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The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es:Observatorium on Ex hange RateEmerson Fernandes MarçalCEMAP-EESP-FGVNovember 30, 2012

Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es:Talking points1 The E onomi s of MisalignmentsEx hange Rate Misalignments.2 Obervatorium on Ex hange Rate:Approa hs for estimating RER misalignment.E onometri Issues.3 Some Results:Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next Steps4 PPP and World Pri e IndexMethodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.5 Main Referen es:Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Ex hange Rate Misalignments.Talking Stru ture1 The E onomi s of MisalignmentsEx hange Rate Misalignments.2 Obervatorium on Ex hange Rate:Approa hs for estimating RER misalignment.E onometri Issues.3 Some Results:Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next Steps4 PPP and World Pri e IndexMethodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.5 Main Referen es:Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Ex hange Rate Misalignments.Dening ex hange rate misalignment.Dieren e between a tual real ee tive ex hange rate and a long termfundamental;Ex hange rate misalignment estimative an dier due to:the e onomi models used to hoose the fundamentals variablesthat drives real ex hange rate in the long run;dieren es in e onometri s te hniques.The onstru tion of misalignment estimative relies on some empiri al andtheoreti al hoi es;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Talking Stru ture1 The E onomi s of MisalignmentsEx hange Rate Misalignments.2 Obervatorium on Ex hange Rate:Approa hs for estimating RER misalignment.E onometri Issues.3 Some Results:Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next Steps4 PPP and World Pri e IndexMethodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.5 Main Referen es:Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Option 1: Ee tive equilibrium ex hange rate based onfundamentals.Fundamental Real ex hange rate is al ulated using ae onometri model:Cointegration te hniques based on sele ted series asso iatedwith fundamentals;Some possible hoi es of the fundamentals variablesan indi ator of relative tradeable and non-tradeableprodu tivity [4;net international investment position as GDP share. [2;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Option 2: Bilateral ex hange rate based on fundamentals.Converting real ee tive ex hange rate misalignment inbilateral misalignments:From real ee tive ex hange rates estimative al ulated underoption 1 for a group of ountries it is possible to al ulatebilateral misalignments for ea h ountry using Alberola,Cervero et al. (1999) [2 ;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Option 3: Bilateral ex hange rate misalignments based onPur hasing Power Parity.Re ent advan es in the literature suggest that PPP may hold after all for some urren ies;Some studies using not temporally aggregated data suggests that PPPmay hold in the long run. (Taylor, 2010 [8);Strong eviden e that PPP holds for dollar-pound sterling parityusing onsumer pri e deators and long time series; (Ahmad &Craighead [1)The possible hoi e of the pri e index to run the analysis are:Consumer pri e index;produ er pri e index;gross domesti pri e deator;What to do if PPP does not hold?Control for Balassa Samuelson ee t;De ompose ex hange rate in permanent and transitory omponents;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Option 4: Sustainable urrent a ount.Current a ount approa h:This methodology has two steps in order to onstru t a misalignmentmeasure.The level of urrent a ount equilibrium is al ulated using panelte hniques;The dieren e between a tual real ex hange rate and the level ofreal ex hange ompatible with the desired urrent a ount result isthe estimated misalignment;This approa h is very losed related to the IMF ma roe onomi equilibrium approa h.One variant of this approa h is the External Equilibrium Approa h. After hoosing some ben hmark value for the Net Foreign Asset, the level ofreal ex hange rate ne essary to rea h this value is estimated and the levelof misalignment an be al ulated (Maya e Ha, 2012 [7);Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Talking Stru ture1 The E onomi s of MisalignmentsEx hange Rate Misalignments.2 Obervatorium on Ex hange Rate:Approa hs for estimating RER misalignment.E onometri Issues.3 Some Results:Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next Steps4 PPP and World Pri e IndexMethodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.5 Main Referen es:Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Dynami Time Series E onometri ModelsThe usual approa h onsists in estimating a traditional VECM:([5, 8, 2, 3, 4, 5, 1)∆Xt = Γ1∆Xt−1+ ...+Γk−1∆Xt−k+1+α[ β ′ µ]

[ Xt−11 ]

