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InFER April 2018 Issue No. 1International Finance and Economics ReviewArticleThe United States of NorthAmerica: Should Canada andMexico Dollarize?ResearchThe Role of Theory-MotivatedFundamentals in Long-RunExchange Rate ForecastingMonetary Policy and its Effecton Inequality: The Role ofUnconventional Monetary Policy

From the editor Dear Readers, Welcome to the inaugural issue of the International Finance and Economics Review (InFER), a student-run, peer-reviewed publication of the Master in International Economics and Finance (MIEF). Our decision to create this publication stemmed from a gap we saw in discussions on issues related to international economics and finance. These discussions were either markedly theoretical—with no focused quantitative analysis but rather argued with rhetoric—or far too convoluted— explained with Greek letters and models only understood by other top-level experts. We wanted clear, data-driven answers, articulated for an audience of specialists and non-specialists alike. As the MIEF program is designed to fill the gap between over-simplification and convoluted, we wanted to apply the skills and theories learned in the classroom to better understand the current state of the world. To do this, we have included two main types of writing—articles that condense economic analyses to core conclusions and implications, and research papers that capture the robust analyses exemplified in the capstone project of the MIEF program. Both take full sets of data and put theory to the test. Our end goal is to provide interesting and relevant answers to pertinent international economics and finance questions asked in the field. We also hope to come full circle and have InFER also join the roundtable. We welcome letters, reviews, and follow-up article submissions and hope that the dialogue continues through the issues, just as InFER and MIEF continue through generations of cohorts. This publication is a testament to the accomplishments and abilities of the MIEF students, and we are proud to be a student-run publication, representing both the MIEF program and the Johns Hopkins School of Advanced International Studies (SAIS) at large. This publication would not have been a possibility without the support of the editorial staff, contributing writers, advisors, and faculty. To them we owe a debt of tremendous gratitude. We hope you enjoy this inaugural issue. Sincerely, Jai-Ryung (Jenny) Lee Editor-in-Chief

From the DirectorDear Readers,It is my pleasure to introduce the inaugural issue of the International Financeand Economics Review (InFER). InFER is a student-run, peer reviewed initiativesponsored by the Master of Arts in International Economics and Finance (MIEF)at Johns Hopkins SAIS.MIEF is an 11-month program, designed to refine theoretical and empiricalknowledge of economics and finance. The program prepares students tounderstand advanced economic theories and to master professional quantitativeand econometric skills. Students integrate these advanced theories to developanalytical frameworks to solve practical problems in international trade,development, and finance.As a STEM-designated program, MIEF places an emphasis on quantitative, data-driven analytical skills. The required courses in international finance, trade, andeconometrics allow MIEF students to become well-versed in the fundamentaleconomic topics. Through electives, each MIEF student develops his or herown unique portfolio of economic theories and quantitative methods whichculminates into a capstone project, a robust analysis of a relevant topic in the field.InFER showcases each step of the MIEF process. Articles and essays focus onthe economic theories while the capstone papers highlight the skillset the MIEFprogram builds. The inaugural issue of InFER manifests the MIEF students’abilities to take all the knowledge, tools and skills they have acquired to producedata driven analyses that make inferences to business and policy decisions.I hope you find this first issue intriguing and insightful. We encourage you tocheck back for new issues frequently and to become involved.Best regards,Gordon BodnarMorris W. Offit Professor of International FinanceDirector of the Master of Arts in International Economics and FinanceJohns Hopkins SAIS

TABLE OF CONTENTSInFER $? EDITOR IN CHIEF 3 ARTICLE Jai-Ryung Lee The United States of North America: Should Canada and Mexico Dollarize? ADVISER Jai-Ryung Lee · Yang'ouxiang Yu Kelley J. Kornell 10 BOOK RECOMMENDATIONS SENIOR EDITOR Recommendations from the Experts Paul Tershakovec Jason Fichtner · Pravin Krishna · Jaime Marquez · Mark White EDITORS 12 STUDENT HIGHLIGHT Soyoung Han Spotlight on MIEF Student Christopher Meijia He Huang Seung Wook Jin 14 NEWSLETTER Ghada Kaddoura Survey of MIEF Experiences Private Equity 101 · Go Ape · IMF/World Bank Annual Hajung Kil Meetings · IFC Workshop · Bloomberg Tutorial DESIGNER 18 RESEARCH Yang'ouxiang Yu The Role of Theory-Motivated Fundamentals in Long- Run Exchange Rate Forecasting COVER PICTURE CREDIT Jared Berry Jaime Marquez 71 Monetary Policy and its Effect on Inequality: The Role of OFFICE ADDRESS Unconventional Monetary Policy1717 Massachusetts Avenue NW Meghan Greene · Medha Nair Washington D.C., 20036 EMAIL ADDRESS [email protected] APRIL 2018 | ISSUE 1

© Chu-wen Lin | Dreamstime.com Photo by Martin Falbisoner | CC BY-SA 3.0 Photo from GettyImages The United States of NorthAmerica: Should Canada and Mexico Dollarize? Jai-Ryung Lee & Yang'ouxiang Yu This article is adapted from a submission for the International Money and Banking course taught by Professor Jaime MarquezIn the early 2000s, hyperinflation and irresponsible monetary policy in developing countries motivated global discussion of dollarization as a stabilizing economic tool. While dollarization was provenineffective as a development strategy, there are many arguments for developed countries to dollarize. Forcountries like the United States, Canada, and Mexico (countries close in proximity and economicallyintegrated) a continent-wide currency could be advantageous, since continent-wide currency wouldstreamline trade, travel, and transactions—further integrating the continent. The European Union’sexperiment with the euro provides these same benefits to the Eurozone, proving that dollarizationtoday is not an outlandish concept. With Mexico and Canada dollarized and USD purchasing powerconsequently massively increased, it is difficult to understand from an economic perspective how uniquepictures, colors, and letters on a country’s currency outweigh the benefits of dollarization. 2018 APRIL|InFER 3

ARTICLEWhat is dollarization? dollarize to currencies of countries they already conduct a significant amount of trade with.Dollarization is when a country officially adopts Finally, the government’s monetary credibilityanother country’s currency, completely replacing will improve. Well-integrated countries, such asall domestic currency with this new currency. the United States, Mexico, and Canada, tend toBy virtue of dollarization, a dollarized country have strongly correlated interest rates, in whichrelinquishes independent monetary policy, which countries with as much economic force as theis a fair sacrifice for now-dollarized countries, United States impact surrounding countries’including: Ecuador, East Timor, El Salvador, The monetary policies. Changes in the U.S.’ interestMarshall Islands, Micronesia, Palau, Turks and rates will cause these countries’ rates to trail theCaicos, The British Virgin Islands, and Zimbabwe. United States’. If this is the case, there will be a great amount of unnecessary interest rate volatilityThe Benefits of Dollarization as other countries’ interest rates will eventually move to gravitate towards the stronger country’sFirst, without dollarization, central banks can interest rate. By eliminating governments’ abilityreclaim credibility they may have lost from to print money and simply unifying the interestconsistently using seigniorage to fund government rate policy, dollarization will eliminate the centralspending. Seigniorage is the revenue generated bank’s previous incredibility, now that interestfrom printing currency, specifically the gap rate speculation is dependent simply on the U.S.between the cost of physically printing currency interest rate, rather than how the domestic interestand the value for which it can be exchanged for rate would respond to the speculated U.S. interestgoods and services. By using seigniorage repeatedly, rate.central banks lose credibility to sustainably fundgovernment spending because this action causes The Costs of Dollarizationhigh inflation, high risk premiums, and decreasedvalue of currency in the domestic economy. Under While the central bank’s main role is to ensurea dollarized currency regime, domestic currency monetary stability through several means,would be eliminated, preventing the government dollarization would prevent monetary authoritiesfrom funding government deficits through newly from exercising these interventional powers,printed currency. With no ability to print currency, namely acting as a lender of last resort and settingthe government would be forced to control and the interest rate. In addition to losing thesefund spending through traditional and sustainable functions, the amount of foreign exchange reservesmeans, such as tax increases or budget cuts, which needed to provide short-term stability in times ofwould represent the actions of a more responsible financial distress poses costs to dollarization.and credible government.Second, prior to dollarization, countries would First, as the lender of last resort, the centralsuffer from exchange rate fluctuations that bank stands ready to absorb negative external orcould significantly impact the value of the goods domestic shocks to the economy by providing loanstraded across borders. Once a country dollarizes, to banks facing liquidity issues. This would allowexchange rate-related transaction costs would be the government to provide short-term assistancesignificantly reduced because the new currency to individual banks although unable to respond toshould have lower exchange rate volatility. This vulnerability of the entire banking sector.1 Further,will especially benefit countries who choose to with enough reserves, the government could1 Berg, A., Borensztein, E. (2000, March). Full Dollarization: the pros and cons, IMF Working Paper, WP/00/05.4 InFER|ISSUE 1

The United States of North America: Should Canada and Mexico Dollarize?shift liquidity between strong and weak banks to costs and benefits of dollarization mentionedprevent a bank run in one or few individual banks.2 above. A closer look at Canada and Mexico’s current economic conditions, it appears that forAnother cost of dollarization is the inability of the Canada, the benefits and costs offset each other,central bank to set interest rates. As mentioned the benefits of dollarization seem minimal whileabove, by dollarizing, the monetary authorities the costs seem significant.would no longer be able to independently set itsinterest rates. In general, developing economies, Benefits of Dollarization for Mexico & Canadalike Mexico, adopt a pro-cyclical monetary policy As shown in Figure 1a, both Canada and Mexico’s(raising interest rates during economic expansions) governments have shown minimal fluctuationswhile developed countries, like the United States in government expenditures from 1990 to 2016.and Canada, pursue a counter-cyclical monetary Figure 1b shows the seigniorage to GDP ratiospolicy. Developing countries follow a pro-cyclical from 2010 to 2015, which on average were 0.4%monetary policy because social spending has and 3.5%, respectively.3,4 Furthermore, Mexicopro-cyclical behavior, leaving governments no had adopted a series of strategies to contract fiscalchoice but to spend during bad times yet still face policy and modify its debt structure, buildingpressure to spend to improve the economy durerdinugce thae grerloiawncine gondeoxmteernstailcdebbotsn.5dDmolalarrkizeattioton wreoduuldcedothlitetle to improve eithgood times. fiscal crerdeibliialintyc.e on external debts.5 Dollarization would do little to improve either Canada or Mexico’s fiscalFinally, a dollarized country will no longer be able credibility.to earn interest with the reserves once held by thecentral bank. When a country dollarizes, the central Figure 1a: General Gov. Total Exp.bank will use its foreign reserves to switch out the as Percentage of GDPdomestic currency. Therefore, the foreign reserves, 60%once invested in interest bearing assets, will cease 50%to earn interest as they are now used as currency 40%in circulation. This foregone interest earnings can 30%be a considerable loss to the dollarizing country,which is quantified by calculating the potential 20%interest earned on the current stock of foreign 10% 0%exchange reserves. 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016Cost-Benefit Analysis of Dollarization Canada Mexicofor Mexico & Canada Figure 1b: Flow of Revenue fromThe decision for a common currency across North Seigniorage as a Percentage ofAmerica would depend on whether dollarization Government Revenuebenefits Canada and Mexico, as it relates to the The Bank of Canada: https://www.bankofcanada.ca/rates/. Retrieved 10% October 20, 2017. Banco de Mexico: http://www.banxico.org.mx/estadisticas/statistics.html.2 Berg, A., Borensztein, E. (2000, March). Full Dollarization: the pros8a%nd Retrieved October 20, 2017. 6% 5 Casagrande, Elton E. & Garcia, Renato V. (2011, July). Fiscal policycons, IMF Working Paper, WP/00/05. contradiction: a perspective on Brazil and Mexico. Investigación Económica,3 gross savings + net capital transfers – gross capital formation – acquisiti4o%ns 70 (277), 127-152.– disposals of non-produced, non-financial assets 2%4 International Monetary Fund (2017, October), World Economic Outl0o%ok 1987Database. Retrieved from https://www.imf.org/en/Publications/WEO/ 1994 2001Issues/2017/09/19/world-economic-outlook-october-2017 2008 2015 Mexico Canada Source: General government total2ex0p1e8ndAituPrRe IaLs|pIenrcFeEntRage5of GDP from Wor (2017). Revenue from seigniorage and government revenue from the Bank of Cana

