Dutch disease dynamics reconsidered

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European Economic Review

journalhomepage:www.elsevier.com/locate/euroecorev

Dutch disease dynamics reconsidered ^R

Hilde C. Bjørnland

^a

, Leif Anders Thorsrud

^a

, Ragnar Torvik

^b,∗

aCentre for Applied Macroeconomics and commodity Prices (CAMP), BI Norwegian Business School, Norway

bNorwegian University of Science and Technology, and Centre for Applied Macroeconomics and commodity Prices (CAMP), BI Norwegian Business School, Norway

a r t i c l e i n f o

Article history:

Received 1 October 2018 Accepted 28 July 2019 Available online 16 August 2019 JEL classification:

C32 E32 F41 Q33 Keywords:

Dutch disease Resource movements Learning by doing

Analytics of multidimensional dynamic systems

Time-varying VAR model

a b s t r a c t

Inthispaperwedevelopthefirstmodeltoincorporatethedynamicproductivityconse- quencesofboththespendingeffectandtheresourcemovementeffectofoilabundance.

Weshowthatdoingsodramaticallyalterstheconclusionsdrawnfromearliermodelsof learningbydoing(LBD)and theDutchdisease.Inparticular,theresource movementef- fectsuggeststhatthegrowtheffectsofnaturalresourcesarelikelytobepositive,turning previousgrowthresultsintheliteraturerelyingonthespendingeffectontheirhead.We motivatetherelevanceofourapproachbytheexampleofamajoroilproducer,Norway.

Empiricallywefindthattheeffectsofanincreaseinthepriceofoilmayresembleresults foundintheearlierDutchdiseaseliterature,whiletheeffectsofincreasedoilactivityin- creasesproductivityinmostindustries.Therefore,modelsthatonlyfocusonwindfallgains duetoincreasedspendingpotentialfromhigheroilprices,wouldconclude– incorrectly basedonouranalysis– thattheresourcesectorcannotbeanengineofgrowth.

© 2019TheAuthor(s).PublishedbyElsevierB.V.

ThisisanopenaccessarticleundertheCCBY-NC-NDlicense.

(http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

In1969Norwaydiscovered off-shoreoilintheNorthSea.Since then,theoilsectorhasbeenoneofthekeydriversof growth,crowdinginmanyoilrelatedindustriesthat,overtime,havedevelopedadvancedknowledgeonhowtooperatein deepwatersunderharshclimateconditions,seee.g. BjørnlandandThorsrud(2016).Likewise,the recentNorth American shalerevolutionhasturnedtheUnitedStatesinthespaceofonlya fewyearsintotheworldlargestoilproducer.Techno- logicaldevelopmentsindrillingandfrackingsincetheturnofthiscenturyhaveunlockedthehugereservesthatlietrapped inshalerock.TheoilboomseemstohavebenefitedlocalindustriesintheU.S.,andtherehasbeennocrowdingoutofthe manufacturingsectorsofar,seee.g.AllcottandKeniston(2018)forsomerecentempiricalevidence.Incontrast,incountries suchasAngolaandVenezuela,decadesofoilabundancehaveledtolowerproductivityandincomelevels,seee.g.Mehlum etal.(2006).

R This paper is part of the research activities at the Centre for Applied Macroeconomics and commodity Prices (CAMP) at the BI Norwegian Business School. We thank the editor Isabelle Mejean and three anonymous referees, and many seminar participants, in particular Knut Are Aastveit, Ida W. Bache, Drago Bergholt, Herman van Dijk, Odd-Helge Fjeldstad, Junior Maih, Knut A. Mork, Øistein Røisland, Øystein Sjølie, Rob Vigfusson, Cynthia Wu, and Egon Zakrajsek. The usual disclaimers apply.

∗ Corresponding author.

E-mail addresses: [email protected] (H.C. Bjørnland), [email protected] (L.A. Thorsrud), [email protected] (R. Torvik).

https://doi.org/10.1016/j.euroecorev.2019.07.016

0014-2921/© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.

( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Fig. 1. Stylized facts. (a) Shows the employment share in traded sectors, normalized to 1 in 1970. (b) Reports the productivity level in the overall economy, normalized to the Norwegian level in 1970. Source: Statistics Norway, Statistics Sweden and authors own calculations.

Inthispaper weaim tounderstandwhy, contrarytothe traditionalmodels oftheDutch disease,theeffects ofoilin countriessuchasNorway, andmorerecentlytheU.S.,havebeensofavourable.We arguethatincorporatingthe dynamic productivityconsequencesofpetroleumrelatedindustriesiskeytounderstandthis,andthatexistingtheoriesoftheDutch diseasehavetobeextended,aswediscussinthefollowing.

One of the most influential explanations of the Dutch disease is that of the Learning By Doing (LBD) models of van Wijnbergen (1984a), Krugman (1987) and Sachs and Warner (1995). According to theseapproaches, a country that discoversoilisessentiallyinreceiptofaforeignexchangegift.Thegiftincreasesincome,andwithtradedandnon-traded goodsboth beingnormalgoods,theincrease indemandpushesworkersoutofthetradedsector andintothenon-traded sector;theincreaseddemandfortradedgoodscanbesatisfiedbyusingtheforeignexchange gift,whiletheincreasedde- mandfornon-tradedgoodscanonlybesatisfiedbyhavingalargershareofthelabourforceproducingnon-tradedgoods.

Thisstructuraltransformationoftheeconomy,however,meansthatlabouristransferredfromstrongtoweakLBDsectors.

Economicgrowthispusheddown.

Whilethesetheoreticalapproachescanexplainthenegativeeconomicdevelopmentsobservedincountriessuch asAn- golaandVenezuela,theyfailtodescribewhatisgoingoninoilproducingcountriessuchasNorway.Thiscanbeillustrated bycomparingtheeconomicdevelopmentofNorwaywiththatofitsneighbourSweden,amajoroilimporter.Asseenfrom panel (a) inFig.1, theshare ofemployment inthetraded sector hasfallenconsiderably fasterin Norwaythan ithas in Sweden.ThisisfullyconsistentwiththetheoriesofDutchdiseasebyvanWijnbergen (1984a),Krugman(1987)andSachs andWarner(1995).Panel(b),however,showsthatdespitethisdecline,labourproductivitygrowthhasbeenconsiderably higherinNorwayrelativetoinSweden.And,thisholdsirrespective ofwhetheronelooksattheNorwegianeconomyasa whole,orexcludetheoilsector(denotedMainlandinthegraph).MostobserverswouldagreethatalthoughNorwayinitially hadverylimitedknowledgeofoffshoredrillingandpetroleum technology,theexperienceithasgainedasanoilproducer formorethan 40yearsis oneofthe mainreasonsforNorway’s favourableeconomic development.Forexample,Norway hastodayahighlyskilledandproductivepetroleumrelatedindustry,andtheknowledgecreatedbythisindustryisoneof themaincontributors tothehighlevelsofincomeenjoyedinNorway,againseeBjørnlandandThorsrud (2016)forsome empiricalevidence.

However, it hasnot always beenthisway. In theearly years, foreigncompanies dominatedexploration andwere re- sponsiblefordevelopingthecountry’sfirstoilandgasfields.Yetgradually,andasaresultofadeliberatepolicy requiring national participation, the country gained experience and wasable to adapt its traditional engineeringskills from ship- buildingtothedevelopmentofoilexplorationanddrillingtechnologiesabletowithstandconditionsatseaandonlandin Norway. Theseexperiences andadvancesintechnology haveextendedthe extractableamountofoil andgasinNorway’s petroleumreserves,transformingNorwegiansfrompassiverecipientsofwindfallgainsintoexportersoftechnicalknowledge on aglobalscale.In fact,thestockofknowledge builtup bythe oilindustry duringtheseyearshas,we wouldcontend, beenofsignificantbenefittomanyotherindustries.