+ εt (1)where εt is a ve tor of innovations not serially orrelated, Ω is a matrixthat ontains all varian es and ovarian es and [Γ1, ...Γk−1,α,β ,µ ] areaparameters to be estimated.Xt ontains the real ex hange rate index and the sele tedfundamentals;The estimation of the long run parameters an be done usingalternative te hniques;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.De omposing series into permanent and transitory omponentsThere is a literature that dis uss how to de ompose the series intopermanent and transitory omponents:Xt = β⊥( ′β⊥)−1 ′Xt + ⊥(β ′ ⊥)−1β ′Xt (2)Pt ≡ β⊥( ′β⊥)−1 ′Xt = A1 ′Xt = A1ft (3)Tt ≡ ⊥(β ′ ⊥)−1β ′Xt = A2β ′Xt = A2zt (4)The ommon approa h onsists in using Gonzalo e Grangerde omposition, ([8), where = α⊥.All matri es are obtained from the estimated parameters of the model (1).Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Is the estimative pre ise? How to address this question.The pre ision of the estimative must be known;The methodology to onstru t onden e bands must avoidfalse misalignment dete tion:Alberola, Cervero et al. (1999) uses Johansen asymptoti results to onstru t onden e errors; ([3)Our approa h onsists in using Cavaliere et al. (2011)bootstrap method to onstru t onden e bands;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.How to transform real ee tive ex hange rate misalignmentsinto bilateral ones.A base ountry must be hosen;Using the fa t that real ee tive ex hange rate onsists in aweighted average of bilateral rates, it is possible to linkee tive real ex hange rate misalignment to bilateralmisalignments;The trade weights for a numerous ountries are ne essary touse this approa h;Further details an be found in Alberola, Cervero et al. (1999)[2;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Approa hs for estimating RERmisalignment.E onometri Issues.Some re ent eviden e on PPPRe ent PPP debate Taylor and Taylor. ([2);Temporal aggregate data seriously distort PPP test ([8);Taylor ([1) tests the PPP using a sample of 20 ountries usinga entury sample and obtains eviden e in favor of PPP;Other studies using Taylor series:Kapetanios, Shin and Snell test is applied to Taylor data set([3);KPSS onrmatory test was applied to Taylor data with goodresults in favour of PPP hypothesis ([3).Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsTalking Stru ture1 The E onomi s of MisalignmentsEx hange Rate Misalignments.2 Obervatorium on Ex hange Rate:Approa hs for estimating RER misalignment.E onometri Issues.3 Some Results:Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next Steps4 PPP and World Pri e IndexMethodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.5 Main Referen es:Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsMultilateral misalignment:


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsNorth Ameri an Ee tive Real ex hange rate misalignment.RER Fundamentals

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The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsBrazilian Real Ee tive Ex hange rate misalignment.

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The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsBilateral Real ex hange rate misalignment - dolar as base urren y.


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsPPP: One Example - UK and USA.UK-USA mean=100

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The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next StepsWork to do:Periodi al Releases of the misalignments estimative usingdierent approa hes;Working on al ulating other methodologhies;Working on understading ee ts of misalignments on tradeows: Is there eviden e of se toral hysteresis?Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.Talking Stru ture1 The E onomi s of MisalignmentsEx hange Rate Misalignments.2 Obervatorium on Ex hange Rate:Approa hs for estimating RER misalignment.E onometri Issues.3 Some Results:Fundamental Approa h.Bilateral Ex hange rate MisalignmentPur hasing Power Parity Strikes Ba k?Next Steps4 PPP and World Pri e IndexMethodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.5 Main Referen es:Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.Motivation to onstru t PPP based on world index.Early test of PPP in the eighties and nineties failed to obtain eviden e infavur of PPP hypothesis;Low power of unit root test;Time aggregation problem;Too short data set in time dimension;No linearity in adjustment towards long run equilibrium;In re ent studies in the literature some authors obtained eviden e in favorof PPP using longer data set:Taylor (2000) - time aggregation problem auses overestimation ofhalf-life of the sho ks;Longer time data set eviden e in favor of PPP;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.How world pri e index was onstru ted.The world pri e index onsists in a trade weighted average of onsumer pri e index for a group of nations that ontains the ountries with the biggest trade volumes ex epting OPECmembers: Ptworld =N∑i=1witP it (5)where wit denotes the trade share of ountry i in period t inthe index;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.How the PPP index was al ulated.The PPP index was al ulated using the following formula:PPP−WTCt j =

(

∑Ni=1witE ijtPtworld )P jt (6)where Eit denotes the nominal ex hange rate expressed as thequantity of urren y of ountry i is ne essary to buy one unitof urren y j;P jt denotes the onsumer pri e index of ountry j at time t;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.Sour es of the dataData Sour es:Consumer Pri e Indexes: IFS-IMF database;Ex hange rate Data;Trade Volumes: IMF;Taylor Data set;Frequen y:Monthly and Anual Data;From 1960 to 2012 and from 1900 to 2012;Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.Summary of Unit Root test - Se ular Time Span.