Canada MexicoARTICLE Figure 1b: Flow of Revenue from Seigniorage as a For Canada, the benefits of eliminating exchange Percentage of Government Revenue rate volatility is significant while for Mexico the benefits are minimal.6 According to an analysis10% on exchange rate pass-through of both countries 9% (results shown in Figure 2), exchange rate volatility 8% can impact GDP growth rates by at most 0.62 and 7% 0.14 percentage points for Canada and Mexico 6% respectively.7,8,9 Given that the respective average 5% economic growth rates were 2.2% and 3.1% after 4% the financial crisis, the gains from eliminating the 3% effect of exchange rate volatility on GDP growth 2% would be a considerable benefit for Canada, but a 1% negligible benefit for Mexico. 0%1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 Mexico CanadaSource: General government total expenditure as percentage of GDPfrom World Economic Outlook. (2017). Revenue from seigniorage andgovernment revenue from the Bank of Canada and Banco de Mexico.45 Casagrande, Elton E. & Garcia, Renato V. (2011, July). Fiscal policy contradiction: a perspective on Brazil and Mexico.Investigación Económica, 70 (277), 127-152. Figure 2 Impact of EXR Volatility on GDP Volatility Source: Author’s calculations based on exchange rates and GDP from OECD, elasticity values from Bahmani et al. (2013) and pass-through values from Choudhri E., Hakura D. (2012). 6, 7, 8Decreased interest rate volatility would be a Canada (Extreme Case)noticeable benefit for Mexico but not so muchfor Canada. Since the 1990s, these two countries’ Export elasticity: -0.1 Import elasticity: -2.6interest rates have been consistently lower than EXR pass-through into imports: 0.5the U.S.’ interest rates. The changes in Canada’s EXR pass-through into exports: 0.4short-run and long-run interest rates changedonly by 1.2 and 1.15 times the U.S.’ previous period Impact of EXR volatility on GDP volatility: 0.62%interest rate, while Mexico’s short-run and long- Average GDP growth rate past 10 years: 2.2%run interest rates changed by 2 and 1.46 times.10By dollarizing and adopting the U.S.’ interest rate Mexico (Extreme Case)policy, both Canada and Mexico could eliminateinterest rate volatility, which would be a small Export elasticity: -0.1 Import elasticity: -0.5benefit for Canada but a significant benefit for EXR pass-through into imports: 0.5Mexico. EXR pass-through into exports: 0.4 Impact of EXR volatility on GDP volatility: 0.14% Average GDP growth rate past 10 years: 3.1%6 holding volume of trade, trade elasticities, government spending, 8 OECD, Monthly Monetary and Financial Statistics. Retrieved October 27,investment, and consumption constant 2017, from http://stats.oecd.org/.7 Bahmani M. et al. (2013) Empirical tests of the Marshall‐Lerner condition: a literature review, Journal of Economic Studies, Vol. 40 Issue: 3, pp.411-443,θx= share of exports in GDP θm= share of imports in GDP https://doi.org/10.1108/01443581311283989.εx= price elasticity of exports εm= price elasticity of exports 9 Choudhri E., Hakura D. (2012) The exchange rate pass-through to importπx= pass-through of exchange rates to export prices and export prices: the role of nominal rigidities and currency choice, IMFπm= pass-through of exchange rates to export prices Working Paper, WP/12/226.φ= pass-through of import prices to domestic prices 10 OECD, Monthly Monetary and Financial Statistics. Retrieved Octoberσ(Ei)= volatility in the percent change in the exchange rate 27, 2017, from http://stats.oecd.org/.σ(Yi)= volatility in the percent change in the GDP6 InFER|ISSUE 1

The United States of North America: Should Canada and Mexico Dollarize?Costs of Dollarization for Mexico & Canada liquidity shocks.11For example, in SeptemberWhile if dollarized, neither countries’ central banks 2015, 60% of all Mexican banks had met the 60%can act as a lender of last resort, this will not be a liquidity coverage ratio requirement, most of themWchoilnesiifddeorlalbarliezelods,snteoithCearncaoduanatrnieds’Mceenxtircaol.bLainqkusicdaintyactmaseaetlienngdetrhoef l1a0st0r%esolriqt,uthidisitwyillrenqout ibrema ent to beCcoabsnntasarineddskaessraatnibendsletCMsloacesnoxsainctdodoauCwacaentnredeaddwMabeyaellnxtedihcqoMeuipwIeMxpeiercFdeo.twioLneidwqlliuicteiahdqtsieuttadyinpsdttphreseaidsgtsntiefesicntasfnoctormcnedaducrciontee2dc0ob1ny9ot(mhFeiicgIuaMnrFed 3ilni)q.d1u2iicdaitteydshthoactkbsa.1n0 kFsoirnmexotaomst powlfe,tihtinhesmSteampntdeeemtisbnieggrnt2hif0ei1c1a50n,06t%0%mliqoaucfirdaolilteyMcoreenxqoiucmiarneicmbeaannntksdtohbade met the 60% liquidity coverage ratio requirement, enforced in 2019 (Figure 3).11 Figure 3: Liquidity Coverage Ratio of Banks in Mexico Figure 3: Liquidity Coverage (RinaptieorcoefnBt)anks in Mexico (in percent) Source: IMF Financial System Stability Report13 Source: IMF Financial System Stability Report12 On the contrary, AmericSa’osurcceo:uIMntFerF-cinyacnlicciaall Sy(stthermeeStaebairlitthyqRueapkoerst13 in September and threeOnmtohneectoanrytraryp,oAlimciersica’csocuoludntesri-gcnycifliiccaalnmtloynetaafrfyecptolichieusrcroicualndessi,gHnifaircvaenytl,yIramffeac,taMndexJoicsoe.iCno2r0re17la)tiaonnd hasaenldgoOanldgnxrioonswroioaahMcwatswonaacwotnlaasybwligestrybetsdtgsterrhetrhhstxeerobeehreeeaiosiernsnwalrcstnswacraitohfh(ntaieatotlt(nhta.ietiabedhthnogtebdhCstlihrrtshecinUlirerardeoecoaeaadettain.teebrtgotcdiSeteerodyoreeea.cea,eiotatuanneoilrhtnAwwnnawrthnndcrajhttdcmoartrjehhttioqrrieetoeyhnqiieyCeauylnlnCna’fuarestasaflhstirteaaaklnchMaeaisaMekntoaeaanietiteatao’sfidsenesuaosfedstanaxiteslaaxncnmaieyirtnmhiowccnrischcSeo2oaoueSode2oiaesn0rsntges0rpragh0.rtapihrei0ntreaon8neletota8hradlwedhhmf-as(wtilma(cgiititeataogcibslyhthtohobshaUhcneicneeatwolgcrsaiages.rscrannSUsawronaattwngo.htlwhbn1i.cr4hdwtbiSmeedahootWteeh.htttUrw’sohhttUrseChhthgrnr.eetheraSr.eeriheaelaSneetlo.aetnne,teU.eatewUriahaTirtnaiah.onnyadhuStn.htuSndhTr.aeedpeT1r.rd13arroci4aicbeiWonilcbaWfnilsctUsnfcaeonlfoliiheyncatnrleeh2.acieeuetS2sslci)itldest,l,oa,)ei.eech,o,ciHtnMtnoHanToenhMtiohgsuacnoeeahcreneloUtxcitdrvoctxehvr.eicsbeocr.irdseeocSyreeoCremiyieorg,r.flUne,arleaownIonagewtIlwnr.riitanlarSmfoieaaiaatmsioeit.i,tncbsldsaotinlrwaaoa,lacrenmwne,renwa,olocytiacibntoeklnutibnaoeyphntednecllhnedtortdaeelewttJltyefltnwyhtJdloifaanyhoecejesierhdeoeieonsehcyeeUinxeyytttgsUinipatn.ibMMbttScnoo.bMhoiSyee.2tlnyee.ei2rswe0ftcaxxbw0hfexs1ifiiahemew1aaccefi7hwcseioomt7l)iUosoceeln.)tieaatnonemaC.aMaennStaMtenngdthoddu.titherddulrwreaeaxoaehtrraxrhhrtsieaiwlaychUlicllaelcmsoaoebtso.ltUphsSiuuihuUksio.honi.naseacSnn.walicslSshtin.ycse’rci.tel’eyibhles’yessslaifk1rf)eae,ltcyMetseedxedaxiadcisceiormnbwcuartcaeehsatsrbheeyecaetcfhnoteeutrlnUy2t.0rhSTy0i.’a’ts8bmbsl(eiyoatusn2faec:twatPiaonrrnneyb/.apePCtousoaelrsniecatanil2eddsi0an.i,0sa8aTlsraCtebeoarldresryeloatnthioaensUsimo.Sifl.a’GrmDbouPnsiaennteadsrsyIcnpyfcloalletiicoainsest.he U.S. would not beCorr. w/ US GDP pre-2008 GDP post-2008 Inflation pre-2008 Inflation post-2008Canada Table 12: Pr0e.7/P7o94st 2008 Corre0la.8ti5o5n8s of GDP and0.I7n1f9l4ation 0.8750MCeoxrric. ow/ US GDP pr0e.-32309068 GDP po0st.-82903048 Inflation pr0e.-22900088 Inflation po0st.-12506018Canada Source: Autho0r.’7s7c9a4lculations based0.o8n55d8ata from the W0o.r7ld19B4ank 0.8750Mexico 0.3396 0.8934 0.2908 0.1561Unlike Canada, Mexico will incur aSosuirgcen:iAfiucthaonrt’socaplcpuloatriotunsnbitaysedcoonstdaotaffhroomldthine Wg ofroldreBiagnnk reserves. A popular andpractical measure of the social cost of foreign reserves is the spread between the private sector’s cost of short-Neither Canada nor Mexico will incur a significant opportunity cost of no longer holding foreign reserves.11111102TT0cs46ho.MMM//11Ihh634nos32ee6toooMtTw96er%nnnr2ho)1eons.eeeen0)ffatttW.Woetto1aaaiithWornarrro7fanreayyyrtysGala,taedhaaalsavarMtnnnnBhiDehnsedadddiossngnrePCnutakCCCtgeaom.gmrtDt1paaaoanae7ipppraotint,ytaHniiieoastttD,lFbaaagtMfDuoealll.ninCattawMMMn.dhhkrrC:k.t:neeeaaaeeI.hv:tirrrntrsn1akkktIeetpDvn0geeeersstt,etter-s:t/sssepnyrg/rroaaeaDDdDinravgtnaattaimteeereeoeatpppf.eninawooineaaannaotnrrrrai.ltrntttdear(lmmemMd2niclrg0b3rMeeeieo1anne06nnnnsna,og-ttttkreN..sy..sneortee(((oeasar222Csagvtret000.earyearimR111rnvnUFye466ebeattau,,,eFr.shdrSirJNNne)una.aev.wdnnMeooeT.dwUiduvvdlerOl.aeexo.eirSmbmiccuanyto.yos)bblc.biFduenefreiCnorerrrtly))aoaae2r..n7nesrsbcMM,aeeiei2gaid.s0llee1nailtxx1S8s7wyiiFrT.rccsoaooteiehentnsFFmreaeelesniiyrrnnS,ce2vtaai0baaf.nneb.o3locc2siiiSl3rtiaa2taeyh%lly%sr,SStAeCetyymhasssos2antteeeenf%SsdmmsatamGa,nd2SSbe3Dnaa.itt8laat%liytabbP9(yRsiin%,lliAiiewdsttop2yy,sorhiMsAA0rnrei4tesld1ssNsee%sssmixpee8ocMsse,i.eassnc1mmcttA6teohet/eex(’iPnn3eRsvt6ittchR1eeao)((oal.pRRnIpyWtoLawee.p1Mralpp|5ystooooh,sINer1uinrrin6txsttlugodFiNNtcn.oEloniooot,R..ysDe.C7.:16/361). Washington, D.C.: International Monetary Fund.13 The World Bank Databank: https://data.worldbank.org. Retrieved October 27, 2017.

ARTICLENeither Canada nor Mexico will incur a significant GDP while Mexico would lose 0.66% of GDP.17opportunity cost of no longer holding foreign However, given increases in the U.S. interestreserves. The 2017 average of the 10-year and 30- rates, both Canada and Mexico’s opportunityyear U.S. Treasury bill were 2.33% and 2.89%, cost of interest rate earnings on foreign reservesrespectively.15,16 Therefore, assuming the average will increase.18 Therefore, the analysis indicate thatinterest rate earned by foreign reserves are 2%, 3%, Mexico stands to lose much more than Canada,orarte4%eash,rtnatarhnidnedgtsoastnoCoavalloeynrssaleiosdmoaskhuw.cohowumsldothrleaottshetahinseComnanloyasdt0a.i,2nw2t%ietrheosCtfanawMdaiet’shxicCcooas’tnssacadotaspt’ssrechsoaesrntdts baet ipnrgenseengltigbiebilne ganndegMliegxibicloe’asncdosts to overlook. Figure 4: Cost of Foreign Reserves as Percentage of GDP Mexico (green lines) and Canada (red lines) 0.70% 2% 0.60% 3% 0.50% 4% 0.40% 2% 0.30% 3% 0.20% 4% 0.10% 0.00% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Source: AuSotuhrocer:’Asucthaolcr’us claaltciuolantisonbs absaseedd oonntottaol treaslerrveessemrivnuessgomldinanudsGgDoPldfroamntdheGWDorlPd Bfarnok.m17 the World Bank (2006).17 Is Dollarization necessary? DsuomldIbl,noeaCnlslraeuaifnrzmiitazas,dintCaaignoaw,dnntaohsdeuingalrnedweicsfioiuneculactslsnudstfrioacnvrorcesyuCrtyr?sanvloieatfrdtyldaeolaibltrlteaelnreiinezbfaceitotnisonenacfinl.tusWdsaicvhnoeidlseatcsstohtosheftesadnbooaefllnldyaesorfiilsizltasacrltiaeiznoaardntliyocwnoahdswtvislihesaieMlrese aMeogxfaeifcixsnoeicsttwtoiMnowgueo. xlTudilchdioenifncprucoourtmervnvetreiyaryl littleIs forInlittle bsemneafliltbseannedfitssigannidficlaacnktocfostigsnoifidcaonlltacroizsatstisoene.mWtohible tihnseuafnfiacliyensitstcolewaralryraandtvaisreescaogmaimnestndMateixoincofofrroCmanadadollaritzoinrge,litnhqeuirsehsuitlstsmfonr eCtaarnyapdoaliacryecionmcopnlectleulys,ivthe earsebthyesubbenjeecftitnsgaintsdelcf otoststhaeremoefrfcsyetotfinthg.e TUhneitepdotSetnatteisa’loUffoopnrrtiiCstomeandbmacnasnoeSlaaolauldtovnlanbyaawettseiertilt:naysasor’’beasymfrbligeeatoooulstivvtonnehaeeq,naorttnudrcahimoirtesyylurhea.enancIiukitnttsrstfygoihanme’ifolssnurotsgeoiifnortgfaycviencl.ute,iiaIrrefnnibrnnocytmamgcnrpeoeeantoanjuoelscntiorrcotfanyreaslyct,ifclsonsoothnsroomeooeeccumipumotlhdliurecebtnctrdeoomteclrnycoybas,luiijesntdonhheeritone.rreyrTusdceutolhobodfnelyflridacocerosomifiueznlolnabairscteritjidei,odzctbeneeotra,ciunsladwiensgnodlaieelsirlost.arsssTnareuinalhztmlfhtalemettoraoietorahferrntoeesihzucrrueeeolotnd,msmpblieotnameisfosrsgenectrahdnyseleldaoaotocvanefotatrihttisolhhdtae-nebeerbtleaenilteofiatresults of the cost-benefit analysis above, there is insufficient reason for either country to dollarize, as issummarized in greater detail below:15 Macrotrends. Retrieved April, 2018 from http://www.macrotrends.net/2521/30-year-treasury-bond-rate-yield-chart16 10-Year Treasury Constant Maturity Rate. Retrieved April, 2018 from https://fred.stlouisfed.org/series/DGS10.17 The World Bank Databank: https://data.worldbank.org. Retrieved October 27, 2017.18 Federal Reserve Press Release. (2018 March). The statement of FOMC March 2018 meeting, pp.1. Retrieved from https://www.federalreserve.gov/monetarypolicy/fomccalendars.htm8 InFER|ISSUE 1