WhydidthetheoriesofLBDandtheDutchdiseaserunashore?Wesuggestinthispaperthattheydidsobecausethey exclusivelyincorporated theproductivitydynamics ofthe spendingeffect,butfailedtotake intoaccountthe productivity dynamicsoftheresourcemovementeffect.Asdescribedingreaterdetailbelow,weformalizethisargumentby construct- ing adynamicthreesector modelthat incorporatestheproductivitydynamicsfromthe spendingaswell astheresource movementeffect.ThemodelpredictionsarethentestedusingdataforNorway.

Indeed, alreadythe influentialcontributions of Corden andNeary (1982)and Corden (1984) hadasa main emphasis thatbecominganoilproducerwouldaffectthegeneralequilibriumofanation’seconomythroughthespendingeffect– oil

meansmoreincomeandthushigherdemand– andthroughtheresourcemovementeffect– factorsofproductionneedto betransferredtotheoilsector.Whenthesemodelswereappliedtodynamicsettingsbyincorporatingknowledgecreation, however,thenewmodelsdevelopedincorporatedthespendingeffect,butnottheresourcemovementeffect.Thisholdstrue notonlyforthemodelsofvanWijnbergen(1984a),Krugman(1987)andSachsandWarner(1995),butalsolatermodelsof LBDandtheDutchdiseasesuchasthoseby Gylfasonetal.(1999),Torvik(2001) andMatsenandTorvik(2005).Infact,to thebestofourknowledge,nosinglemodelintheliteratureincorporatesproductivitydynamicsoftheresourcemovement effect.

Tostudythisdevelopmentweneedtounderstandtheroleofoilrelatedindustryasanengineforgrowth,which,inturn, requirestheapproachesofvanWijnbergen(1984a),Krugman(1987),SachsandWarner(1995),Gylfasonetal.(1999),Torvik (2001)andMatsenandTorvik(2005)toincludearesourcemovementeffect.Togiveanexample,textilemanufacturingused tobean importantindustry inNorway;itislessso today,becausetheoilrelatedindustry hastakenits place.While one mightcertainlybelievethatthetextileindustryhasstrongerknowledgecreationthannon-tradedsectors,itwouldbediffi- culttoarguethatexperienceintextileproductionhasstrongerproductivityeffectsthanexperienceindeepseatechnology.

Anapproach that focusessolelyonthe productivitydynamicsofthe spending effect,whileignoring theproductivitydy- namicsoftheresourcemovementeffect,islikelytofocusontheleastimportantproductivitydynamics,whileoverlooking themostimportantones.

Toinvestigateempiricallythepotential productivityspilloversandthedynamicadjustmentafteroilmarketshocks,we estimateatime varyingVectorAutoregressive(VAR)modelforamajoroilproducer(Norway)torecoverstructuraldistur- bances,anduselocal linearprojectionsto trace out the productivityresponses acrossa broad setofsectors. Inthe VAR modelwe includethree variables; globalactivity,real oilprices andoilactivity, withassociated structuralshocks,global activityshocks,oilpriceshocksandaresourceboom, all motivatedby thetheoretical modelpresentedhereandfindings intherecentoil-macro literature.Importanttoourset-up istheseparationofa windfallgain duetoresourcemovement andspending effects.Thisallowsthedomestic economytoresponddifferentlytoawindfallgain duetoincreasedactivity inthepetroleumsector(i.e.,thediscoveryofnewproductivefieldsorincreasedextractionrates)andawindfallgaindueto higheroilprices.GlobalactivityisincludedintheVARmodelmainlytocontrolforinternationalbusinesscycleconditions thatcanaffectboththeoilpriceandthepetroleumsector.Thisallowsusinturntoidentifytwooilmarketshocks:aglobal activityshockandan oil priceshock, both of whichincrease the realpriceof oil,though withpotentially very different macroeconomicimplicationsfortheotherindustries intheresourcericheconomy. Finally,theVARisspecified withtime varyingparameterstoallowforchanges(overtime)intheproductivitydynamicsduetolearning,whilealsocontrollingfor changesinthevolatilityoftheshocks.

