions of the two governments sum tozero, as required.It is therefore the case that, once x and R are determined, afl other steady state equilibriumquantities can be recovered. I turn next to an analysis of the determination of these values.3.5.2 CharacterizationThe steady state version of equations (40) and (41) can be rearranged to yield the equivalentconditionsf7d= [ud——(1— — (51)i4/[o—4 —(1—4 —ir)oRj. (52)Equation (51) describes a downward sloping locus, as depicted in Figure 3.2, while equation (52)describes an upward sloping locus, shown in the same Figure. Evidently, then, (51) and (52) havea unique intersection at a positive value of x jif (.d—> 4/(f— 4)While this restriction on parameter values is necessary for the existence of a steady state equilibrium it is not sufficient. In particular, the analysis of the banks’ problems in Section 3.3 waspredicated on F’ = cr’R > 1 and F’ = > 1 holding in equilibrium. Thus, a necessary andsufficient condition for the existence of a unique steady state equilibrium is that the solution toequations (51) and (52) satisfy152> max(1/o1,1/o). (53)A necessary and sufficient condition for (53), m turn, is that (51) he above (52) at the pomt= max(1/o4, i/of); this is implied by the following two assumptions, which I maintain throughout the remainder of the analysis:(A.1) (o.d + — 1)/irs >— 4 — uf(l— 4 —(A.2) [-- ud(1 --r)frf]/pi > /( +r -1).(A.1) and (A.2) require that rates of money growth must be sufficiently large for positivenominal interest rates to be observed. As such, these constitute standard assumptions. Underthem, equations (51) and (52) have the configuration depicted in Figure 3.2, and they determine aunique steady state equilibrium with strictly positive nominal interest rates.3.5.3 Comparative StaticsIn the following three subsections, I consider the comparative static consequences - for steadystate equilibria - of changes in the money growth rate of each country, of changes in the relativeoutput levels in the two countries, and of changes in liquidity preference paramaters respectively.As indicated by equations (51) and (52), these are the fundamental determinants of both realexchange rates and real interest rates in this economy.3.5.4 Comparative Statics: Money Growth RatesThe result of an increase in the rate of domestic money growth is (partially) depicted in Figure3.3. For real interest rates satisfying 1 > (1 — — r)R - which includes any equilibrium realinterest rate - an increase in 4 shifts the locus defined by (51) up and to the right in Figure 3.3.Since the locus defined by (52) is unaffected by o’, the evident consequence is that an increase inthe money growth rate of the domestic country causes an increase in the domestic country’s realexchange rate and an increase in the (world) real rate of interest. Since an increase in er’1 leads toan increase in R, clearly it also leads to an increase in 1d (and If). The fact that the real rate isaffected by the increase in er also implies that the nominal interest rate in the domestic countryrises by more than the increase in the rate of inflation.The rise in the real interest rate is due to the fact that money creation finances debt repayments. The increase in the real rate then raises the real income and demand of bond holders in153both countries but, in particular, engenders an increase in the relative demand for foreign goods.For foreign and domestic goods markets to be simultaneously re-equilibriated there is a reallocation of purchasing power away from domestic consumers of foreign goods and towards foreignconsumers of domestic goods; a real depreciation of the domestic country’s currency. Notably, then,monetary changes cause both intra-national and inter-national redistributions of real income andconsumption.The nominal exchange rate effects of a rise in o can be deduced as follows. Since the initialreal exchange rate - x1 - equals x, the change in the initial nominal exchange rate, e1= iP/P, isgiven by(&ei/ô)(/ei) = (ap/d)(d/j4) - (Op/od)(/p) + (8x/8)(/xi) (54)The fact that p and p are predetermined implies that c9j4/&rd /0d=(); hence a changein the rate of domestic money growth induces the same proportional change in the real and initialnominal exchange rates. The nominal exchange rate then rises at the rate 0/f to keep the realexchange rate constant at its new steady state value given (new) rates of price inflation.The effect of an increase in , is depicted in Figure 3.4. Evidently, an increase in o does notaffect the position of the locus defined by (51), while it shifts the locus defined by (52) down andto the right (for values of R satisfying 1> (1— 4 — ir)R, which includes the equilibrium valueof R). Thus an increase in the rate of growth of the foreign money stock causes the real exchangerate of the domestic country to fall, while