The United States of North America: Should Canada and Mexico Dollarize?Mexico ISSUANCE OF CURRENCY AND FISCAL BALANCE Seigniorage CanadaMexico has a relatively low currency replacement Canada has a lower start-up currency replacementimplementation cost and seigniorage earnings, implementation cost and seigniorage earnings thanindicating that it would have little to gain from Mexico.dollarization.Mexico Roles of the Central Bank CanadaMexico's financial sector passes the liquidity stress Canada's financial sector can withstand potentialtests with flying colors, implying that there is little bank runs, thus implying that there is little to loseto lose from the central bank no longer being able from the central bank no longer being able to be ato be a lender of last resort. lender of last resort. Government Credibility in Fiscal PolicyMexico CanadaThe government of Mexico is not as credible as Though Canada’s government expenditures andCanada's, but its debt-to-GDP ratio and debt-to-GDP ratio have been slightly over those ofgovernment deficit do not imply a trend of fiscal Mexico, these indicators have remained stable forindiscipline. Dollarization also does not necessarily decades. Dollarization would not mean an obviousentail fiscal discipline. improvement in fiscal discipline for Canada. FOREIGN EXCHANGE VOLATILITY AND MONETARY POLICY Foreign Exchange ReservesMexico CanadaAfter dollarization, Mexico would use its foreign With relatively small amount of foreign reserves,reserves to substitute for domestic currency, which Canada has a little to lose if dollarized but the costswould be a considerable loss in foregone interest might go up as the U.S. keeps raising interest rates.income. Bilateral TradeMexico CanadaIf the trade pattern with the U.S. remains, thechange in exchange rate would not have a large Due to the large elasticities of price, exchange rateimpact on Mexico's GDP growth. It is also fluctuation would influence the GDP growth to aimportant to consider Mexico’s exchange rate is considerable extent. Dollarization would helpmore volatile than Canada. eliminate this negative effect on the economy. Interest Rates and Monetary PolicyMexico CanadaMexico suffers from exchange risk volatility, which Canada's exchange rate has remained stable over theimplies that sovereign risk would decrease if the past couple decades and boasts the highestcountry dollarized. However, examples of other sovereign credit rating since 2002. However, as itsdollarized countries show that dollarization does interest rate also rise, the costs of dollarization willnot necessarily guarantee lower cost of credit. increase. APRIL 2018|InFER 9

Book Recommendations Clashing Over Commerce: A History of US Trade Policy by Douglas A. Irwin University of Chicago Press; 1 edition (November 29, 2017) “This stylish and immensely readable book tells us the history of American trade policy, tracing its path from colonial times, through its support for the multilateral trade order in the form of the GATT-WTO, to the protectionist challenges of the day. At once entertaining and enlightening, this is a must-read for anyone interested in trade policy or the evolution of world economy more generally.” - Pravin Krishna Chung Ju Yung Distinguished Professor of International Economics and Business, Johns Hopkins SAIS The World Trade System: Trends and Challenges by Jagdish Bhagwati, Pravin Krishna and Arvind Panagariya The MIT Press; 1 edition (December 16, 2016) “A remarkable group of trade specialists and scholars, including the editors themselves, have produced a fine volume showing that there is much value to be had in a well-functioning trade system and much to lose if it is allowed to deteriorate. The contributions in this excellent book are particularly valuable at a time of senseless protectionist threats.” - Ernesto Zedillo Director, Yale Center for the Study of Globalization Former President of Mexico QED: The Strange Theory of Light and Matter by Richard P. Feynman Princeton University Press; With a New introduction by A. Zee edition (October 26, 2014) “The book introduces the layman (me) to quantum electrodynamics. The exposition rests on “Feynman diagrams” which are compact representations of the paths traveled by particles. For me, the book underscores that the pursuit of a seemingly silly question is what keeps one alive – just for the pleasure of finding out. A key concept in this field is the path integral: that the direction a particle follows recognizes all the paths that are available to that particle ex- ante. (See an illustration inhttps://en.wikipedia.org/wiki/File:Path_integral_ example.webm.)” - Jaime Marquez Associate Director of MIEF Program, Johns Hopkins SAIS10 InFER|ISSUE 1

Thinking, Fast and Slowby Daniel KahnemanFarrar, Straus and Giroux; 1 edition (October 25, 2011)“I find behavioral economics quite fascinating. This book introduces manyfoundational ideas in the field in a very accessible way. The mix of anecdote andresearch makes the work both accurate and clear.” - Mark White Associate Practitioner-in-Residence Johns Hopkins SAISRaising the Floor: How a Universal Basic Income CanRenew Our Economy and Rebuild the American Dreamby Andy SternsPublic Affairs (June 14, 2016)In Our Hands : A Plan To Replace The Welfare Stateby Charles MurrayAei Press (February 21, 2006)Has the Time Come for Universal Basic Income?“There is a growing consensus in the United States that the current slate ofwelfare programs are unable to meet the increasing challenges of the nation’sdiverse population and changing nature of employment. Scholars on both theright and left of the political spectrum are considering the idea of a UniversalBasic Income (UBI), a cash payment every citizen. Some proposals wouldreplace all forms of government assistance with a single UBI payment, whileothers would add UBI to the existing slate of entitlement and welfare programs.Two recent books consider the concept of a UBI from different politicalspectrums. Noted conservative thinker Charles Murray, “In Our Hands: A Planto Replace the Welfare State,” seeks to create a UBI payment as an alternative tothe current welfare state. Andy Stern, former President of the Service EmployeesInternational Union (SEIU), sees a future in which automation and driverlessvehicles lead to mass unemployment and further income inequality. In “Raisingthe Floor: How a Universal Basic Income Can Renew Our Economy andRebuild the American Dream,” Stern argues for a UBI system, but maintainssome existing programs. Both Murray and Stern discuss whether there is a needfor a UBI, whether it’s practical, affordable and politically possible. - Jason J. Fichtner Senior Research Fellow, Mercatus Center at George Mason University APRIL 2018|InFER 11

STUDENT HIGHLIGHT MIEF Class of 2018 Christopher Mejia ···················· Briefly introduce yourself and summarize your work and academic experience before coming to SAIS. My name is Christopher Mejia. I am from Brooklyn, NY and lived in Guatemala for eight years. Prior to coming to SAIS, I worked at Bank of America Merrill Lynch, for three years, as a credit analyst, covering Latin American financial institutions. Before working full-time I attended Pace University in New York, where I majored in Economics. QWhat internships have you completed while at SAIS?A During the Fall semester, I interned at the U.S Department of Commerce in the International Trade Administration of the Office of Trade Negotiations and Analysis. In this unit, I supported the team with various tasks related to trade data and understanding trade patterns in the services sector. QWhat skills that you learned in the MIEF program did youA use as part of your internship? When collecting trade data, the unit on Balance of Payments (conversion between BPM5 and BPM6) from our International Finance class was useful. Econometrics also proved useful, seeing as I built a cross-sectional model that aimed to explain U.S exports of services to the world. Lastly, while our International Trade class was more theoretical, it was exciting to understand the practical aspects of international trade applied in my internship. 12 InFER|ISSUE 1

Q Q In your experience, what is Describe MIEF in one word.A Athe main difference between working in the private and public I would describe MIEF as rewarding. The program has sectors? challenged me both academically and professionally. One of the aspects that immediately stoodout to me was that the private sector, The coursework, while complex, is very applicableespecially in finance, is a lot more fast paced. to the real world. For example, in courses such asNonetheless,thereweretimeswhenIfeltthat Econometrics, we learned various econometric methodsboth were equally demanding. An exciting which are being used in current economic research,aspect about the public sector was that I such as those found in economist Acemoglu’s work.could find articles on the Economist and the Due to the length of the program, time is a considerableWall Street Journal related to trade issues constraint, so MIEF tests your capacity to work underwhich our office was working on. It was also pressure and perform to the best of your ability. Overall,interesting to work in International Trade the growth I have gained through MIEF has made theduring President Trump’s administration. challenge worth it. Private Equity 101 Seminar Kris Huang NovemberOn Nov.7th, Professor Roger Leeds delivered a seminar to the MIEF 2017-2018 7th cohort on Private Equity (PE), giving a brief overview of the industry as awhole. This overview highlighted the different types of PE organizations; the jobmarket within the PE industry; and the experience necessary for succeeding in PE.Professor Leeds emphasized that the PE industry is exceptionally competitive butthat the SAIS curriculum has prepared a number of SAIS alumni well for dynamicroles in PE. To start, Professor Leeds discussed a fundamental difference betweenPE in emerging and developed markets: the underperformance of PE in emergingmarkets could be attributed to the lack of long term capital and employees withthe required skill sets. While the majority of PE job market is saturated due to therelatively small size of the industry, the need for employees with a strong skill setin emerging market PE offers potential employment opportunities. In conclusion,Professor Leeds mentioned that despite the competitive nature of the industry, anumber of SAIS alumni are now professionals in the PE industry. For the MIEF2017-2018 cohort, this seminar provided an indispensable opportunity to becomemore familiar with the PE industry and learn from a well-regarded member ofindustry. APRIL 2018|InFER 13

NEWS LETTER© Jaime Marquez | Jaimemarquez.comPhoto by Kelley J. Kornell14 InFER|ISSUE 1

Photo by Kelley J. Kornell Go Ape! Team Building Ruidi Wang September 23rdAfter completing an intensive Summer term, the MIEF 2017-2018 cohort celebrated the end of the first term with intensive team-building andbonding activities. Over two-thirds of the cohort and SAIS faculty participatedin these activities as part of a ropes course called Go Ape! The ropes course,comprised of ladders, ledges, zip lines, swings, and adjoining ropes, allowed usthe opportunity to overcome fears as a group, laying the foundation for a morecohesive cohort. Professor Marquez documented this team-building exercise inmany albums of photographs and videos. After completing the ropes course,everyone received completion certificates as souvenirs marking the beginning ofa successful MIEF year. APRIL 2018|InFER 15

NEWS LETTER Seminar IMF/World Bank Annual OctoberMeetings9TH-15TH Cathy Kil In October 2017, the MIEF 2017-2018 cohort participated in the 2017 IMF-World Bank Annual Meetings, including “Macro-Trade-Development Linkages” featured Paul Krugman from Princeton University, Keyu Jin from the London School of Economics, and Dani Rodrik from Harvard University. This forum explored issues concerning trade barriers, currency manipulation, and non-tariff barriers related to e-commerce, touching on a number of issues discussed in MIEF courses. As a whole, the speakers emphasized that as trade structure changes, trade policy should change with it too. By hearing and participating in discourse with world-renowned economists on the future trade policy, the MIEF 2017-2018 cohort developed a new understanding of trade policy scenarios to investigate in future research.16 InFER|ISSUE 1

IFC Workshop Training Jason Jin October 31stOn October 31, 2017, the World Photo by Kelley J. Kornell Bank Group invited members ofthe MIEF 2017-2018 cohort to attendtraining on Disaster Relief Finance andInsurance. This training included twoscenarios simulating the financial policyproblems that arise following a naturaldisaster. Within each of these scenarios,students played finance ministers left todecide how to allocate financial resourcesappropriately for rebuilding andrestructuring. This experience providedan indispensable opportunity for MIEFstudents to see firsthand what financialpolicy instruments are used in the realworld to avert major negative economiceffect on a country following a naturaldisaster.Bloomberg Training Tutorial November Cathy Kil 14thIn November 2017, the MIEF 2017- Photo from Bloomberg.com 2018 cohort visited the BloombergD.C. office for the Bloomberg Terminaltutorial, introducing different terminalfunctions calling numerous countryeconomic and financial databases to thestudents. With growing demand fordata for various research projects, thisexperience provided a new resource forthe MIEF 2017-2018 cohort to utilize.Following this training, many members ofthe cohort plan to take Bloomberg MarketConcepts certification course as well. APRIL 2018|InFER 17