Althoughthe empiricalstrategy is simple,ourresults are striking.A resourceboomthat increases productivity(value addedperworker)intheoilandgasrelatedindustries,increasesproductivitysignificantlyinnearlyallindustries,including manufacturing.Hence,valueaddedper workerincreaseswiththeoilboom,aspredictedbythetheorymodelinasetting oflearningbydoing intheoilserviceindustries,andspillsovertothe otherindustries.Incontrast,wefindnosuchpro- ductivityspilloversfollowinganoilpriceshock.Hence,modelsthatfocusonwindfallgainsduetoanincreaseinspending potentialresultingfromhigheroilprices,wouldlikelyconclude(incorrectly) thattheresourcesectorcannot bean engine ofgrowth.

Wenote thatNorway, andmanyothercountries, haveintroducedpetroleum funds,whichfurther strengthenstheim- portanceoffocusingmoreontheresourcemovementeffectrelativetothespendingeffect.Inparticular,amainaimofsuch fundsisto decouple,andlimit, currentspending fromoilincome.Thus, incountrieswithpetroleum fundsthespending effectbecomeslessimportantrelativetotheresourcemovementeffect,inlinewithourempiricalfindings.

InadditiontotheliteratureonLBDandDutchdisease,ourpaperisrelatedtofourotherstrands oftheliterature.First, we relate toseveral recentpapers, usingcross-sectional data,that document strongpositive spillovers tothe restof the economyfollowingoildiscoveries,inparticularthe recentfracking boominNorthAmerica, seee.g.Weber (2012),Allcott andKeniston(2018),Beineetal.(2015),Feyreretal.(2017)andGiljeetal.(2016).Despitedifferentmethods,areasofstudy andtimeframes,theresultspresentedintheserecentempiricalpapersstandincontrasttothepredictionsofthedominat- ingtheoretical modelsofvanWijnbergen (1984a),Krugman(1987)andSachsandWarner (1995),butare fullyconsistent withthetheoreticalpredictionsofourmodel.AllcottandKeniston(2018) developaninteresting modelwhere,likeinour model,aresourceboommayincreaseproductivity.Unlikeours,theirmodelisofaclosedeconomywithmigrationbetween counties. Aresourceboomstimulates migration intothe boomingcounty, andthusincreases theiravailable labourforce.

Ifthereareagglomerationeffects, inthesense thatproductivitygrowthishigherthemore labourthere isinacounty, a resourceboommaythuspushproductivityup.TheLBDeffectofresourcemovementsintheir model,unlikeinours,pulls inthedirectionofdecreasedtradedsectorproductivity.Intheirmodeltradedsectoremploymentdecreases,andsincethere isnolearningspilloversfromothersectors,theproductivityinthesectoralsodecreases.¹

Second,ourpaperrelates totheliterature ofvander PloegandVenables(2011,2013) whostudy optimalspending of resourceincomeindevelopingcountries.Inthesepaperstheeconomy(orasectorwithintheeconomy) isconstrainedby capital,such thatto extractamorefavourableeffectfromthespendingofoilincome,theeconomy,ora sectorofit,will

1Nevertheless, although our model is very different from Allcott and Keniston (2018) , the mechanisms they focus on are consistent also with our approach. For example, if we also had the effect that a resource boom increases the amount of available labour, then the positive productivity effects on which we focus would be strengthened.

first have to expand. Although ours is a very different model, whereproductivity dynamics are endogenous, a common featureofourapproachandthesepapersisthattheeffectsofoilactivityareconditionalontheinitialsectoralstructureof theeconomy.