it causes the (world) real interest rate to rise - as aconsequence of the same mechanisms described above. The effect on nominal interest rates, andon the initial nominal exchange rate, induced by an increase in of is analyzed exactly as before.Thus, a rise in CT’ causes the initial nominal exchange rate, e1, to fall in proportion to the declinein the real exchange rate.In short, increases in the rate of money growth in either country raise the (world) real interestrate and depreciate the real value of that country’s currency.3.5.5 Comparative Statics: Relative Output LevelsAn examination of equations (51) and (52) indicates that an increase in the ratio y1/y’ affectsneither the real rate of interest nor the equilibrium level of xy11d• Thus an increase in yf /y’1 leadsto a proportional decline in the domestic country’s real exchange rate. Here, however, there is nochange in the nominal exchange rate, as the change in yf1d induces a proportional change in theratio p/p (see equations (42) and (43)). In this sense, the initial impact of a change in relative154output levels on the nominal exchange rate (zero) differs substantially from the initial impact of achange in (either) rate of money growth.3.5.6 Comparative Statics: Liquidity Preference ParametersThe relocation probabilities, 4, ir and ir govern the composition of money holdings betweendomestic and foreign real balances in each country. Thus a change in any of these parametersaffects the composition of money demand in either country. Here I analyze the consequences of areduction in irs; the consequences of changes in other relocation probabifities is analyzed similarly.For values of R > l/o” (and hence for equilibrium values), a reduction in ir causes the locusdefined by (51) to shift in a maimer similar to that associated with an increase in Since irdoes not appear in equation (52), a fall in ir has the same qualitative impact as an increase in thedomestic country’s rate of money growth. This should be an intuitive result, since a decline inlowers the demand (ceteris paribus) for real balances of the domestic country; this has the samequalitative consequences as a monetary expansion by that country.3.5.7 An Example: The Case Of A Small Open EconomyThe case of a small open economy is particularly simple to analyze; here we consider the case wherethe domestic country is ‘small’. By ‘small’ I mean that the domestic country parameters have noconsequences for real (or nominal) interest rates - or prices- in the foreign country. This situationarises 1ff 4 = 0, which I now assume. This restriction implies that small country residents holdno foreign currency, and may be interpreted as the case in which small country demand for largecountry goods constitutes a negligible fraction of the total demand for large country goods.When 4 = 0 and Xt=Xt_1 hold, equation (41) reduces to, in a steady state equilibrium,=(o — 4)/o’(l—4 — irs). (55)Substituting this into (40) then yields= (if1)[(t7d_ir)_ (i—ir)er’(a1 — r)/o.1(l—4 —irs)] (56)which, like (51), represents a downward sloping locus in (x, R) space. While, from (55), the foreigncountry’s parameters alone determine the world real interest rate, both domestic and foreign countryfactors influence the steady state real exchange rate.Evidently, then, an increase in d does not affect R, and hence an increase in the domesticmoney growth rate has the usual ‘Fisher effect’ on the domestic nominal interest rate. Moreover,from (56),155(.d/r)(/8t,.d) = .d(xyf/yd)_l[1— (1 — ir)(o —4)/0J(i— 4 — ir)]/ir > 0 (57)describes the change in the real (and initial nominal) exchange rate. Since the foreign goods marketclearing locus is now independent of x (vertical at the steady state value of R), such a domesticmonetary change simply raises the steady state real exchange rate.An increase in o does, of course, affect the equilibrium value of the real interest rate, as before,and it induces the following change in the real (and initial nominal) exchange rate:= _d(xyf /yd)-l[(1- )4/(uf)2(1-4- r)ir] <0. (58)I wifi later use equations (57) and (58) to compare how changes in money growth rates affectthe real exchange rate under fixed versus flexible exchange rate regimes.3.6 On The Indeterminacy Of The Real Exchange RateThe steady state equilibrium analyzed in Section 3.5 can be thought of as a ‘fundamental equilibrium’; initial price levels are determined by the supply of money in each country relative tooutput and, thereafter, money growth rates determine the rate of inflation.14 In this section I showthat there is a continuum of dynamical equilibria, indexed- in effect - by the initial real exchangerate x1. In the sense just described, these are ‘non-fundamental equilibria’; in afl such equilibriaeach country has an inflation rate that permanently differs from its money growth rate. By implication, these equilibria also have the property that the nominal exchange rate deviates from its‘fundamental value’ at each date.In addition, dynamical equilibria here have the feature that the real exchange rate either appreciates or depreciates permanently. It follows that real exchange rate appreciations and depreciationscan occur for ‘non-fundamental’ reasons.3.6.1 Dynamical EquilibriaSolving equation (40) for R_1, substituting the result into (41), and rearranging terms yields thefollowing law of motion for Xt:— dd + [oJf (1— 4 — ir)(o — )/o.d(1 — — r)]xt (59)— (uf— ir)yf + [7ryf(a1yf)(1— 4 — i)/o.dyd(l — ir —which holds for t>l.