RESEARCHThe Role of Theory-MotivatedFundamentals in Long-RunExchange Rate ForecastingJared BerryAdvisor: Professor Jaime Marquez (Johns Hopkins SAIS)The Research Paper is submitted to fulfill the capstone requirement for theMaster of Arts in International Economics and Finance degreeJohns Hopkins SAISWashington, D.C.1. Introduction Exchange rate forecasting is one of the most contentious and widely disputed topics in the moderneconomics literature. Following largely from the seminal work of Meese and Rogoff (1983), analysis hasfound, time and time again, that the random walk or random walk with drift model regularlyoutperforms “structural models” which incorporate actual realized observations into the developmentof forecasts. By construction, however, the forecasts based on the random walk implicitly assume thatthe only information that can be used for a forecast at any future time horizon is the realization of thevariable of interest today. Accordingly, shocks accumulate at random to construct a series that serves asthe counterpart random walk series for forecast evaluation. The predominant argument that the random walk outperforms models with structuralcomponents, while convincing at shorter time-horizons, becomes increasingly suspect as that time-horizon increases beyond the initial few months. For instance, when attempting to construct forecastsat horizons of greater than one year, or with displacements of many years, it seems ill-advised to rely onlyon the current realization of the exchange rate—for instance, in the valuation of a multinationalcorporate project involving foreign cashflows. The inherent impracticality of this approach arises largelybecause it ignores the possible role broader theoretical or structural elements play in exchange ratedetermination when looking at a longer time frame. In this spirit, there are a number of well-established structural factors that, in theory, should play acrucial role in exchange rate determination, such as money supply, economic growth, interest rates, andinflation. Moreover, it is sensible to assume that these effects would be especially pronounced over18 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecastinglonger-time horizons (particularly those related to prices and growth), as it may take more time for themto be reflected in exchange rates which fluctuate on a moment-by-moment basis. A theory-based modelmight incorporate these determinants, but, as Meese and Rogoff deduce, theory based structural modelsperform poorly against the random walk in the short-run in terms of estimate error. As such, I posit thatthe reason these theory-based structural models perform so poorly relative to the random walk,particularly in the context of Meese and Rogoff, is largely a function of the time horizon. I seek to address these tensions in this analysis by employing a well-established hybrid model forexchange rate forecasting from Mark (1995) that incorporates both structural elements and time-serieselements (i.e. realized exchange rate data). The motivation for the specification of the Mark model is suchthat exchange rates are anchored to some fundamental value and, by extension, deviations from afundamental value ought to be self-correcting. Accordingly, a sufficiently long-run time horizon isnecessary to observe this self-correction to the core, fundamental value. By employing this uniquespecification, I capture not only the importance of previous period’s exchange rate (per the methodologythat underlies the random walk), but the impact of the structural components indicated above that arelikely to have an impact on these rates in the long-run. Further, this approach allows for a parsing out ofthe relative contributions of both the random walk and monetary factors over time, and is naturallybefitting of a graphical analysis that maps these contributions over a given time-horizon. Given the importance of the time-horizon in this context, I employ two different frequencies ofdata in this analysis from two different sources. In the spirit of the Mark (1995) analysis, and more directlyin accordance with the work done in Meese Rogoff (1983) and other work that relies on the use ofsimilarly specified hybrid models, I apply the model to monthly exchange rate and price data with direct,k-step ahead forecasts of exchange rates from 1 to 60 months (covering a span of 1 to 5 years) for fourcurrencies: the British Pound Sterling, Canadian Dollar, Japanese Yen, and Swiss Franc. While this servesto bolster the external validity of this analysis and frame it within the existing literature with morecurrent data, this analysis is novel in its use of truly long-term data at truly long-run time-horizons. To my knowledge, little has been done in the existing literature to apply this framework to horizonsbeyond 16 quarters (the scope of the Mark (1995) analysis). Intuition would suggest that the value of thefundamental is most pronounced at longer-horizons, and, as such, seek to contribute to the existingliterature by applying the model to data from the Bank of England’s “Three Centuries MacroeconomicDataset” (2016). The dataset, which contains (as the title suggests) almost three centuries of observationsof bilateral exchange rates, price data, etc., provides a unique opportunity to not only assess the degreeto which structural components can motivate existing exchange rate forecasting frameworks in long-runtime-horizons, but to assess the degree to which the structural component is invariant to institutionalconsiderations. The Bank of England dataset spans approximately two centuries of observations of bilateral dollar-pound exchange rates and price data for use in this analysis, which offers a rich opportunity for ananalysis of historical periods (chiefly the Gold Standard, Bretton Woods, and current-float periods) andthe extent these periods have bearing on the fundamental. So, the scope of the analysis moves beyondexchange rate forecasting in the sense it has been applied to post-Bretton Woods quarterly or monthly APRIL 2018|InFER 19

RESEARCHdata and exploits available data to provide a richer analysis of theory versus the role of institutions and abroader analysis of historical periods in this context. As stated, in this analysis, I seek to determine the economic role of theory versus data (i.e. therandom walk) at medium- and long-run exchange rate forecasting horizons and the degree to whichincorporating a structural, theory-motivated component can improve upon the random walk. I assessthe robustness of these results by conducting the analysis with two different frequencies of exchange rateand price data (annual and monthly) and with additional currencies in accordance with the existing workof Mark (1995). Second, regarding the exchange rate data at the annual frequency from the Bank ofEngland database, I seek to determine the degree to which the fundamental rate vis-à-vis theory issensitive to institutional considerations. Third, after determining the additional forecasting value thismodel can provide to the random walk through a number of evaluation metrics, I seek to determine towhat extent the forecasts developed in the hybrid model can improve on or be improved by forwardexchange rates, thereby connecting the findings of the results in this analysis to actionable behavior inthe forward markets. Section two will provide a brief review of the literature surrounding exchange rate forecasting,particularly related to the work of the hybrid model used in this analysis and other work related moretangibly to medium- and long-term exchange rate forecasting that employs the use of structural variables.Section three provides a detailed description of the data utilized in the long-term forecasting componentsof the analysis, related to the Bank of England data that spans two-centuries of annual observations.Section four provides a discussion of the time-series properties of the series I utilize in this analysis.Specifically, I am concerned with the stationarity of the processes and the cointegrating relationshipbetween both the exchange rate and structural component which serves as a theoretical counterpart forthe role of an underlying fundamental value for exchange rate movements. Section five recounts themethodology of the Mark (1995) model and how it is adapted for use in these data and this analysis,section six will include results and subsequent discussion, and section 7 will conclude, addressinglimitations of the current analysis and offer suggested next-steps for future research on the subject.2. Literature Review The work of Meese and Rogoff (1983) and Mark (1995) serve as the predominant theoreticalfoundations upon which this analysis expounds. Meese Rogoff (1983) serves as the predominant workon exchange rate forecasting that suggests a random walk outperforms several structural models offorecast error in the 1-12-month time-horizon. Using mean error, mean absolute error and root meansquare error in 1, 3,6 and 12 step-ahead forecasts, the random walk regularly outperforms structuralmodels in terms of forecasting error in all time horizons. The authors declare that they, “find that arandom walk model would have predicted major-country exchange rates during the recent floating-rateperiod as well as any of our candidate models… the structural models fail to improve on the random walkin spite of the fact that we base their forecasts on actual realized values of future explanatory variables”(3). Further, the results suggest that one possible explanation for the poor out-of-sample fit areunderlying shocks that cannot be adequately forecasted using data that does not take these into account.20 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting Per the discussion above, these results seem suspect beyond the 12-month time horizon—to believethat the random walk will continue to regularly outperform the theory-based models is to say that theonly information of value of long-horizon forecasting is the value of the exchange rate today and somefundamental understanding of the shocks that accumulate in the construction of the series. Further, onpotential weakness of using the theory-based models in isolation could be just that—in isolation, themodels are not accounting for the more potentially volatile shocks to exchange rates. A model thataccounts for both elements, therefore, could be a useful forecasting tool. This serves as the intuitive basis for the Mark (1995) analysis that serves as the empirical basis for theanalysis at hand. This work approaches the question of exchange rate forecasting as an exercise inadjusting to deviations from a “fundamental value,” (i.e. in this case, the relative ration between moneysupply and GDP between domestic and foreign counterparts, but, more succinctly, purchasing powerparity, a widely touted “structural” model variable) in the long-run. The author postulates that, if thereis some fundamental value, deviations in the exchange rate from the fundamental ought to be self-correcting in the long-run, and, more importantly, finds that “long-horizon changes in the log nominalexchange rates contain an economically significant predictable component” (Mark, 1995, 201). Thisanalysis, and the analysis of Mark, seek to exploit this economically significant predictable componentwith the use of structural components that could feasibly serve as “fundamentals” in the long-run. As such, the model postulated by Mark serves as the empirical basis for this analysis—it establishesa “hybrid model” that incorporates both a long-run fundamental component, substantiated with theuse of theory, and a time-series component that captures the shorter-term fluctuations in the exchangerate, i.e. a lagged exchange rate component which directly incorporates those shocks indicated in MeeseRogoff (1983). By including both, the model is not solely an autoregressive time-series model, nor is it apure theory model. By including both, further, I hope to improve upon the use of the two types ofmodels in isolation, recognizing the power of the random walk/univariate time-series regressions in theshort- and medium-term. The use of the theory component, therefore, ought to be motivated by self-correcting behavior of exchange rates from a fundamental like purchasing power parity. I posit that theestablishment of some cointegrating relationship between the two serves as adequate evidence to justifythe use of a given structural variable as a corresponding fundamental for the exchange rate series inquestion. In accordance with the evaluation metrics of Meese Rogoff (1983), the author utilizes RMSE,but extends the analysis to incorporate the trajectory of R2 values and constructs Diebold-Mariano teststo assess the predictive power between models. The work of Lothian and Taylor (1991, 1996) serve as a further theoretical precedent for the use ofthe long-run data samples to motivate a long-run mean-reverting, fundamental relationship in exchangerates. Using bilateral data spanning two-centuries in much the same way they are utilized in this analysis,the authors find that there is “strong evidence of mean-reverting real exchange rate behavior” (Lothianand Taylor, 1996, 488), which, while not directly related to the use of fundamentals in the hybrid model APRIL 2018|InFER 21

RESEARCHcontext, lends credibility to the “self-correcting” (488) behavior observed in the Mark (1995) analysisregarding long-run exchange rate forecasting. Furthermore, the authors find that “simple, stationary,autoregressive models estimated on pre-float data, easily outperform nonstationary real exchange ratemodels” (488). The results from both the 1996 and 1991 analyses cover similar time-horizons for twodifferent currencies, notably the pound sterling and Japanese Yen, both of which are utilized in thisanalysis. Broadly, the work serves as a precedent for analyses seeking to improve upon a weakness in existingliterature related to small-sample issues—long-term horizons provide a better measure of non-stationarity, the trade-off being the inclusion of wide-ranging institutional considerations. Moretangibly, (in the context of this analysis), an extension of the 1996 work entitled “Two Hundred Yearsof Sterling Exchange Rates and the Current Float” (Lothian and Taylor, n.d.), finds “that real exchangerates revert to equilibrium values over the long run and correspondingly that nominal exchange ratesand relative price levels converge” (1). This analysis seeks to directly expound upon this finding byLothian and Taylor, using a similar dataset and the application of the Mark (1995) hybrid model whichincorporates both elements. Further, the authors acknowledge the potential issues surrounding out-of-sample forecasting when incorporating dramatic shocks implicit in changing political and economicinstitutions, further motivating an approach that splits the sample into institutional segments and thenconducts the analysis on those in addition to the broader 200-year sample. The original Mark (1995) work defers to the use of the relative (domestic to foreign) ratio of moneysupply/GDP for the “structural” component of the hybrid model. While this is a direct corollary for theuse of purchasing power parity (i.e., the relative price ratio), in this analysis, there is a wider literaturesubstantiating the use of a number of structural variables in the context of this analysis, includingpurchasing power parity as I have defined it. Engel et al. (2012) extend the logic advanced by Mark (1995)by constructing “factors from a cross section of exchange rates and [using] the idiosyncratic deviationsfrom the factors to forecast” (2), instead seeking to exploit the deviations from the fundamental rationaleon a panel of bilateral USD exchange rates with several fundamentals, including Taylor rule factors,monetary models and purchasing power parity. The authors use a similarly specified hybrid model and more broadly define the “fundamental” asa central tendency that can be composed of a number of structural values. In doing so, the authors againfind that this approach improves forecasts in the long-horizon in a 1999-2007 time-series sample.Similarly, Molodtsova and Papell (2009) conduct forecast evaluations of short-term forecasts ofexchange rates (bilateral USD) using structural variables from Taylor rule equations, and find that theyimprove on interest rate, PPP and monetary models. This work also serves as an extension of the Mark(1995) approach, using a similar specification, but again, limits the analysis to the post-Bretton Woodsfloat time horizon. The work of Simpson and Grossmann (2011 and 2010), Marsh and MacDonald (1997)and Taylor (2002), all lend further credibility to not only the use of fundamentals in long-run exchange22 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecastingrate forecasting, but do so in the particular context of purchasing power parity, and find that, withparticular specifications that rely on the use of purchasing power parity, such models can outperformthe random walk even at time-horizons of only 1-month displacement. One other possible explanation for the predominance of the random walk in existing exchange rateforecasting literature is the use of conventional evaluation metrics. Engel, Mark, and West (2007), offersalternatives to the existing criteria of outperforming the random walk as the benchmark for determiningthe forecasting power of an alternative model in the context of this particular framework, and a vastliterature exists to support the use of profitability/utility measures (Leitch and Tanner (1991); Abhyankar,Sarno and Valente (2005); Boothe and Glassman (1987); West, Edison and Cho (1993); and Diebold(2006) to name a few). Perhaps more directly related to the analysis at hand, Christofferson and Diebold(1998) recognize that mean squared error estimates do not account for the improvement provided bycointegrating relationships as I will establish. In this spirit, Burns and Moosa (2012) propose alternative measures that focus more directly on thedirection of error, rather than the magnitude. Rather than focusing specifically on these alternativemeasures, I will defer to the existing metrics utilized in Meese and Rogoff (1983) and Mark (1995).Utilizing existing metrics is useful for framing the analysis in the context of the existing literature, whilethe reporting of beta coefficients for the structural component, along with R2 values more directlyaccount for the rule of theory in the context of the hybrid model beyond the evaluation metrics. Asstated above, to more directly relate the results of this analysis in realistic markets, I apply the forecaststo forward markets conducting forecast encompassing regressions to see to what extent patterns in theforward market are useful for these forecasts and vice versa. This is in line with existing literatureregarding forward rates and their ability to predict future spot rates from Simpson and Grossman (2014,2015).3. Data DescriptionTo motivate the use of purchasing power parity as a structural variable for use in the hybrid modelspecification for exchange rate forecasting, plots of the data are helpful for illustrative purposes. This isparticularly important in the context of the annual data from the Bank of England dataset, whichcontains annual bilateral dollar-sterling exchange rate and price data for both the UK and the US forover 150 years of observations, with a full sample of annual data points from 1861 through 2015.Recognizing that the data covers fundamentally different, economic institutions/climates, it isappropriate to attend briefly to the character of these periods and the impact they might have on thelong-run exchange rate forecasting model to be specified below. For completeness, I first attend to plotsof monthly bilateral exchange rates for the dollar against the pound sterling, Japanese yen, Swiss franc,and Canadian dollar. APRIL 2018|InFER 23