Third,byfocusingonthechallengesexperiencedbyhighlyvolatileresourceprices,ourpaperrelatestocontributionsby vanderPloegandPoelhekke(2009),LeongandMohaddes(2011)andRobinsonetal.(2017)thatpointtodifferentchannels bywhichresourcepricevolatilitycouldhurtanoilproducingeconomy.Noneoftheseapproachesincorporateproductivity dynamicsfromthe resourcemovement effect;i.e., themain mechanismsinourmodel,nor dothey analysethe dynamic effectsofoilandgasboomsonoilrelatedindustries.

Fourth,ourpapercontributestotheliterature ontheresourcecurse.Awellestablishedresultinthisliterature,seee.g.

Mehlumetal.(2006)andBoschinietal.(2007),isthat resourceabundanceincreasesaggregateincomewheninstitutions arestrong,butdecreasesaggregateincomewheninstitutionsareweak.Althoughwedonotmodelinstitutionaldifferences betweencountriesperse, ourmodelclarifies apossiblemechanismforthisfindingthat hasnot previouslybeen pointed out. When institutions are weak, oil abundance willmost likelynot result inthe developmentof a domestic oil service industry.In such countries, therefore,the spending effectof resourceabundance maybe the dominantone. In countries withstronginstitutions,ontheotherhand,adomesticoilserviceindustryismorelikelytodevelop.Inthesecountries,the resourcemovementeffectthereforecomesintoplay.Sincethelattereffect,inourmodel,ismorelikelytoincreaseincome than theformereffect,thisis onepossible explanationof thedivergingeffects ofresourceabundance betweencountries withweakandwithstronginstitutions.Sowhileoilactivitymaycontributetogrowthine.g.NorwayorintheU.S.,itmay belesslikelytodosoine.g.VenezuelaorinAngola.Inthesecountries,aswellasinothercountrieswithweakinstitutions, theoilservicesaretypicallyimportedfromabroad.

Therestofthepaperisorganizedasfollows.InSection2wesetupathreesectormodelthatexplicitlyincorporatesado- mesticoil(service)sectorfacilitatingtheextractionofoil.Weallowforendogenousproductivitygrowthinallthreesectors:

thenon-tradedsector;thetradedsector;andtheoilrelatedsector.InSection3wediscussthestaticeffectsinthemodel.

Section4looksatthedynamicequilibriumandsteadystategrowth,andshowsthatevenifthedynamicsaregovernedby fivedifferentialequations,thedynamicscanbestudiedanalytically,withoutresortingtosimulations.Section5thenanaly- sesthedynamicsofanincreasedoilpriceandofincreasedoilactivity.InSection6wepresenttheempiricalapplicationand results.Section7concludes.Someoftheanalyticaldetailsandderivations ofthedynamicpartofthemodelarerelegated totheappendix.

2. Themodel

In thissection,we develop a modelof an oileconomy which,inaddition to oilextraction,includes productionofoil servicesasnecessaryinputstothe extractionofoil,productionofnon-tradedgoods,andproductionoftraditionaltraded goods. We leteach good be producedin a separate sector. Thissector structure isassumed fornotational purposesonly andiswithoutlossofgeneralityinsofarasnothingpreventsgoodsgroupedindifferentsectorsfrombeingproducedbythe samefirm.ThemainnoveltyofthemodelistoextendtheearlierliteratureonlearningbydoingandtheDutchdiseaseby incorporatingthe resourcemovement effect,endogenousproductivitydynamicsinthe productionofall goods,aswell as thepossibilityoflearningspillovers.

Wethusconsideraneconomyconsistingofthreesectors,andwetermthesectorthatproducesinputsnecessaryinoil extractiontheoil servicesector.We denotetheoilservicesector byS,the non-tradedsector byN,andthetradedsector byT.The sizeofthelabourforceisnormalizedtounity,andateachpointintimet employmentintheoilservicesector isdenoted lt,employment inthenon-traded sectornt,and, givenfull employment,² employment inthetradedsector by 1−l_t−n_t.WedenotetheoutputofsectoriattimetbyX_it,andtheproductivityofsectoriattimetbyH_it,i∈{S,N,T}.

