Modern Time Series Analysis in Forest Products Markets

219 Pages·1999·4.62 MB·English

by  F. Helles

MODERNTIMESERIES ANALYSIS IN FORESTPRODUcrS MARKETS
FORESTRY SCIENCES
Volume58
Thetitlespublishedinthisseriesarelistedattheendofthisvolume.
Modem Time Series Analysis
in Forest Products Markets
Editedby
JENS ABILDTRUp, FINN HELLES.
PER HOLTEN-ANDERSEN,
JAKOB FROMHOLT LARSEN
and
BO JELLESMARK THORSEN
The Royal Veterinary and Agricultural Uhiver$ity,
Department ofE conomics and Natural Resources,
Copenhagen, Denmark
SPRINGER-SCIENCE+BUSlNESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-6005-9 ISBN 978-94-011-4772-9 (eBook)
DOI 10.1007/978-94-011-4772-9
Printed on acid-free paper
All Rights reserved
©1999 Springer Science+Business Media Donlrecht
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint ofthe hardcover 1st edition 1999
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
Contents
Foreword . vii
Preface
Berek, P . ix
Introduction
Helles, F., P. Holten-Andersen, J Abildtrup, JF. Larsen, andB.1. Thorsen:
IntroducingUnit Roots and Cointegration 3
ChapterI InternationalPriceRelationsand ExchangeRates
Thorsen,B.1.:
SpatialIntegrationintheNordicTimberMarkets: Long-RunEquilibriaand
Short-RunDynamics......................... 27
Hanninen, R.:
ExchangeRatePass-Throughin Finnish SawnwoodExportstoTheUnited
Kingdom 41
Hanninen, R.:
TheLawofOnePricein United KingdomSoftSawnwood Imports-A
CointegrationApproach .. .. 5S
Thorsen, B.1., J. Riis, F. Helles, and P. Holten-Andersen:
IntemationalisationofRoundwood Markets-theCaseofDenmark 69
ChapterII Demandand SupplyModels
Hansen, H., JF. Larsen, B.1. Thorsen, and J Abildtrup:
ModellingtheDanishDemandfor Roundwood Imports-aCointegration
and CommonTrendsAnalysis... .. . 85
TC'ppinen, A.:
QuarterlyModeloftheFinnish SawlogandPulpwoodMarkets-
ACointegrationAnalysis . .. 103
Chapterill Causality, Forecasting,and Expectations
Berek, P.:
EstimationinaLong-Run, Short-RunModel 117
vi
Chao, W.-S., and1. Buongiorno:
DoExports StimulateGrowth?Evidencefrom InternationalWoodpulp Data 127
Riis, 1.:
ForecastingDanishTimberPriceswithan ErrorCorrectionModel 141
Toppinen, A., S. Laaksonen, and R. Hanninen:
ForecastingInternationalPulpPriceswith ProducerInventories 151
ChapterIV CapitalAsset Evaluation
Larsen,1.F., and1. Riis:
TestingaPresent ValueModel ofForestLand 161
Larsen,1.F., and1. Riis:
ExploringSourcesofSystematicRisk inDanishForestAssetReturns 173
ChapterV ManagementImplicationsofTimeSeries Properties
Hultkrantz, L.:
TheBehaviourofTimberRentsin Sweden, 1909- 1990 187
Plantinga, A.J.:
OptimalHarvestingPolicieswith StationaryandNon-StationaryPrices:
AnOptionValueApproach 199
ListofAuthors........................................................................................................... .217
Foreword
Since 1993 a major research programme, "Stochastic Decision Analysis in Forest
Management" has been running at Department of Economics and Natural Resources, The
Royal Veterinary and Agricultural University (KVL), Copenhagen, in collaboration with
InstituteofMathematical Statistics, University ofCopenhagen(KU). The research is funded
by the two Universities; The Danish Agricultural and Veterinary Research Council; The
DanishResearchAcademy; TheNationalForestandNatureAgency; andDanishInformatics
Network in the Agricultural Sciepces (DINA).
A first international workshop in the research programme was held 5 - 8 August, 1996 at
Eldrupgaard,Denmark,withintheframeworkofacollaborationagreementbetweenUniversity
of California at Berkeley (UCB) and the Danish Universities, and funded by The Danish
Research Academy and the L0venholm Foundation.
Havingparticipated inthe workshop, ProfessorPeterBerck(UCB) suggestedthatthepapers
bepublished along withselected papers inthe samescientificfield, i.e. mainlycointegration
analysis oftime series inforestry.
Theeditors express their sincere appreciations to the many persons who havecontributed to
therealisationofthepresentbook: participantsintheresearchprogrammeandtheworkshop,
in particular Professors S0ren Johansen (KU) and Peter Berck (UCB); authors outside the
programme/workshop; reviewers of the papers not previously published, in particuler
Associate Professors Niels Haldrup (Aarhus University) and Henrik Hansen (KVL); and
finally Mrs Mette Riis and Lizzie Rohde who did the tedious work ofgiving the papers a
uniform style.
Copenhagen, October 1998.
Jens Abildtrup, FinnHelles, PerHolten-Andersen,
Jakob FrornholtLarsen, Bo JellesmarkThorsen
vii
Preface
PeterBerck
Thisvolumeistheresultoftworemarkablecollaborationsandawonderfulconference. TheUnit
of Forestry in the Department of Economics and Natural Resources at the Danish Royal
Veterinary and Agricultural University embarked on an exploration ofthe uses ofmodern
time-series techniques for solving forest economics problems. In this they were joined by
Professor Seren Johansen, a statistician renowned for his maximum-likelihood methods for