24 InFER|ISSUE 1 Jan-71 Figure 2: Monthly Exchange Rate and PPP – USD/Swiss Franc Jan-71 RESEARCH May-72 May-72 Log ($/₣) Sep-73 0.4 Log ($/$) Sep-73 Figure 1: Monthly Exchange Rate and PPP – USD/Canadian Dollar Jan-75 0.2 Jan-75 Log (P/P*) May-76 Log (P/P*) May-76 0.1 Sep-77 0 Sep-77 0 Jan-79 -0.2 Jan-79 May-80 -0.4 May-80 -0.1 Sep-81 -0.6 Sep-81 -0.2 Jan-83 -0.8 Jan-83 -0.3 May-84 May-84 -0.4 Sep-85 -1 Sep-85-0.5 Jan-87 -1.2 Jan-87 May-88 -1.4 May-88 Sep-89-1.6 Sep-89 Jan-91 Jan-91 May-92 May-92 Sep-93 Sep-93 Jan-95 Jan-95 May-96 May-96 Sep-97 Sep-97 Jan-99 Jan-99 May-00 May-00 Sep-01 Sep-01 Jan-03 Jan-03 May-04 May-04 Sep-05 Sep-05 Jan-07 Jan-07 May-08 May-08 Sep-09 Sep-09 Jan-11 Jan-11 May-12 May-12 Sep-13 Sep-13 Jan-15 Jan-15

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting Figure 3: Monthly Exchange Rate and PPP – USD/Japanese Yen0 4.5 4.4-1 4.3-2 4.2 4.1-3 4 3.9-4 3.8-5 3.7 3.6-6 3.5Jan-85 Feb-86 Mar-87 Apr-88 May-89 Jun-90 Jul-91 Aug-92 Sep-93 Oct-94 Nov-95 Dec-96 Jan-98 Feb-99 Mar-00 Apr-01 May-02 Jun-03 Jul-04 Aug-05 Sep-06 Oct-07 Nov-08 Dec-09 Jan-11 Feb-12 Mar-13 Apr-14 May-15Log ($/¥) Log (P/P*) Figure 4: Monthly Exchange Rate and PPP – USD/Pound Sterling 1.2 1 0.8 0.6 0.4 0.2 0-0.2Jan-71 Jul-72 Jan-74 Jul-75 Jan-77 Jul-78 Jan-80 Jul-81 Jan-83 Jul-84 Jan-86 Jul-87 Jan-89 Jul-90 Jan-92 Jul-93 Jan-95 Jul-96 Jan-98 Jul-99 Jan-01 Jul-02 Jan-04 Jul-05 Jan-07 Jul-08 Jan-10 Jul-11 Jan-13 Jul-14Log ($/£) Log (P/P*) At first pass, the log purchasing power parity series tracks, more or less, the average trajectory of thebilateral exchange rates for both the Swiss franc and the Canadian dollar without any transformation.While the effect is not immediately clear in the case of the Japanese yen or pound sterling, I posit that thedegree to which the two relative purchasing power parity series tracks the bilateral exchange rates wouldbe remarkably similar to the previous two series with the simple addition of a constant. This is likelymore a function of the characteristics of these particular exchange rates and their relation to the United APRIL 2018|InFER 25

RESEARCHStates dollar over the course of the sample, while the Canadian dollar and Swiss franc have largelyfluctuated above 1:1 value with the dollar over the course of the past three decades the same cannot besaid of the pound sterling or yen. The sterling has been strong relative to the dollar throughout thesample, and the exchange rate series may be unconditionally higher than that of the purchasing powerparity series as a result. In regression analysis, this should be dealt with accordingly with a mean effectvis-à-vis a constant. Shifting the purchasing power parity series up would more directly plot the trajectoryof the exchange rate series. The same bias holds for the yen, particularly due to the units of the yen againstthe dollar. Since the relationship is never 1:1, a downward adjustment of the series would accurately trackthe average movement of the exchange rate series. I posit that the trajectory of both series for all currencies, along with existing literature as discussedabove, provides a firm justification for the use of purchasing power parity as a fundamental series whichserves to plot an average effect of the exchange rate movements less the shocks that exchange rates aremore subject to. Major differences in series seem to be the result of unconditional bias that is easilyameliorated with a constant, and does not represent a fundamental threat to the use of the series in thiscontext. Cointegration, as discussed below in Sections 4 and 8, will further motivate the use of thisstructural variable and better contextualize the use of these plots. Attending, now, to the annual data from the Bank of England dataset, I observe similar behaviorin both plots throughout the sample for both series. The plot, for the log purchasing power parity andbilateral exchange rate series for both samples is as follows: Figure 5: Annual Exchange Rate and Purchasing Power Parity - 1861-2015 Log ($/£) Log P/P*32.521.510.50 1861 1865 1869 1873 1877 1881 1885 1889 1893 1897 1901 1905 1909 1913 1917 1921 1925 1929 1933 1937 1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 2009 201326 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate ForecastingDespite the obvious impact of different institutional frameworks, the log purchasing power parity seriesdoes a surprisingly fair job of matching the relative trajectory of the log bilateral exchange rate seriesacross all years in the 150-year sample. Again, we observe the same mean effect where one series isunconditionally above the other, but the addition of a constant would ameliorate the bias handily. Regardless of degree to which log purchasing power parity matches the trajectory of log bilateralexchange rates throughout the sample, one of the key objectives of this analysis is to parse out the impactof institutional considerations on both exchange rate determination and the behavior of thefundamental. As such, I will subdivide the broader sample into three separate institutional frameworks:The Gold Standard, the Bretton Woods system, and the post-Bretton Woods Float. Each separate time-series represents broadly different economic climates and exchange rate regimes, which cannot beignored when looking at a sample this broad in scope. To better empirically motivate the choice of thesesubperiods, I conduct Quandt-Andrews Structural Breakpoint tests 1 on the broader sample todetermine whether there are empirically valid break dates in the broader sample that coincide witheconomic intuition. Figure 6: Annual Exchange Rate and Purchasing Power Parity - 1861-1939 Log ($/£) Log P/P*32.521.510.50 1861 1863 1865 1867 1869 1871 1873 1875 1877 1879 1881 1883 1885 1887 1889 1891 1893 1895 1897 1899 1901 1903 1905 1907 1909 1911 1913 1915 1917 1919 1921 1923 1925 1927 1929 1931 1933 1935 1937 1939 I consider the 1861-1939 period the “Gold Standard.” At a time where the United States is still afledgling nation and the pound-sterling is king, we should expect vastly different behavior in both seriesthan we would in, say, the post-Bretton Woods float. Notably, the inherent hegemony of the poundsterling in economic terms, and the degree to which currencies are backed by gold during this time frame,would imply that prices should be more closely linked with exchange rates and, furthermore, exchange1 Results of Quandt-Andrews Structural Breakpoints tests are discussed in Section 7. APRIL 2018|InFER 27

RESEARCHrate movements should be less volatile. This is clearly borne out in the data- from 1870 until 1918, thereis very little, if any, movement in the exchange rate and little movement in the purchasing power parityvariable. Any instances of spikes in the exchange rate series (a jump at the outset of the sample and twosmall drops, seemingly, around World War I and the Great Depression) are closely matched with similarspikes in the price series. Given the degree to which movements in each series track one another, I wouldexpect to find the strongest evidence of cointegration during this subperiod, relative to the other two,further motivating the use of the fundamental in this context. Figure 7: Annual Exchange Rate and Purchasing Power Parity - 1940-1973 Log ($/£) Log P/P*21.81.61.41.210.80.60.40.20 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 The Bretton Woods period (1944-1973 subperiod in this analysis), similarly features very littlevariable in either the exchange rate or prices—in fact, in stark contrast to the monthly series from abovefrom recent years (these series largely correspond to post-Bretton Woods data), relative prices seem toexhibit somewhat more variability than the generally-volatile exchange rate counterparts. This shouldcome as no surprise given the nature of exchange rate regimes under the Bretton Woods era. Byconstruction exchange rates are essentially fixed in response to depression-era fluctuations, largely tostave off incipient capital flows in a fragile period for both representative economies. Thus, by design,there is little fluctuation in exchange rates much like that of the Gold Standard. However, prices do notexhibit the same degree of constancy relative to exchange rates they did during the Gold Standard. Sinceprices are not fixed as strictly, and neither series is backed commonly by Gold, the way in which the seriesbehave ought to be fundamentally different than observed in the prior subperiod. Most dramatically,however, one would expect the post-Bretton Woods float to be altogether structurally different thaneither of these subperiods.28 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting Figure 8: Annual Exchange Rate and Purchasing Power Parity - 1974-2015 Log ($/£) Log P/P*1.41.210.80.60.40.20 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Following the breakdown of the Bretton-Woods system, we observe freely floating exchange ratesthrough present day. While the pound sterling has remained strong against the dollar, the dollar servesas the international reserve currency and, therefore, is largely considered the predominant currency usedthroughout the world. These characteristics suggest the present day is, unsurprisingly, fundamentallydifferent from the prior two periods in terms of exchange rate regimes and the relative importance of thetwo currencies in the global economy. Moreover, the current float incorporates several otherunprecedented institutional characteristics not present in the prior two periods, including the rise of theEuropean Exchange Rate Mechanism (ERM), the rise of the euro in its current manifestation, in thelatter decades of the century, the advent of high-frequency trading, and the 2008 financial crisis. One cannot ignore the possible impact these considerations might have on the fundamentalexchange rate, and leads us to question whether the “fundamental” of the prior periods is different fromthe “fundamental” here. While there are inherent benefits to using such a long-run sample when seekingto better explain exchange rates with fundamentals, it is crucial to attend to these tensions that arise fromusing a dataset that spans inherently dissimilar structures. As such, I see this subdivision of the data as anecessary component of any analysis regarding the Bank of England dataset in this context.4. Time-Series Properties To fully understand the methodology established henceforth, it is crucial to understand the time-series properties of the series in question, beyond the simple plots provided in the previous section.Understanding whether bilateral exchange rates are stationary and, if non-stationary, whether they arecointegrated, is valuable for estimation purposes and interpretation of results. I begin by attending totests of stationarity. APRIL 2018|InFER 29

RESEARCH It is well-established in existing literature that exchange rates exhibit remarkably non-stationarybehavior and are often described as random walk series, naturally giving rise to the predominance of theuse of the random walk for forecasting purposes. Random walk series are remarkably persistent, andfeature moments that are ill-defined. Random walks are, more generally, a special case of the broadercollection of unit root series which exhibit the same characteristics. To better understand the underlyingtimes-series properties of the data series in question, I conduct Augmented Dickey-Fuller (ADF) testsfor all bilateral exchange rate time series. Results are as follows:Figure 9: Augmented Dickey-Fuller Unit Root Tests & Regressions for Exchange Rate Series Dependent Variable: ∆(Log Exchange Rate) Exchange Rate Series Canadian Swiss Japanese British British Yen Pound Pound Dollar Franc (Monthly) (Annual)ADF Test Statistic -1.805 -2.275 -2.030 -2.791 -0.445p-value 0.378 0.181 0.274 0.060 0.897Log Exchange Rate (-1) -0.008* -0.007** -0.005** -0.016*** -0.006 (0.004) (0.003) (0.003) (0.006) (0.013)∆(Log Exchange Rate (-1)) 0.277*** 0.27*** 0.317*** 0.355*** 0.29*** (0.042) (0.042) (0.041) (0.04) (0.079)∆(Log Exchange Rate (-2)) -0.246*** (0.080)Constant -0.002* -0.001 -0.025* 0.008** -0.0003 (0.001) (0.002) (0.013) (0.003) (0.017)Observations 532 532 532 532 155R2 0.081 0.083 0.109 0.135 0.112Note: Augmented Dickey-Fuller Tests are performed by regressing combinations of differenced and laggedexchange rate variables on the first difference of the respective exchange rate series. Both regression output and teststatistic evaluation are included in the table above. Upon determining the appropriate t-statistic from the firstdifferenced log exchange rate is tested against Dickey-Fuller distribution test critical values. As such, p-values fromthe ADF test statistic portion correspond to the appropriate critical values for the test. I test against the nullhypothesis that each respective exchange rate series has a unit root. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 As the results above imply, I fail to reject the null of a unit root for all series with the notableexception of the monthly log dollar/pound exchange rate for the United States and United Kingdom.This result is robust to change in frequency, as the trimmed annual sample (including only thoseobservations used in estimation which correspond to the available price data) from the Bank of Englanddataset also implies there is no unit root in the bilateral exchange rate data annually. There are possibleconsequences for this regarding cointegration results and use of the hybrid model—I suspect that, giventhe apparent stationary behavior of this exchange rate data, a simple univariate autoregressive model mayoutperform the hybrid model. This will be tested below.30 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting While results from the ADF test clearly indicate the underlying exchange rate series are unit root(or I(1)), this does not imply they are random walk series—random walks are, as indicated briefly above,a special case of unit root which feature more significant challenges for estimation and interpretation.Using Variance Ratio Tests for all log bilateral exchange rate series, I reject the null hypothesis of arandom walk in each series at the 95% level for all series except the log dollar/pound exchange rate forthe United States and United Kingdom, this time at the annual frequency. Similarly, Augmented Dickey Fuller tests are performed on all log purchasing power parity seriesto determine whether they exhibit the same non-stationary characteristics: Figure 10: Augmented Dickey Fuller Unit Root Tests & Corresponding Regressions for Purchasing Power Parity Series Dependent Variable: ∆(Log Purchasing Power Parity) Purchasing Power Parity Foreign Price Series Canadian Swiss Japanese British British Dollar Franc Yen Pound Pound (Monthly) (Annual)ADF Test Statistic -0.568 -1.067 -2.035 -3.941 -1.056p-value 0.875 0.730 0.272 0.002 0.732Log Purchasing Power Parity (-1) -0.0017 -0.001 -0.002** -0.007*** -0.006 (0.003) (0.001) (0.001) (0.002) (0.006)∆(Log Purchasing Power Parity (-1)) 0.061 0.124** 0.151*** 0.609*** (0.041) (0.052) (0.044) (0.061)∆(Log Purchasing Power Parity (-2)) 0.007 0.022 0.076* (0.041) (0.052) (0.044)∆(Log Purchasing Power Parity (-3)) -0.094** -0.194*** -0.012 (0.041) (0.052) (0.039)Constant 0.008 0.004 0.011** 0.033*** 0.006 (0.014) (0.003) (0.011) (0.009) (0.010)Observations 533 521 362 519 153R2 0.001 0.254 0.062 0.373 0.399Note: See notes for the ADF test statistic procedure from the previous figure. Further, the results from the monthlyBritish Pound data and Swiss Franc data are truncated as the regression estimated for determining the respectivetest statistic extends to 14 and 12 lagged differences, respectively. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 In line with the results from the bilateral exchange rate data, I fail to reject the null of a unit rootfor all series except for the monthly United States and United Kingdom dollar/pound sterling exchangerate. Again, this is consistent with the ADF test conducted on the annual frequency data of the sameexchange rate. Further, I reject the null hypothesis that the series are random walk at the 95% level for alllog purchasing power parity series at the monthly frequency and at the 90% level for log purchasingpower parity at the annual frequency. APRIL 2018|InFER 31