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.Summary of Unit Root test - Shorter Time Span.


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.WTC- United States Curren y against world Index


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.WTC- Se ular - United States Curren y against world IndexUnited States Fundamentals

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The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.PPP - Brazilian Curren y against world Index


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.PPP - Brazilian Curren y against world IndexPPP-WTC-Brazil 2 std 1 std

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The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es: Methodology to al ulate World Pri e Index:Some Preliminary Results.Challenges to over ome.Problems to be addressedProblems to be addressed:Investigate the time series properties of these indexes;Investigate alternative options su h as Gross Domesti Deators;The N-1 problemTo al ulate and ompare dierent de ompositions;


The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es:Sele ted Referen es:Ahmad, Yamin & Craighead, William D., 2011. "Temporal aggregation and pur hasing powerparity persisten e," Journal of International Money and Finan e, Elsevier, vol. 30(5), pages817-830, September.Alberola, E., S. Cervero, H. Lopez, and A. Ubide (1999): "Global Equilibrium Ex hange Rate:Euro, Dolar, 'Ins', 'Outs' and Other Major Curren ies in a Panel Cointegration Framework,"Washington: IMF.BAHMANI-OSKOOEE, M.; KUTAN, A.; ZHOU, S. A entury of pur hasing power parity: furthereviden e. E onomi s Bulletin, vol. 6, n. 31, 2007.Balassa, B. (1964): "The Pur hasing Power Do trine: A Reappraisal," Journal of Politi alE onomy, 72, 584-596.Engle, R. F., and C. W. J. Granger (1987): "Co-Integration and Error Corre tion: Representation,Estimation and Testing," E onometri a, 55, 251-276.Faruqee, H. (1995): "Long-Run Determinants of the Real Ex hange Rate: A Sto k FlowPerspe tive," IMF Sta Paper, 42, 80-107.Froot, K. A., and K. Rogo (1995): "Perspe tives on Ppp and Long-Run Real Ex hange Rates,"Amsterdam: North-Holland.Gonzalo, J., and C. W. J. Granger (1995): "Estimation of Common Long-Memory Components inCointegrated Systems," Journal of business and E onomi s Statisti s, 13.Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es:Sele ted Referen es:Johansen, S. (1988): "Statisti al Analysis of Cointegration Ve tors," Journal of E onomi Dynami s and Control, 12, 231-254.−−− (1990): "Maximum Likelihood Estimation and Inferen es on Cointegration - withAppli ations to the Demand for Money," Oxford Bulletin of E onomi s and Statisti s, 52,169-210.−−− (1995): Likelihood-Based Inferen e in Cointegrated Ve tor Autoregressive Models. Oxford:Oxford University Press.Johansen, S., and K. Juselius (1992): "Testing Stru tural Hypothesis in a MultivariateCointegration Analisys of the Ppp and Uip for Uk," Journal of E onometri s, 53, 211-224.Johansen, S., R. Mos oni, and B. Nielsen (2000): "Cointegration in the Presen e of Stru turalBreaks in Deterministi Trends," E onometri Journal, 1(3).Kubota, M. (2009): "Real Ex hange Rate Misalignments: Theoreti al Modelling and Empiri alEviden e," York: University of York.Maya, E.; Ha, N. (2012); Corre ting real ex hange rate misalignment : on eptual and pra ti alissues; World Bank Poli y Resear h Working Paper - 6045.TAYLOR, A.T., Potential Pitfalls for the Pur hasing-Power-Parity Puzzle? Sampling andSpe i ation Biases in Mean-Reversion Tests of the Law of One Pri e, E onometri a Volume 69,Issue 2, pages 473498, 2001Emerson F. Marçal, November 30th, 2012.

The E onomi s of MisalignmentsObervatorium on Ex hange Rate:Some Results:PPP and World Pri e IndexMain Referen es:Sele ted Referen es:TAYLOR, A.T. A entury of pur hasing-power parity. Review of E onomi s and Statisti s, n. 84,2002.TAYLOR, A.T.; TAYLOR, M.P. The pur hasing power parity debate. Journal of E onomi Perspe tives, n. 18, 2004.WALLACE, F. Nonlinear unit root tests of PPP using long-horizon data. E onomi s Bulletin, vol.6, n. 33, 2008.Emerson F. Marçal, November 30th, 2012.

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