‘41f the economies were growing (at the same rate), inflation rates would be the difference between the rate ofmoney growth and the (common) rate of real growth in each economy.156The equilibrium law of motion for Xt is depicted in Figure 3.5. Evidently, equation (59) has anon-negative intercept, and differentiation of (59) yields the following slope for the equilibrium lawof motion:d d=(f— )yf + [yf(fyf)(i — — ——(60)Since the steady state equilibrium satisfies (d— r)/ir > xyf/yd (see Figure 3.2), it is apparentthat dx+,/dxt > 0 holds at any non-zero intersection of (59) with the 450 line. The same conditionimplies that - at such an intersection- dx+, /d < 1 holds. This confirms the uniqueness of thesteady state and establishes that it is asymptotically stable.The asymptotic stabifity of the steady state equilibrium, of course, implies that the equilibriumreal exchange rate is indeterminate; there is a continuum of possible choices for the initial exchangerate, x1, all of which imply different perfect foresight paths.’5 Some such equilibrium paths aredepicted in Figure 3.5. All such paths have the feature that the real exchange rate either appreciatesor depreciates permanently.Once x1 is chosen, the time path for Xt is fully determined. Equation (40) then yields the sequence while m and m are determined by (34) and (35). Equation (36) gives the equilibriumsequence b + bfxt; the real bond values outstanding of the individual countries are indeterminate(and irrelevant to allocations), and need be selected only to satisfy the government budget constraints. The next section explores the properties of the equilibrium rates of inflation in the twocountries.3.6.2 Inflation Rates In Non-Stationary EquilibriaEquation (34) implies thatM/j4 = m = + 7rd’y-xt;t 1. (61)Thus= [(.4,d + yt+i)/(lryd + 7ry’x)j; t 1, (62)also holds. If x1 <x (where x is the steady state equilibrium value of the real exchange rate),then Xt is an increasing sequence; it follows that /‘+1 > i/ox’. Iii other words, the domestic151 should note that arbitrary choices of initial x may not be consistent with equilibrium. In particular, the choiceof Xi must produce a pair of nominal interest rate sequences I, i( satisfying I, I >1 for all t. Satisfaction of thisrequirement is guaranteed if Xi is selected sufficiently close to x.157country’s inflation rate will be permanently below its rate of money growth when its currency isexperiencing (permanent) real depreciation in equilibrium. Similar reasoning applied to equation(35) establishes thatp+1/pt = o[(i4y1+ 4y!/at)/(7rcyf + 4yd/xt+i)] > o; t 1 (63)holds. Clearly, these inequalities wifi be reversed if x1 >x is observed, since then Xt will be adecreasing sequence.3.6.3 Nominal Exchange Rate DepreciationBy definition,(64)holds. Using (62) and (63) in (64) gives (upon rearranging terms)et+i/et = (ud /.f )(dyd+fyfx)(dyd+.fyfx )/(.dd+f I t+i)(4yd+4yt);t> 1.(65)If x1 <x, then it is straightforward to verify that et+1/et > o/o•f holds, Vt> 1, ff1’rr > 4ir. (66)This condition is satisfied if the probability of within country relocation exceeds the probability ofcross-country relocation, and it certainly holds if either of the two countries is ‘small’ in the sensedefined in Section 3.5.Equations (62), (63) and (65) yield a set of empirically testable implications that apply tonon-stationary equilibria. Specifically, countries whose real exchange rate is rising should - ceterisparibus - have a lower inflation rate relative to their rate of money growth than countries whosereal exchange rate is falling. If (66) is satisfied, the rate of nominal exchange rate depreciation forsuch countries should be high compared to their relative rate of money growth in contrast to thatof countries whose real exchange rate is falling.3.6.4 DiscussionThis analysis predicts that, in non-stationary equilibria that are undisturbed by changes in exogenous variables, any country’s real exchange rate should either rise or decline monotonically.Edwards (1989), in a study of real exchange rate behaviour in 33 developing countries, reports thatthe time path of the real exchange rate in each country almost always fits one of