RESEARCH Recognizing the degree to which all series in this analysis (again, apart from post-Bretton WoodsUSD/GBP exchange rates) are I(1), there are serious consequences for forecasting and interpretation ofresults. First, as discussed in previous sections, if a series is truly random walk, then forecasting beyondthe information available today is inappropriate. Since a random walk series is highly persistent, the seriesevolves by the accumulation of random shocks in each subsequent period. As such, there is no meanreversion (the series stays constant at the current value) and variance is unbounded as time increases toinfinity. From a practical standpoint, however, as discussed, it seems illogical to assume that the onlyinformation that is of value for prediction in long-term time-horizons is the realization of the series today,so this serves more as a justification of the use of the random walk, and it’s predominance as an exchangerate forecasting model, in the short term. Note, further, that while unit root series are also highlypersistent, the possibility of a cointegrating relationship between two I(1) series could be helpful inmotivating the inclusion of a fundamental.25. Methodology Mark’s fundamental exchange rate model serves as a natural departure from the work of Meese andRogoff that incorporates both theory and the random walk in exchange rate forecasting. This “hybrid”model assumes a “fundamental” exchange rate, ������������, and further assumes that, if this is truly a fundamentalexchange rate, deviations from the fundamental ought to be self-correcting in the long-run. In thecontext of this analysis, ������������, the “theory” component of the model, is assumed to be purchasing powerparity (PPP) such that ������������ = ���������������������∗��� , where P is the domestic price level and P* is the foreign price level, bothmeasured in Consumer Price Index (CPI) terms. Taking logs, in accordance with the original approachof Mark, we have ������������������������ = (������������������������ − ���������������∗��������� ). I defer to the log-form of these variables for the remainder of theanalysis. Based on these assumptions underlying this fundamental exchange rate, I seek to determine to whatextent the gap between an observed exchange rate ������������������������ and the fundamental ������������������������ can be used to model actualchanges in the exchange rate with ������������ periods of displacement from time ������������. The regression is postulated assuch: ������������������������+������������ − ������������������������ = ������������������������ + ������������������������(������������������������ − ������������������������) + ������������������������+������������, ������������������������+������������~������������(0, ������������2) Which can be further rewritten as: ������������������������+������������ = ������������������������ + ������������������������������������������������ + (1 − ������������������������)������������������������ + ������������������������+������������ This is the regression equation of interest in this analysis. As postulated, it implies that, whenforecasting the exchange rate ������������������������+������������ , ������������ periods from now, there is both a fundamental (“theory”)2 See Section 8 for detailed analysis and discussion of cointegration in the context of vector error-correction models.32 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecastingcomponent and random walk component which uses the past exchange rate ������������������������ as the independentvariable. Further, the regression is structured such that these components are weighted in theircontribution per the coefficient ������������������������. This coefficient is the chief focus of this analysis. If ������������������������ is equal to zero, all weight is given to the past exchange rate and, as such, the random walk (orpast data) is the appropriate model for forecasting this relationship. If, however, ������������������������ is greater than zero,the “theory” component (i.e. purchasing power parity) meaningfully contributes to the predictive powerof the model in modeling changes in exchange rates at across displacements of time. HAC standard errorsare reported in all regressions to account for the implicit serial dependence in forecasting regressions, andthe impact of non-stationarity in series and residuals. Accordingly, using this specification for both the monthly and annual series, forecast estimates areestablished by running k-step ahead forecast regressions—increasing lags serve as estimates of exchangerates made with increasing displacements of time, thereby making for longer-run estimations. To capturean appropriately long time-horizon, displacements of 1 through 12 will be used for the annual data, suchthat the longest time-horizon forecast is 12-years ahead. While this is truly a long-term horizon, it is notunrealistic—it would not be unreasonable to attempt to forecast exchange rates at such a horizon whenconducting the valuation of a multinational venture with cash flows denominated in foreign exchangerates. Displacements of 1 through 60 will be used for the monthly data, such that the longest time-horizon forecast is 5-years ahead (the Mark (1995) analysis conducts analysis with the largest displacementat 64-months ahead). All data is at the monthly frequency from January 1971 for the Canadian dollar,pound sterling, and Swiss franc. The sample begins in January 1985 for the Japanese yen due toavailability of price data. As discussed briefly above, the predominant outcome coefficient from the regression as specified is������������������������ . A positive, statistically significant ������������������������ coefficient in and of itself implies that the structuralcomponent log purchasing power parity contains information that can improve upon the predictivepower of the forecast with past exchange rate data alone. While I view the interpretation of thiscoefficient as a sufficient measure of improvement on the random walk by including it as a special case,additional evaluation metrics are employed in accordance with existing literature. Per the methodologyof Mark (1995), I report and plot R2 values for each k-step ahead regression, which serve as indicators ofthe explanatory power of each k-step ahead regression with respect to the actual data, as well asconstructed RMSE values to capture the relative magnitude of the forecasting error for each regressionat each forecast horizon. To further establish the predictive power of this hybrid specification, I conduct additional forecastevaluation with respect to a univariate autoregressive time-series model of the log exchange rate. Thisapproach is utilized in Meese and Rogoff (1983) but must not be confused with a pure random walk—in the case of the random walk, the only information used for the forecast of any k-step ahead realizationof the exchange rate is the information available today. The univariate unit root autoregressive model APRIL 2018|InFER 33

RESEARCHserves to model the predictive power of the lagged log exchange rate without the contribution of theory.This merely serves to provide an additional benchmark for the measurement of forecast quality betweenthe hybrid model and other, more parsimonious specifications that implicitly assume theory is unhelpfulin improving forecast accuracy. Regressions will be of the specification: ������������������������+������������ = ������������������������ + ������������������������������������������������ + ������������������������+������������ Which is essentially the same regression specified for the hybrid model where the original coefficient������������������������ is simply assumed to be equal to 0 at all forecast horizons and is therefore excluded from the forecasts.Further, in accordance with the existing literature, Diebold-Mariano tests are performed to assess therelative accuracy of the hybrid forecast model with respect to the parsimonious univariate time-seriesmodel. Difference series of squared errors for each k-step ahead forecast are constructed and, accordingly,run on a constant—as constructed, a negative, statistically significant coefficient serves as evidence ofstatistically valid improvement in accuracy for the hybrid model relative to the univariate time-seriesmodel. Expanding the analysis beyond spot bilateral exchange rate data and the relative price ratio, I willconduct forecast encompassing regressions incorporating historic exchange rates from the forwardmarket. Since the approach taken in this analysis involves conducting direct forecasts of k-displacements(i.e., a forecast for 3-months ahead is estimated directly, rather than rolling an autoregressive modelforward as in the case of multistep ahead forecasting), each k-month ahead forecast will have acorresponding rate from the forward market that originated at the start date, and would allow a holderto transact at the forward rate k-periods ahead. Given information available at time t, when conductinga k-step ahead forecast, I hope to determine to what extent forward rates, which determine acorresponding k-period ahead price for a given currency, can contribute to those k-step ahead forecastsfrom the hybrid model specified above. To empirically assess this contribution, I construct series of errors based on the difference betweenthe log monthly average exchange rate at period k and the log monthly average forward rate for period kwith information at time t for a given currency. I then conduct forecast encompassing regressions todetermine to what extent forecast errors implicit from the difference in the forward rate and actual ratehave predictive power relative to the forecast errors that result from the k-step ahead hybrid modelforecasts. The broad specification of the regression run, in this framework is: ������������������������,������������+������������ = ������������ + ������������������������������������������������,������������+������������ + ������������������������,������������+������������ Where ������������������������,������������+������������ is the hybrid model forecast error series from the k-period ahead forecast for a givencurrency ������������ , and ������������������������,������������+������������ is the error series constructed from the differences between log spot exchange ratesat period k and the forward exchange rates established with information at time t to be transacted k-periods ahead.34 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting6. Monthly Frequency Exchange Rate Forecasting Results Attending first to the results at the monthly frequency most closely in line with the approach ofMark (1995), I will proceed systematically through the regression output and coefficient estimates foreach currency. Broadly, across all four currencies, I find that the role of the fundamental vis-à-vis logpurchasing power parity becomes increasingly economically and statistically significant as the forecasthorizon increases. ������������������������-values that are both positive and statistically significant indicate statistically andeconomically valid contributions to the predictive power above and beyond what a simple univariateautoregressive model or random walk model that contain only past realizations of the exchange rate forprediction provide. Further, increasing contribution of the fundamental demonstrated in the ������������������������coefficients signify that the content of the forecasts of future exchange rates is being driven increasinglyby the information from the fundamental alone. This will be further substantiated throughout theremainder of the section. APRIL 2018|InFER 35

36 InFER|ISSUE 1 Figure 11: Hybrid Model Forecasting Regression Output (1- to 60-month Ahead Forecast Horizons) – Canadian Dollar/USD Exchange Rate Forecasts Dependent Variable: Log of Dollar-Canadian Dollar Exchange Rate k-months ahead 1 3 4 6 9 12 16 24 32 36 48 60 Log(P/P*) 0.01 0.039 0.052 0.084 0.141 0.207** 0.285** 0.439*** 0.596*** 0.666*** 0.824*** 0.945*** (0.014) (0.038) (0.049) (0.067) (0.087) (0.103) (0.119) (0.148) (0.164) (0.168) (0.174) (0.171) Log($/$) 0.991*** 0.964*** 0.95*** 0.918*** 0.873*** 0.825*** 0.767*** 0.648*** 0.522*** 0.461*** 0.27*** 0.094 (0.094) (0.006) (0.017) (0.022) (0.032) (0.043) (0.052) (0.06) (0.075) (0.085) (0.09) (0.096) Constant -0.048 -0.182 -0.245 -0.398 -0.66* -0.967** -1.331** -2.048*** -2.775*** -3.104*** -3.851*** -4.433*** (0.061) (0.172) (0.22) (0.304) (0.394) (0.464) (0.54) (0.673) (0.745) (0.765) (0.788) (0.775) Observations 533 531 530 528 525 522 518 510 502 498 486 474 R2 0.990 0.958 0.940 0.556 0.512 0.382 0.300 0.014 0.028 0.034 0.902 0.854 0.810 0.757 0.657 0.09 0.094 0.103 0.108 RMSE 0.043 0.053 0.06 0.068 0.079 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 12: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 60-Month Ahead Forecast Horizons) – Canadian Dollar/USD Dependent Variable: Log of Dollar-Canadian Dollar Exchange Rate k-months ahead 13 4 6 9 12 16 24 32 36 48 60 DM Constant 0.000 0.000 0.000 0.000 -0.0001 -0.0002 -0.0003 -0.0008 -0.0014* -0.0018* -0.003** -0.004*** (0.000) (0.000) (0.000) (0.000) (0.0001) (0.0002) (0.0003) (0.0005) (0.0008) (0.0009) (0.0012) (0.0013) Log($/$) 0.993*** 0.974*** 0.964*** 0.941*** 0.911*** 0.88*** 0.842*** 0.76*** 0.667*** 0.621*** 0.454*** 0.288*** (0.005) (0.015) (0.019) (0.028) (0.037) (0.044) (0.05) (0.061) (0.073) (0.079) (0.092) (0.101) Constant -0.002 -0.006 -0.008* -0.013* -0.019** -0.025** -0.033*** -0.05*** -0.069*** -0.078*** -0.113*** -0.149*** (0.001) (0.004) (0.005) (0.007) (0.009) (0.01) (0.011) (0.012) (0.015) (0.016) (0.018) (0.02) Observations 533 531 530 528 525 522 518 510 502 498 486 474 R2 0.99 0.957 0.94 0.9 0.478 0.414 0.226 0.091 0.014 0.029 0.034 0.044 0.85 0.8 0.74 0.616 0.097 0.103 0.115 0.123 RMSE 0.053 0.061 0.07 0.084 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting Plotting the evolution of both the theory coefficients of interest (������������������������) and the foil coefficients (thatwhich determines the contribution of the lagged exchange rate, or the role of the past in determinationof future rates) from the regression output above, the following pattern is observed: Figure 13: Evolution of Coefficients for USD/CAD Forecasts - Monthly Frequency - HAC Error Bars Lagged USD/CAD XR P/P*βk 1.4 1.2 10 20 30 40 50 60 1 k-months 0.8 0.6 0.4 0.2 0 -0.2 0 The relative contribution of both past realizations of exchange rates (the contribution that wouldbe the sole focus of a random walk forecast) is an unequivocally downward, almost linear trend, with theexact opposite observed in the contribution of theory per the relative price ratio. Notably, thecoefficients behave almost as mirror images of one another—they almost exactly fit the construction ofthe specification wherein the coefficient on the lagged spot rate is one minus the ������������������������. This is indicative ofan almost unequivocal improvement upon the random walk by simply including the fundamental valueexhibited by purchasing power parity. Beyond the economic significant of these plots, note that bothcoefficients are statistically significant in forecasts of 10 to 56 months. Purchasing power parity does not contribute meaningfully until the 10-month ahead forecast, butbecomes (and remains) significant at the 99% level from the 20-month ahead forecast and beyond. Therole of the past is no longer statistically significant at the horizons beyond 56-months. This points further,to the importance of theory’s relative predictive power in the long-run. The contribution is minimal atthe outset, which is in line with the results of existing literature that points to the dominance of therandom walk. In terms of forecast performance, I defer to plots of R2 (as a measure of explanatory power) andRoot Mean Squared Error (as a measure of model fit) to graphically depict the evolution of model fit asthe forecast horizon increases from 1- to 60-months ahead. APRIL 2018|InFER 37