cointegrationanalysis. Thiswasanalltoorarecollaborationbetweenascholarontheforefront
ofa theoretical field and a group ofscholars "pushing the envelope" on an applied field of
knowledge. ThesecondcollaborationwasbetweentheUniversityofCaliforniaandtheRoyal
VeterinaryandAgriculturalUniversity. StudentstrainedbyProfessorJohansenandbytheUnit
ofForestry came to Berkeley to learn about resource economics. I do not know how much
resource economics they learned, but I shall be forever in their debt for teaching me about
maximum-likelihoodanalysisofcointegratedtimeseries.Theformal collaborationbetweenthe
twoUniversitiesledtotheconferenceatEldrupgaard,wheremostof thepapersinthisvolume
were presented. After several days oflistening to these papers and several long nights of
discussing them, I suggested to ProfessorHellesthat these papers would make an interesting
volume,fardifferentfromothervolumesofpapersaboutforesteconomics. Iamgratefulthathe
andhiscolleagues,PerHolten-Andersen,JensAbildtrup,JakobRiis,andBoJellesmarkThorsen,
undertookthehardworknecessarytopublishthisvolume.
Thisvolumebeginswithanexplanationoftheeconometricsofunit-rootprocesses. Itisindeed
atechnicalareabutanareaopentoanyonewithagoodknowledgeoflinearalgebra. Muchof
whatfollows inthisvolumedependsuponbutafewoftheideaspresentedinthe introduction.
Thekeyideasare: (l)theexistenceofcointegration,thatthereareseries, suchasthepricesof
thesamewoodintwotradingcountries,thatmaysteadilygainonthegeneralpricelevelyetnever
become very far from each other, (2) the corollary that two series may have no long-run
relationship, and (3) a series may be (weakly) exogenous so that it does not respond to
movementsinotherseriesinthelongrun. Manyofthepapersinthisvolumeusetheseideasto
test the relationship among price series with results such as "Swedenand Finlandactasprice
leaders..."orpulpwoodimportpricesare weaklyexogenous. Thevolume includestestsofthe
law ofone price, ofa land valuation model, ofthe importance ofunanticipated changes in
demand, and of the export-led growth hypothesis. The consequences of integration and
cointegrationformanagement,includingtheexistenceofoptionvalue, andforforecastingare
explored in other chapters. In all, there is a thorough exploration ofthe consequences of
time-series methods, particularly cointegrated time-series methods, for the analysis offorest
economicsproblems. Thereaderofthisvolumewilllearnagreatdealabouttheforesteconomies
ofNorthernEuropeand aboutthepractical use oftime-series methods. Theverymodestdata
requirementsofthesemethodsandthestrongresultsavailablehavemuchtorecommendthem.
Onreturninghomefromthe conference inEldrupgaard, Ifinallysawhowto bringrealdatato
bearonthe questionofemploymentmultipliersfrom forest activity. Icanonlyhopethatthis
volumewillbeasinspiringtothereaderastheconferenceandthesepapersweretome.
ix
Introduction
Introducing UnitRoots and Cointegration
F.Helles,P. Holten-Andersen,1. Abildtrup, J.F. LarsenandB.1.Thorsen
Abstract
Traditionalmethodsineconometrictimeseriestheoryandpracticerelyonasetofassumptions
concerningthestochasticpropertiesofthetimeseriesanalysed.Oneoftheseassumptionsisthat
thetimeseriesare(weakly)stationary,whichimpliesthatthetwo firstmomentsoftheseriesare
invarianttodisplacementsintime-atleastwhensomedeterministictrendhasbeenfilteredout
ofthe data. However, many economic time series do not satisfy this assumption - even after
deterministic 'detrending'. In particular, many time series seem to belong to a class of
nonstationaryprocessestermed integrated processes, which is the majorthemeofthe present
volume. A formaldescriptionofthemajordifferencebetweenintegratedprocessesandtheclass
ofstationaryprocesses,whichmosttimeserieseconometricshavebeendirectedtowardssofar
isthefirst topicweaddress.
1.Stationarityand UnitRootInducedNonstationarity
Avectorautoregressivemodelisused forhighlightingtheconceptsandproblemscentraltothe
statistical analysis ofnonstationary data. However, many points could be illustrated just as
preciselywithunivariateexamples.Thenotationissimilartothatusedin,e.g.Johansen(1995a).
Considerthep-dimensional stochasticprocessX;withak-orderautoregressiverepresentation,
whereweforsimplicitysetk= 1:
(I)
assuming£,- Np(O,Q).Theinitialobservations~areconditionedupon,and~ isaconstant.This
is an exampleofa vectorautoregressive process, a socalled VAR-process. The characteristic
polynomialforthisprocessisgivenby:
k
A(z) =I-LIItz; =I-II\z, (2)
;;01
sincek=1andwherezcanbeacomplexnumber.WeassumethatA(z)satisfiestheconditionthat
ifIA(z)1 =0thenIzl> 1orz=1,andbythisexcludingexplosiverootsaswellasseasonalroots
withIzl=1.Thecasewherez=Iisarootistheinterestingone,andzisreferredtoasaunitroot.
Itisinterestingbecausearootz= I producesakindofnonstationaritythatcanberemovedby
differencing. As an example, consider the case where III is the identity matrix. Clearly, the
processhaspunitrootsandX;consistsofpnonstationaryprocesses. Ifthecovariancematrixis
diagonal,theyare independent. If~ = 0thesearerandomwalks,andthe firstdifferenceofthe
3