four patterns.Either the real exchange rate rises or declines (with minor exceptions) monotonically, or the real158exchange rate rises (declines) almost monotonically up until some date, and then experiences an(almost) montouic reversal.The first two patterns are clearly consistent with the real exchange rate behaviour predictedhere, and the last two are as well in the presence of an unanticipated exogenous event. In particular,suppose that a country has a rising real exchange rate, and that at some date T, an unanticipatedexogenous event reduces the new steady state exchange rate below XT. At this point there is a freechoice of ‘initial conditions’; one possibility is that there is no change in the real exchange rate attime T. Since the real exchange rate will be above its new steady state value, the real exchangerate must monotonically decline after that date. This is very consistent both with the empiricalfindings reported in Edwards (1989, pp. 104-5), and with his interpretation of those findings.As the foregoing discussion suggests, exogenous events can clearly be accompanied by ‘overshooting’ or ‘undershooting’ of real and nominal exchange rates. Thus such phenomena are alsoconsistent with the present analysis.3.6.5 A ConjectureThe close relationship between the asymptotic stability of steady state equilibria with money,on the one hand, and the existence of sunspot equilibria on the other is a common theme ofthe sunspot literature.16 The construction of sunspot equilibria in this context would not bestraightforward, and therefore an investigation of this connection in this model is left as a topicfor future investigation. However, I conjecture that it is possible for there to be equilibria wherethe real exchange rate displays sunspot fluctuations. These fluctuations, if they can be observed,would then be transmitted to the nominal exchange rate and to the price levels of the individualcountries.3.7 Fixed Exchange RatesThis section describes the determination of a steady state equilibrium under a regime of fixedexchange rates. Thus, in this section, I assume that et= eVt1 is given and fixed. How this exchangerate is maintained will generally matter; therefore I begin with a description of government policy.The policy regime I analyze is meant to resemble the Bretton Woods system in its central features;in particular, I assume that one (large) country is free to set its own money growth rate and thatall other countries ‘accomodate’ their rates of money growth in order to maintain the fixed nominalexchange rate target.16See, for instance, Azariadis (1981), Peck (1988) and Woodford (1984).1593.7.1 Government ActivityI assume that the foreign country is free to select its own monetary policy (within the limits impliedby the existence of an equilibrium), and that it behaves exactly as described in Section 3.4. Thus,M > 0 is given and fixed, and the foreign country selects a value o’ that governs its money growthrate after the first period; that is,Mf1/ /o>1;tl. (67)M must be endogenous as before.The domestic country must adjust the time path of its money supply in order to maintain thefixed nominal exchange rate at each date. At t=1 this is accomplished by levying a lump-sum taxof -r1 (in real terms) on the initial old agents; thereafter M is endogenous, and= o;t> 1 (68)must be satisfied in a steady state equilibrium (which is clear from (13) and (131) when et+i/et = 1and Xt+i/Zt = 1).In the initial period, (44) determines p. Once the initial real exchange rate x is determined(see below), p = ep/1 must hold. Thus Ti must be selected so thatMff/p — = xiMg/epf—= xiMgy’/M— (69)3.7.2 A Steady State EquilibriumThe set of steady state equilibrium conditions is exactly as described in Section 3.4, except thatequation (69) replaces (42). Tn addition, 0.d = 0•f holds. Thus a steady state equilibrium satisfies(51) and (52) when o = o is imposed; that is= {oJ— — (1— ir— ir)R]/ir, (70).d/[.ul.f(1lrfTf)o.fRd] (71)Equations (70) and (71) have a unique solution (depicted in Figure 3.2) which satisfies Rr > 1Hf(A.3) ((cry +ir- 1)/irs)> 4/( +ir -1). ‘717(A.3) is just (A.1) and (A.2) with 0A = 0j imposed.160Evidently, the choice of the fixed nominal exchange rate value has no implications for theequilibrium real exchange rate, or indeed, for any equilibrium quantities other than the domesticprice level. This result is of some importance, since in discussions of the EMS’8 it is often suggestedthat the nominal exchange rate between currencies should be selected (given initial price levels) toyield (approximate) purchasing power parity. Since purchasing power parity wifi (generically) nothold at any date (or asymptotically) here, such policies will not prevent the necessity of domesticprice level adjustments. Here such adjustements would be accomplished by varying