RESEARCH Figure 14: Model Fit for USD/CAD Forecasts - R2 and Root Mean Squared Error R-squared RMSFE1.2 0.12 1 0.10.80.6 0.080.40.2 0.06 0 0.04 0 0.02 0 10 20 30 40 50 60 k-monthsR-squared RMSFE Despite the promising results exhibited in the coefficient evolution plot, RMSE increases as theforecast horizon increases, while the R2 of the regression simultaneously decreases. The decline in R2 canbe described with a gently sloping, almost linear, curve beginning remarkably close to 1 and ending atapproximately 0.30 by the 60-month ahead forecast horizon. RMSE, conversely, increases rapidly at theoutset, almost logarithmically, and then growth slows. Beginning at a value of approximately 0.014,RMSE appears to plateau at approximately 0.108. I do not see this necessarily as a repudiation of the significance of the hybrid forecasts, by likelymore a product of the dramatic displacement in the data itself—as I will address more significantly in theannual results, forecasts at this horizon may be attempting to explain realizations under widely differentinstitutional or economic climates that cause the accuracy of the forecasts to decline over time. Further,while this specification and data is not an exact replication of that used in Mark (1995), I maintain R2levels higher than those realized in the Canadian dollar regressions from that analysis. While these resultsserve to provide sufficient evidence of the contribution of theory at the monthly frequency withUSD/CAD exchange rates, I assess the performance of the hybrid model relative to the univariateautoregressive exchange rate model specified in the methodology section. I find that, at all forecasthorizons, the hybrid theory model outperforms the parsimonious univariate time-series model in termsof RMSE and R2. Diebold-Mariano tests performed at each forecast horizon further imply a statisticallyvalid difference in terms of model accuracy from the 30-month ahead forecast horizon and beyondfavoring the hybrid model.33 Refer to Figure 12 above for results of Diebold Mariano tests for USD/CAD exchange rate forecasts, represented withestimates in the DM constant row—negative, statistically significant coefficients signify better forecasts in the hybridmodel, in terms of forecast accuracy measured via mean squared error, than the univariate regression.38 InFER|ISSUE 1

Figure 15: Hybrid Model Forecasting Regression Output (1- to 60-month Ahead Forecast Horizons) – Swiss Franc/USD Exchange Rate Forecasts Dependent Variable: Log of Dollar-Franc Exchange Rate k-months ahead 134 6 9 12 16 24 32 36 48 60 Log(P/P*) 0.016 0.076* 0.107** 0.165** 0.244** 0.34*** 0.464*** 0.723*** 0.905*** 0.963*** 1.169*** 1.443*** (0.015) (0.041) (0.053) (0.074) (0.095) (0.108) (0.123) (0.137) (0.147) (0.147) (0.154) (0.174) Log($/₣) 0.983*** 0.93*** 0.902*** 0.851*** 0.78*** 0.699*** 0.594*** 0.377*** 0.222** 0.168** -0.012 -0.226** (0.009) (0.026) (0.034) (0.047) (0.061) (0.085) (0.083) (0.112) (0.07) (0.079) (0.082) (0.088) Constant -0.076 -0.354* -0.497** -0.764** -1.132*** -1.573*** -2.147*** -3.344*** -4.181*** -4.447*** -5.393*** -6.657*** (0.069) (0.19) (0.244) (0.34) (0.435) (0.498) (0.566) (0.627) (0.674) (0.673) (0.702) (0.799) Observations 533 531 530 528 525 522 518 510 502 498 486 474 R2 0.994 0.976 0.966 0.949 0.769 0.756 0.729 0.739 0.028 0.057 0.067 0.082 0.924 0.897 0.865 0.81 0.15 0.151 0.151 0.143 RMSE 0.097 0.111 0.125 0.141 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 16: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 60-Month Ahead Forecast Horizons) – Swiss Franc/USD Dependent Variable: Log of Dollar-Franc Exchange Rate k-months ahead 13 4 6 9 12 16 24 32 36 48 60 DM Constant 0.000 -0.0001 -0.0001 -0.0003 -0.0006 -0.0011 -0.0021* -0.005** -0.008*** -0.009*** -0.014*** -0.022*** (0.000) (0.0001) (0.0001) (0.0002) (0.0005) (0.0007) (0.0012) (0.0021) (0.0031) (0.0033) (0.0043) (0.0063)APRIL 2018|InFER 39 Log($/₣) 0.992*** 0.973*** 0.963*** 0.945*** 0.918*** 0.89*** 0.855*** 0.779*** 0.721*** 0.697*** 0.627*** 0.559*** (0.004) (0.01) (0.013) (0.018) (0.023) (0.027) (0.031) (0.037) (0.042) (0.042) (0.045) (0.053) Constant -0.001 -0.004 -0.006 -0.009 -0.014 -0.019 -0.025 -0.04* -0.05** -0.054** -0.063* -0.076* (0.002) (0.006) (0.008) (0.01) (0.013) (0.015) (0.018) (0.022) (0.026) (0.027) (0.034) (0.042) Observations 533 531 530 528 525 522 518 510 502 498 486 474 R2 0.994 0.975 0.966 0.946 0.683 0.655 0.56 0.456 0.028 0.057 0.068 0.083 0.919 0.888 0.847 0.759 0.175 0.18 0.192 0.206 RMSE 0.1 0.116 0.133 0.158 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

RESEARCH Again, the contribution of the fundamental purchasing power parity component is near zero in theinitial forecast and increases linearly as the forecast horizon increases to a maximum value of 1.443 at the60-month ahead exchange rate forecast. While I expect, based on the specification detailed in themethodology section above, the coefficient ������������������������ to remain below one, it is not mechanically bound tobehave in this fashion. The coefficient is statistically significant at the 99% level, again, from the 10-month ahead forecast and beyond, and stays remarkably significant when it is above 1.0. This implies anoutsize contribution of the fundamental purchasing power parity relationship at longer-term horizons,perhaps to offset the negative impact of the exchange rates observed in the same time-frame. Theestimates of ������������������������ for the Swiss Franc in Mark (1995) also tend above 1.0 at the 16-quarter ahead forecast, sothis result is not particularly surprising relative to existing literature. Correspondingly, the contribution of the lagged exchange rate is near one at the initial one-monthahead forecast and decreases linearly as displacements increase, becoming negative at forecast horizonsincluding and beyond four years ahead. Since these coefficients are not statistically significant, they arecontributing little to no economic or statistical information to the prediction of the forecasts beyond the38-month ahead horizon, so the negative coefficients are not troubling in this context. Regardless, theresults of the Swiss franc forecasts via the hybrid model suggest that theory improves upon the randomwalk in terms of the ������������������������ coefficient, and this improvement is magnified as the time-horizon of theforecasts increases. Results for forecast evaluation and model fit are more comforting in the context of the monthlyUSD/CHF forecasts relative to the other currencies examined at the monthly frequency. Figure 18: Model Fit for USD/CHF Forecasts - R2 and Root Mean Squared Error R-squared RMSFE1.2 0.16 1 0.14 0.120.8 0.10.6 0.080.4 0.060.2 0.04 0.02 0 0 0 10 20 30 40 50 60 k-monthsR-squared RMSFE40 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting As observed in the other currencies, R2 indicators of explanatory power decrease modestly as theforecast horizon increases, but the decline is much less rapid than observed in all other currenciesresulting in the highest relative R2-value of 0.739 at the 60-month ahead forecast horizon. Further, thisis the only currency in this analysis that engenders an increase in the R2 value at the tail-end of the forecasthorizon, dropping to its lowest around the 52- and 53-month ahead forecasts and then recovering someof the explanatory power lost. This implies that the hybrid theory model can more reliably explainvariation in the USD/CHF exchange rate at longer-horizons than the other currencies in question. In terms of RMSE, the consistent pattern of marked initial increases, a near-logarithmic trend ofevolution across forecast horizons, and a plateau in those increases is observed. Incidentally, while theUSD/CHF forecasts with the hybrid model feature the most impressive metrics in terms of explanatorypower, the model is subject to the largest incidences of RMSE across the four currencies examined at themonthly frequency, reaching 0.15184 at the 42-month ahead forecast horizon. Despite this, theUSD/CHF forecast series is the only series of those sampled to exhibit a decline in the RMSE figures atthe longest forecast horizons, complementing the trajectory of the R2 values described above. Relativeto the univariate autoregressive exchange rate model, the USD/CHF exchange rate forecasts generatedfrom the hybrid theory model exhibit higher explanatory power and lower RMSE values at all forecasthorizons, with statistically valid improvements in model accuracy vis-à-vis Diebold Mariano testsbeginning at the forecasts beyond 1-year ahead.44 Refer to Figure 15 above for results of Diebold Mariano tests for USD/CHF exchange rate forecasts. APRIL 2018|InFER 41

42 InFER|ISSUE 1 Figure 19: Hybrid Model Forecasting Regression Output (1- to 60-month Ahead Forecast Horizons) – Japanese Yen/USD Exchange Rate Forecasts Dependent Variable: Log of Dollar-Yen Exchange Rate k-months ahead 134 6 9 12 16 24 32 36 48 60 Log(P/P*) 0.002 0.027 0.043 0.071 0.102 0.161* 0.262*** 0.439*** 0.6*** 0.652*** 0.616*** 0.526*** (0.012) (0.034) (0.043) (0.058) (0.073) (0.085) (0.1) (0.11) (0.094) (0.091) (0.1) (0.118) Log($/¥) 0.973*** 0.889*** 0.844*** 0.76*** 0.654*** 0.531*** 0.355*** 0.08 -0.138** -0.204*** -0.137 -0.042 (0.013) (0.036) (0.046) (0.06) (0.071) (0.076) (0.077) (0.078) (0.065) (0.064) (0.09) (0.114) Constant -0.132 -0.637** -0.917** -1.436*** -2.064*** -2.90*** -4.166*** -6.225*** -7.946*** -8.473*** -7.99*** -7.135*** (0.107) (0.299) (0.381) (0.504) (0.616) (0.691) (0.76) (0.798) (0.642) (0.619) (0.745) (0.932) Observations 365 363 362 360 357 354 350 342 334 330 318 306 R2 0.984 0.931 0.901 0.848 0.458 0.475 0.458 0.397 0.027 0.054 0.064 0.076 0.785 0.698 0.583 0.464 0.116 0.113 0.115 0.119 RMSE 0.085 0.096 0.109 0.118 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 20: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 60-Month Ahead Forecast Horizons) – Japanese Yen/USD Dependent Variable: Log of Dollar-Yen Exchange Rate k-months ahead 1 34 6 9 12 16 24 32 36 48 60 DM 0 0 -0.0001 -0.0002 -0.0005 -0.001 -0.0023* -0.005*** -0.009*** -0.011*** -0.009*** -0.0068** Constant (0) (0.0001) (0.0001) (0.0002) (0.0005) (0.0008) (0.0012) (0.0019) (0.0025) (0.0029) (0.0031) (0.0029) Log($/¥) 0.98*** 0.924*** 0.899*** 0.855*** 0.805*** 0.75*** 0.677*** 0.57*** 0.498*** 0.475*** 0.453*** 0.464*** (0.009) (0.026) (0.034) (0.046) (0.062) (0.072) (0.079) (0.086) (0.089) (0.09) (0.082) (0.077) Constant -0.11** -0.355*** -0.476*** -0.681*** -0.913*** -1.169*** -1.512*** -2.016*** -2.349*** -2.456*** -2.548*** -2.478*** (0.044) (0.124) (0.16) (0.221) (0.293) (0.343) (0.378) (0.411) (0.429) (0.434) (0.396) (0.372) Obs. 366 366 366 366 366 366 366 366 366 366 366 366 R2 0.985 0.936 0.911 0.868 0.455 0.423 0.39 0.419 0.027 0.055 0.065 0.079 0.82 0.754 0.661 0.531 0.161 0.165 0.17 0.166 RMSE 0.092 0.108 0.127 0.149 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting The USD/JPY and USD/GBP exchange rate forecasts do not exhibit the same uniform, linearbehavior that the USD/CAD and USD/CHF forecasts do above. Moreover, the behavior of bothcurrencies across the forecast horizon, though decidedly nonlinear, is remarkably similar between bothseemingly dissimilar currencies. Attending first to the forecasts of the Japanese Yen (I attend to those ofthe pound sterling last to more seamlessly transition into the discussion regarding long-run forecastingusing the annual data from the Bank of England dataset), I observe the following: Figure 21: Evolution of Coefficients for USD/JPY Forecasts - Monthly Frequency - HAC Error Bars Lagged USD/JPY XR P/P* 1 0.8 0.6βk 0.4 0.2 0 -0.2 -0.4 10 20 30 40 50 60 0 k-months While the contribution of the fundamental and the lagged exchange rate do continue to mirror oneanother as observed in the previous bilateral exchange rate forecasts, the trajectory is not perfectly linearas before. There is a steady linear decline in the contribution of past exchange rate through the 38-monthahead forecast, and the contribution drops below zero shortly past the 2-year ahead forecast horizon.Unlike in the case of the Swiss franc forecasts, the negative coefficients in this context are statisticallysignificant, implying that the past data, detracts from the contribution of the fundamental, in economicterms, at these horizons. This does effect does not persist through the remainder of the sample, however,and becomes insignificant past the 4-year ahead forecasts. Further, the decline is reversed somewhat pastthe 3-year ahead forecast horizon, though the coefficients remain negative indefinitely. Correspondingly, the contribution of the theory component increases linearly, approximatelythrough the 3-year ahead forecast, peaking at a value of 0.68, well below the maximum engendered inother currency forecasts. However, unlike the previous forecasts, this effect is not homogenousthroughout the forecast horizons, and the contribution decreases somewhat beyond this horizon(though the ������������������������ coefficients are statistically significant at the 99% level at all horizons beyond 16-monthsahead). This implies there may be some optimization effect underlying the forecasts, where the APRIL 2018|InFER 43