rj.Once the equilibrium values of x and R are determined, all other equilibrium quantities (exceptp) are determined as in Section 3.5. As noted, all of these - except for the domestic price levelsequence p - are determined independently of the choice of e.3.7.3 Comparative Staticslii this section, I analyze the steady state equilibrium consequences of a change in the (common)money growth rate, o-1. These will generally differ from the consequences of changes in either thedomestic or foreign money growth rates in the flexible exchange rate case, since here both moneygrowth rates must move together. Other comparative static results do coincide with the flexibleexchange rate case; therefore they are not reconsidered here.As will be demonstrated, the effects of a change in cr’ for the real exchange rate are necessarilyambiguous since both the domestic and foreign goods markets are affected. To simplifr calculations,I henceforth comfine attention to the case where the domestic country is ‘small’. Thus, in theremainder of this section, I assume that 4=0. This case is adequate to illustrate the general tenorof the results obtained.‘When 4=0 holds, equation (55) continues to describe determination of the real interest rate.(56) gives the real exchange rate when o = o- is imposed; that is= [(oi— 4) — (1 — )(0.f — 7rç)/(l — ir — 7r)]/ir. (72)Thus8R/Oo4 = 4R/o.f(o.f — irç) > 0, (73)and= [1— (1 — ir)R]/ir — [(1 — ir’/7r]aR/oo. (74)18Williamson (1985, 1993) for example, discusses criteria for estimating fundamental equilibrium exchange rates inthe context of countries’ choices of central exchange rate values in managed rate systems (and the EMS in particular).See also Kenen (1988) and Krugmau and Miller (1992).161Under flexible exchange rates= [1 — (1 — ir)R]/Tr > 0 (75)9(xyf /Yd)/9o = —[(1 — iro/ir]aR/c9o < 0, (76)(evaluated at 0,d = f). Since R and OR/8u1 are unaffected by the choice of exchange rateregime, a comparison of equations (74)-(76) indicates that&e/t9od f1eib1e> 0x/Uo fi,r,.ed> f1eiib1eThus, the fact that the maintenance of a fixed exchange rate requires both money growth ratesto move together weakens the impact of a change in the (common) rate of money growth, relative toa regime of flexible rates. In particular, when the impact of an increase in o on the real exchangerate is positive under fixed exchange rates, it is smaller than the positive impact of an equivalentchange in o under flexible rates. Similarly, when an increase in a1 reduces x under fixed rates,the absolute value of the change in x is smaller than the absolute value of the (negative) change inx that would be induced by an equivalent increase in cr1 under flexible rates. This result reflectsthe fact that a change in the money growth rate o now induces a reduction in the purchasingpower over goods of currency holders in both countries, and requires simultaneous adjustment ofthe real interest rate to satisfy the government budget constraint in both countries. Thus, theinternational reallocation of purchasing power needed - in the form of real exchange rate changes -to simultaneously re-equilibriate both goods markets is reduced.In order to obtain the sign of ôx/ôu in a fixed rate system, substitute (73) into (74) andrearrange terms to getô(xy1/yd)/crn=[cry 4 — (1 — )cr R]/(cr1— 4)= xyf/yd(o_4_ (4 )/(.f —4) (77)where the last equality makes use of (55) and (72). ThenProposition 1. (a)Suppose that 4. Then O/o4 >0. (b)b/8crf <0 if(i — 4)/.f >Thus, when the nominal exchange rate is fixed, an increase in the common money growth ratecan either raise or lower the equilibrium real exchange rate.1623.8 Reserve Requirements And Exchange ControlsIn this section I examine how the imposition of either reserve requirements or exchange controlsimpacts on the equilibrium values of the real (and, under flexible rates, nominal) exchange rate, andon the real rate of interest. I focus here on steady state equilibria; for fixed exchange rate regimesthese are the only equilibria examined, while for flexible exchange rate regimes I have shown thatany non-stationary equilibria asymptotically approach the steady state. Thus, in the latter case,the analysis of this section is informative regarding the long-run impacts of these regulations ondynamical equilibria. Finally, in order to simplify the exposition, I focus throughout on the casewhere the domestic country is small; thus r=0 is assumed to hold.3.8.1 Domestic (Small) Country Reserve RequirementsImagine that banks in the domestic country are subject to a binding reserve requirement; that is,they are obligated to hold a minimum amount of domestic currency per unit deposited. Such arequirement is represented by the regulatory restrictiond-... d fd1.‘Ydt—‘ d, ),The assumption that > ir, of course, implies that the reserve requirement is binding.Banks in the domestic country now must solve the problem’9(P.3) max irlnr + (1 — i4’)lnrsubject to (9) to (11), (78) and non-negativity, and where I have used the assumption ir=0. Thesolution to this problem clearly sets-y = y; the solution to the problem of banks in the foreigncountry is obviously unaffected. In addition, (13) must continue to hold to preclude arbitrageopportunities.With TrfrO, the money market clearing conditions now become, in a steady state equilibrium,(compare with 34 and 35)md = 7yd+yf, (79)m1 = rçy’. (80)consider here only legal restrictions on banks that do not cause some savings to leave the banking system.Disiutermediation will generally be a possibility, but only if the legal restrictions imposed on banks are sufficientlysevere. Thus the focus in the text is on ‘mild’ but binding restrictions.163The bond market clears in a steady state equilibrium if (13) and m’ + b’ + x(m1 + bf) d + xy1hold, and goods market clearing obtains in each country in such an equilibrium if= md/s + (1 — ydR, (81)= m/o + (1— 4 — (82)Using (79) and (80) to eliminate m and m from (81) and (82) yields the following steady stateequilibrium conditions:= (yd+fyf)/eyd+(1_)ydRdd, (83)= (4y’)/o+(1—4—ir)yR. (84)Evidently, the choice of reserve requirement by the (small) domestic country has no effect onwhich is determined by foreign goods market clearing alone. From (83), then,_yd/.fyf <0.This should be intuitive; an increase in the domestic country’s reserve requirement raises thedemand for its currency, and so its goods, with consequences opposite to those of a monetaryexpansion; a real appreciation of that country’s currency is observed which offsets the rise indomestic goods demand with a reduction in the purchasing power of foreign consumers of thosegoods. Since the regulatory actions of the smafl, domestic economy do not affect the time path ofthe price level (in either country), an increase in the reserve requirement of the domestic countrymoves the nominal exchange rate in its favour as well under a regime of flexible exchange rates.3.8.2 Foreign (Large) Country Reserve RequirementsI now consider the consequences of a reserve requirement imposed by the large, foreign economy.Its banks face the regulatory restriction(85)The assumption that 4 > 4, again, implies that the reserve requirement is binding. Domesticbanks are assumed to be unencumbered by the reserve requirement.2°Banks in the foreign country are now faced with the problem20The analysis would be unaltered if domestic banks faced a binding reserve requirement that is held fixed.164(P.4) max 4in4, + (1 — — ‘r)lnr(,subject to (18)-(20), (85) and non-negativity. The solution to this problem is easily shown toset=and= ir{(1 - 4)/(i -4)] <ir;t> 1, (86)where (13) must continue to hold. (86) shows that a foreign country reserve requirement causesforeign country banks to reduce their holdings of domestic real balances in proportion to therise in their holdings of foreign real balances. The same is true of their bond holdings since(1-- ) = (1-4_ r)[(1-y)/(1-4)] <(1-4- 7r);t 1.The money market clearing conditions in a steady state equilibrium under this regime are nowm’ = dyd+fyfx(1_7ff)/(1_4), (87)m1= (88)and, again, the bond market clears in such an equilibrium if(13) and md+bd+(mf+bf) = yd+xyfhold. Goods market clearing now obtains in the steady state if= md/o.d + (1 — rjydR, (89)= m’/’+(1—7ç—7)i/R. (90)From (86)-(90) the following steady state equilibrium conditions are obtained:2’=(yd+ yfx(l_)/(l_4))/ud+ (1—ir)y’R, (91)= (7çyf)/o.f +yfR(1—4)(1—4 —ir)/(i—4). (92)Again, R is determined in the foreign goods market, (and so is directly affected by the impositionof a reserve requirement in the large country), while the steady state value of x follows from thedomestic goods market clearing condition (91).Straightforward differentiation of (92) yields that=(o— 1)R/(o — -yç)(i—y) > 0.Thus, an increase in the reserve requirement on (large) foreign country banks raises the real interestrate by causing a fall in the real value of bonciholdings which more than offsets the effect for foreigngoods demand of the rise in foreign country currency holdings. Upon differentiating (91), somemanipulation yields21j is easy to show that these conditions have a unique solution with positive nominal interest rates in each countryif o and cr’ are set sufficiently large.165= (xyf /d) --- r)/(l - - 4)/(i-which is ambiguous in sign.An increase in the large foreign country’s reserve requirement reduces the (foreign) demand forreal balances of the (small) domestic country and also, therefore, the foreign country’s demandfor domestic goods. This tends to raise the real exchange rate of the domestic country; a realdepreciation of the domestic currency raises the purchasing power of foreign agents in domesticmarkets. However, the