contribution of theory is maximized around the 3-year forecast horizon, and the predictive power ofthese forecasting elements decreases summarily beyond this horizon as the contribution of the past is nolonger significant and the contribution of theory decreases. In this spirit, plots of R2 and RMSE suggest similar patterns for the explanatory power and fit offorecasts relative to those exhibited in the USD/CHF forecasts. Note, however, while the trends aresimilar, the level values are altogether different. Figure 22: Model Fit for USD/JPY Forecasts - R2 and Root Mean Squared Error1.2 R-squared RMSFE 1 0.140.8 0.120.6 0.10.4 0.080.2 0.06 0.04 0 0.02 0 0 10 20 30 40 50 60 k-lagsR-squared RMSFE As before, the trajectory of R2 values relative to the forecast horizon is negative—the decrease islargely linear through the 2-year ahead forecasts and then remains relatively constant at approximately0.45 then exhibits further modest decreases past the 4-year ahead time horizon. While the plateaubehavior is comforting and suggests, generally that the explanatory power of the model does not decreaseindefinitely once it reaches a certain displacement, the 0.45 R2 value is not particularly impressive,implying just less than half of the variability in the exchange rate movements can be explained by thehybrid model at these horizons. RMSE, similarly increases rapidly through the initial 2-years of forecasts,and then plateaus around 0.12 through the remainder of the sample. The relative stability of RMSE, inthis context, is particularly comforting and seems to suggest that hybrid model may be better suited toaccurate forecasting of the Japanese yen, consistently, for longer forecast-horizons. In this spirit, as withthe prior currencies, the hybrid theory model outperforms the univariate autoregressive model more so,and more quickly, than the other hybrid theory models with respect to their given currency. Similarly,too, Diebold Mariano tests suggest the improvement in accuracy is statistically significant as soon as 1-year ahead relative to the univariate autoregressive model.55 Refer to Figure 20 above for results of Diebold Mariano tests for USD/JPY exchange rate forecasts.44 InFER|ISSUE 1

Figure 23: Hybrid Model Forecasting Regression Output (1- to 60-month Ahead Forecast Horizons) – British Pound/USD Exchange Rate Forecasts Dependent Variable: Log of Dollar-Sterling Exchange Rate k-months ahead 1 3 4 6 9 12 16 24 32 36 48 60 Log(P/P*) 0.014 0.065* 0.093** 0.148** 0.218*** 0.279*** 0.35*** 0.503*** 0.613*** 0.659*** 0.76*** 0.676*** (0.013) (0.037) (0.047) (0.062) (0.071) (0.073) (0.07) (0.093) (0.08) (0.095) (0.098) (0.1) Log($/£) 0.98*** 0.895*** 0.851*** 0.762*** 0.645*** 0.535*** 0.391*** 0.09 -0.166** -0.272*** -0.534*** -0.512*** (0.078) (0.077) (0.092) (0.1) (0.015) (0.044) (0.057) (0.076) (0.088) (0.09) (0.087) (0.077) Constant -0.052 -0.247 -0.35* -0.558** -0.819*** -1.042*** -1.294*** -1.839*** -2.213*** -2.366*** -2.695*** -2.326*** (0.053) (0.15) (0.191) (0.253) (0.289) (0.297) (0.291) (0.344) (0.411) (0.423) (0.421) (0.39) Observations 533 531 530 528 525 522 518 510 502 498 486 474 R2 0.98 0.912 0.876 0.808 0.374 0.375 0.455 0.401 0.024 0.049 0.058 0.071 0.726 0.655 0.569 0.433 0.114 0.111 0.098 0.098 RMSE 0.084 0.093 0.102 0.113 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 24: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 60-Month Ahead Forecast Horizons) – British Pound/USD Dependent Variable: Log of Dollar-Sterling Exchange Rate k-months ahead 13 4 6 9 12 16 24 32 36 48 60 DM Constant 0.000 -0.0001 -0.0001 -0.0003 -0.0006 -0.001* -0.0016** -0.003*** -0.005*** -0.006*** -0.008*** -0.006*** (0.000) (0.0001) (0.0001) (0.0002) (0.0004) (0.0006) (0.0007) (0.0012) (0.0017) (0.0019) (0.0024) (0.0018) Log($/£) 0.987*** 0.945*** 0.922*** 0.876*** 0.812*** 0.749*** 0.659*** 0.476*** 0.306*** 0.236*** 0.054 0.014 (0.095)APRIL 2018|InFER 45 (0.008) (0.025) (0.032) (0.044) (0.056) (0.063) (0.069) (0.08) (0.085) (0.088) (0.093) Constant 0.007 0.028** 0.04** 0.064*** 0.096*** 0.129*** 0.176*** 0.271*** 0.359*** 0.396*** 0.489*** 0.505*** (0.005) (0.014) (0.018) (0.024) (0.031) (0.034) (0.037) (0.042) (0.044) (0.046) (0.047) (0.048) Observations 533 531 530 528 525 522 518 510 502 498 486 474 R2 0.98 0.91 0.872 0.797 0.129 0.08 0.005 0.000 0.024 0.049 0.059 0.073 0.703 0.615 0.503 0.284 0.134 0.135 0.133 0.127 RMSE 0.088 0.099 0.11 0.127 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

RESEARCH Transitioning now to a discussion of the pound sterling forecasts, I begin with the monthly analysisand then transition into the key discussion of annual forecasts using the Bank of England dataset. Theevolution of ������������������������ coefficients is like that of the Japanese yen forecasts. Figure 25: Evolution of Coefficients for USD/GBP Forecasts - Monthly Frequency - HAC Error Barsβk 1 Lagged USD/GBP XR P/P* 0.8 0.6 10 20 30 40 50 60 0.4 k-months 0.2 0 -0.2 -0.4 -0.6 -0.8 0 Both coefficients mirror one another in relative contribution, as observed previously, with a steadylinear decline in the contribution of past exchange rate realizations that becomes negative shortly beyondthe 2-year ahead forecast horizon. Unlike other exchange rate series, the hybrid model generatesstatistically significant negative coefficients for the lagged spot rate for the duration of the forecasthorizon, which broadly reach larger magnitudes than any other series either. Similarly, there is an upwardlinear trend exhibited by the theory coefficient ������������������������ representing increasing contribution through the 4-year ahead forecast of the USD/GBP exchange rate, peaking at a value of approximately 0.76. Followingthis, the forecasts through the fifth-year exhibit modest decreases in the contribution of the theory—thelong-term trajectory beyond this point can be examined, somewhat, in the annual forecasts in the nextsection. With these results, the inclusion of a theory component that serves as a fundamental for exchangerate deviations to self-correct about can unambiguously improve upon the random walk for medium-term exchange rate forecasts, with the effect becoming most prominent at longer time-horizons. Thiseffect is robust to the choice of currency about which the exchange rate is anchored—while eachcoefficient series exhibits unique characteristics reflective of the underlying economic relationshipbetween currencies, the broader trends are consistent across all four hybrid models.46 InFER|ISSUE 1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting Figure 26: Model Fit for USD/GBP Forecasts - R2 and Root Mean Squared Error1.2 R-squared RMSFE 1 0.140.8 0.120.6 0.10.4 0.080.2 0.06 0.04 0 0.02 0 0 10 20 30 40 50 60 k-lagsR-squared RMSFE In the case of forecast accuracy/model fit for the monthly USD/GBP forecasts, R2 again begins nearto 1 and decreases as the forecast horizon increases, dropping to a low of 3.72 around the 3-year aheadforecast and then recovering slightly to 0.4 by the end of the forecasting sample. As exhibited in the otherexchange rate forecasts, the explanatory power of the hybrid theory model decreases as the forecasthorizon increases, despite the continued statistical and economic contribution of the theory componentat these horizons. RMSE exhibits near the exact same trajectory of the other three currencies, risingrapidly through the first 2-years of k-step ahead forecasts, peaking at 0.114 and then declining somewhatto 0.098 at the end of the forecast horizon. Despite the somewhat unintuitive results borne out in theestimation of the theory coefficients, the monthly pound sterling forecasts exhibit, on average, the lowestRMSE of the forecasts in question and, unlike those of the Swiss franc and Canadian dollar, seems tostabilize in terms of forecasting accuracy and fit, with less indication of an interminable deterioration ofthe model as the forecast horizon increases. As with the other forecasted exchange rates, the hybrid modelcontaining the theory component reliably outperforms the univariate autoregressive model in terms offorecast accuracy and explanatory power as soon as 2-months ahead. The difference in forecast accuracy,furthermore, is statistically significant at 1-year ahead forecasts per the results of the Diebold-Marianotests.6 Broadly speaking, each series of exchange rate forecast exhibits the same general trajectory for bothforecasting accuracy and coefficient evolution. The role of purchasing power parity, which serves as thefundamental in this context, through the ������������������������ coefficient, becomes more economically and statisticallysignificant as the forecast horizon increases. Conversely, the contribution of past exchange raterealizations (which serve as a proxy for the random walk from previous literature) declines in the presenceof the fundamental at these horizons. While not all series exhibit an unequivocally positive linear trend6 Refer to Figure 24 above for results of Diebold Mariano tests for USD/GBP exchange rate forecasts. APRIL 2018|InFER 47

in the ������������������������ coefficients, this behavior is widely exhibited in all currencies through at least the first 3-yearahead forecast horizon, which constitutes a lag of 36 months—this behavior is summarily mirrored inthe random walk component coefficients in all cases, which serves as a justification for our choice ofspecification which implies that the two will contribute to the forecast opposite of one another byconstruction. The consistency of these results across currencies suggests the specification and, byextension, the fundamental’s improvement upon the random walk, is robust to exchange rate selection. In all forecast series, I observe similar trends for model fit and forecasting accuracy measured by R2and RMSE. On one hand, R2-values are highest at the lowest displacements in forecast horizon andunequivocally decrease as that horizon increases. The pace at which this deterioration in explanatorypower occurs, as well as the resulting value after the 5-year ahead forecast horizon is currency specific.RMSE, on the other hand, increases rapidly as the initial forecast horizon increases and then, seems tostabilize as the horizon becomes increasingly long-term. Projections of RMSE could be neatly fit with alogarithmic curve, with rapid deterioration of forecast accuracy observed immediately, and a seeminglyterminal value of error exhibited at some horizon in the future with respect to a given currency. These results suggest that, despite the contribution of the purchasing power parity fundamental inthe forecast specification increasing with forecast horizon, the relative performance of the modeldeteriorates across all currencies. I suspect, however, this is less a repudiation of the model itself and morea reflection of the challenges of forecasting exchange rates at such large displacements—despite theforecast horizon extending to only 5-years ahead, such a forecast encompasses 60-months of lagged datato develop the forecast. It is not terribly surprising that the quality of the model suffers somewhat. I findit more comforting that, in most cases, the effect does not seem permanent. Generally, explanatorypower and accuracy stabilize throughout the forecast horizons—more research would be appropriate todetermine how long these measures would remain stable for. Based on the results of the forecasts, I consider the evolution of the theory coefficients acrosscurrencies to be a sufficient justification for an improvement upon the random walk that is robust tounderlying exchange rate currency choice. To further bolster these results, and demonstrate theimprovement that including purchasing power parity represents in this context, I conduct the sameanalysis with a univariate autoregressive model containing only lagged exchange rates as the independentvariable to serve as a baseline for comparison of model fit and forecasting horizon. In all cases, the hybridmodel outperforms the univariate autoregressive model in terms of R2 and RMSE almost immediately(at either the 1-month ahead or 2-month ahead forecast horizon). The contribution of the past exchangerate data, in this specification, deteriorates both economically and statistically as the forecast horizonincreases. Further, Diebold-Mariano tests of comparative forecast accuracy imply that, in all exchangerate forecasts, the difference in forecast accuracy is statistically significant, and in favor of the hybridmodel, at around the 1-year ahead forecast horizon.48 InFER|ISSUE 1