increase in the world real interest rate described above raises the income ofbondholders, raising the domestic demand for domestic goods and so tending to reduce the steadystate real exchange rate of the domestic country; a real appreciation of the domestic country’scurrency will reduce the purchasing power of foreign agents transacting in domestic goods markets.The net effect on the real exchange rate depends on the relative magnitude of these two factors.The same comment, of course, applies to the initial nominal exchange rate under a flexible nominalexchange rate regime.Another consequence of foreign country reserve requirements is that they magnify the impactof monetary policy changes which take place in the large foreign country. In particular, a givenchange in o•f has a larger impact (in absolute value) on both R and x (and hence, under flexibleexchange rates, the initial nominal rate as well) when a binding reserve requirement is imposed.Thus reserve requirements can be employed not only as direct instruments of policy, but can alsobe used to augment the effectiveness of other policy measures.3.8.3 Foreign (Large) Country Exchange ControlsAnother common policy intervention is the imposition of controls on foreign exchange holdings.‘When the domestic country is small its residents hold no foreign currency; hence I consider theconsequences of foreign exchange controls imposed by the large foreign country on its own residents.Such controls here take the form of a requirement that-c r e [O,ir), (93)so that the fraction of the value of total assets that can be held as foreign currency is limited byregulation. The fact that <irs implies that the foreign exchange control is binding on foreignbanks.The problem of these banks is now to maximize166(P.5) 4inr + irinrj + (1 ——ir)lnr(,subject to (18)-(20), (93) and non-negativity. The solution to this problem obviously sets=, and in addition,4t =4[(l—-y)/(1—ir)];t> 1, (94)holds. Thus, foreign exchange controls cause foreign country banks to increase their holdings offoreign real balances in proportion to the reduction in their holdings of domestic country realbalances. Similarly, (l——= (1 — 4 — )[(1 — )/(1 — > (1 — 4 — r)]; t> 1.It is straightforward to verify that - in the presence of the binding exchange control- the goodsmarket clearing conditions in a steady state equilibrium take the form22(yd+yfx)/c,.d+(l_)ydR, (95)=—ir)(1—-y)/(l—r). (96)Differentiating (96),= (1—i)/(l— 4 — ir)(l — > 0.Differentiating (95) then gives= _(xyf /d)/— [o(i—/jc9R/Oy <0.Thus a relaxation of exchange controls in the large foreign country (an increase in ‘y) tends toraise the real interest rate and lower the real exchange rate of the domestic country. Conversely,then, the imposition or tightening of exchange controls on foreign country banks acts to reduce thereal interest rate and raise the real exchange rate of the domestic country.Reserve requirements and exchange controls imposed by a large country are not, then, equallygood instruments for manipulating either real or nominal exchange rates. Notice that both anincrease in reserve requirements and a tightening of exchange controls operate to raise the foreigncountry demand for foreign country real balances (and goods). However, the two policies havedifferent effects on the demand for bonds and so on the real interest rate and bondholder income anddemand for domestic country goods. An increase in reserve requirements acts to reduce the demand22A unique steady state equilibrium with P,i >1 exists if o and o are sufficiently large.167for bonds by foreign banks and so raises the real interest rate. The opposite effect follows from atightening of exchange controls, which operates to raise the demand for bonds by foreign banks andso reduce the equilibrium real interest rate. Thus, increasing the stringency of foreign exchangecontrols unambiguously reduces the demand for domestic country goods (both foreign agents andbondholders now have lower real income) and therefore unambiguously raises the steady stateequilibrium real exchange rate. This real depreciation of the domestic country’s currency offsets thefall in demand by increasing the purchasing power of foreign agents over domestic goods. However,as shown above, reserve requirements engender an ambiguous real exchange rate response. Thisobservation is suggestive of why governments often object to the imposition of exchange controlsby other countries, whereas the manipulation of reserve requirements rarely draws inteniationalcomment.3.9 ConclusionI have developed a two-country model in which spatial separation and limited communicationcreate a role for money and in which stochastic relocation - which acts like a liquidity preferenceshock - creates a role for banks. Money and banking behaviour together play a central role in thedetermination of real and nominal exchange rates in this economy. In particular, spatial separationallows permanent deviations from purchasing power parity to be observed, and monetary factorsare ‘fundamental’ determinants of the steady state equilibrium real exchange rate.The model can account for at least three empirical regularities that were discussed in theintroduction. First, the impact of monetary factors on real exchange rates in this economy isconsistent with evidence supporting the importance of nominal disturbances for real exchange ratefluctuations. Second, the initial impact of monetary policy changes is the same for both real andnominal exchange rates, which is suggestive of why the real and nominal exchange rates appear tomove together during flexible exchange rate regimes. Third, under a fixed exchange rate regime,the impact of monetary factors on the real exchange rate is muted. This is consistent with theobservation that real exchange rates have been less volatile under fixed than under flexible exchangerates over the last thirty years.I also find that under flexible exchange rates there exists a continuum of ‘non-fundamental’dynamical equilibria, so that the real and the nominal exchange rates are indeterminate. Dynamicalequilibria have the property that cross-country differentials in real interest rates are observed, andthat rates of inflation and currency depreciation deviate from what would be expected on the basisof money growth rates alone. Moreover, dynamical equilibria generate real exchange rate paths168that are widely observed in data from developing countries.The existence of a continuum of perfect foresight equilibria under flexible exchange rates issuggestive of possibilities for future investigation. For example, one can consider notions of nominalexchange rate overshooting and undershooting of the following form. Consider a world economyin a steady state equilibrium, if there is an increase in, say, the domestic country’s money growthrate, this will raise the steady state real exchange rate. However, there also exists a continuum ofequilibria in which the initial real exchange rate in the new equilibrium is either above or below itsnew steady state value, and in which the real exchange rate asymptotically converges to the newsteady state from its ‘over’ or ‘under-shot’ initial level. This interpretation seems to be consistentwith at least some empirical evidence on the behaviour of real exchange rates.The model also makes a number of empirical predictions which I intend to pursue in future work.For example, under flexible exchange rates, xy1 / y’ should be positively (negatively) related to 4(o.f) in the steady state (and hence in the ‘long-run’ under non-stationary equilibria). In addition,again under flexible exchange rates - and with reference to steady state equilibria - changes inrates of money growth initially induce an identical proportional change in real and nominal ratesof exchange. The same is not true for changes in real factors, since these influence the initial pricelevels. With respect to non-stationary equilibria, countries whose real exchange rates are rising(failing) should have rates of inflation below (above) their rate of money growth (less the real rateof growth). These are implications of the model that can be easily investigated empirically.While these results have been obtained in a model where a number of simplifying assumptionshave been made, I conjecture that most of them wifi survive generalization. For instance, havingmultiple goods, with some being internationally traded and others not, is a conceptually straightforward extension. So is a consideration of more general utffity functions, or an examination of aworld with non-unitary savings rates. Finally, some introduction of stochastic elements is straightforward- as in Champ, Smith and Williamson (1992) - and I conjecture that some version of all ofmy results will obtain in such extensions.169Figure3.1Timingof Transactionsgoodsmarketbanksmakecashwithdrawalstradeoccuxsportfoliodecisionsoccurfrombanks4,t1’1t+I1youngagentsassettradeyoungagentsmakedepositsoccursarerelocatedxy/yXyt/ydFigure 2Determination of a Steady State Equilibrium1t(52)(5)max (1/ad ‘ia)(5,.)(sr)(SI)Figure 3.3Au II1CrCaSC in a’t171xy(/ydxt*1x:(5Z)— (5)(5,)Figure 3-An increase in a45XIFigure .SDynamical Equilibria172References[1] Abuaf, N. and P. Jorion (1990) ‘Purchasing Power Parity In The Long-Run’ Journal ofFinance, 45: pp.157-74[2] Adler, M. and B. Lehmann (1983) ‘Deviations From Purchasing Power Parity In The Long-Run’ Journal of Finance, 38: pp.1471-1487[3] Abmed, S., B.W. Ickes, P.Wang and B.S. Yoo (1993) ‘International Business Cycles’ AmericanEconomic Review, 83 : pp. 335-359[4] Azariadis, C. 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