Theoilindustry dependsontheservicesoftheoilservicesector,andateachpoint intimethelabourusedintheoil servicesectorincreasesinthequantityofoilextracted,and(giventhequantityextracted)decreasesintheproductivitylevel ofthesector.DenotingtheoilextractionmeasuredintradedsectorproductivityunitsattimetbyR_t,implyingthatH_TtR_t is theoilextractionmeasuredintradedsectorgoodsunits,employmentintheoilservicesectorisgivenby

lt=

α

HSt

HTtRt, (1)

with

α

≥0,andwhere _H^α

St is thelabourrequirementforeach unit ofoilextraction.Ahigherproductivitylevel intheoil servicesectorimpliesalowerlabourrequirement.Thehigher

α

^{is,thestrongertheresourcemovementeffectofoilactivity.}

The standard two-sectormodel witha traded andnon-traded sector, that assumes away the resource movement effect, arisesasthespecialcaseofthemodelwhere

α

=0.

Productioninthenon-tradedsectorisgivenby

XNt =HNtf

(

ⁿt

)

, f

(

ⁿt

)

>0, f

(

ⁿt

)

<0, (2) andproductioninthetradedsectorby

XTt=HTtg

(

¹−nt−lt

)

, g

(

¹−nt−lt

)

>0, g

(

¹−nt−lt

)

<0. (3)

2Throughout we assume full employment. For an analysis of the effects of resource booms on unemployment, see van Wijnbergen (1984b) .

Weallowforlearningbydoinginallsectors,aswellaslearningspilloversbetweenthem.DenotingH˙_St asthederivativeof H_St withrespecttotime,andsoon,theproductivitydynamicsaregovernedbythefollowingthreedifferentialequations:

H˙St

HSt =qlt+

δ

Nunt+

δ

T

v (

¹−nt−lt

)

, (4)

H˙Nt

HNt =unt+

δ

Sqlt+

δ

T

v (

¹−nt−lt

)

, (5)

H˙Tt

HTt =

v ₍

1−nt−lt

)

+

δ

Sqlt+

δ

Nunt. (6)

Intheseequationsthethreefirsttermsontherighthandside;qlt,unt,and

v

(¹−nt−lt),representthedirectlearningby doingeffectsintheoilservicesector,thenon-tradedsector,andthetradedsector,respectively.Weassumethatq,u,v≥0, rulingoutthepossibilityofnegativelearningbydoing.Theremainingtermsontherighthandsidesofthesethreeequations representlearningspillovers, where

δ

Sqlt,

δ

Nunt,and

δ

T

v

(¹−nt−lt)^{arethelearningspilloversfromtheoilservicesector,} thenon-tradedsector,andthetradedsector,respectively.Weassume that0≤

δ

i≤1,i∈{S,N,T},wherethefirstinequality rulesoutthepossibilityofnegativelearningspillovers,andthesecondinequalityrulesofthepossibilityofindirectlearning effectsdominatingdirectlearningeffects.

ThetraditionalmodelsoflearningbydoingandtheDutchdiseaseariseasspecialcasesofthesemoregenerallearning mechanisms;allthepreviousmodelsassumethat

α

=0,andinadditionvanWijnbergen(1984a)andKrugman(1987)as- sumethatq=u=

δ

S=

δ

N=

δ

T=0,SachsandWarner (1995)andMatsenandTorvik (2005)thatq=u=

δ

S=

δ

N=0and

δ

^T=1,andTorvik(2001)thatq=

δ

^S=0.Thus,theearlierliteratureonlearningbydoingandtheDutchdiseasehasfocused exclusivelyondifferentproductivitydynamicsarising fromthe spendingeffect.We extendthe literatureby incorporating theresourcemovementeffect.³

Consumersallocatetheirspendingbetweentheconsumptionofnon-tradedgoodsC_Ntandconsumptionoftradedgoods C_Tt according to a CES utility function. Each consumeris too small to take intoaccount how her consumption demand affects the productivitygrowth ofthe aggregate economy. We normalize the numberof consumers to one, andthe per periodutilityfunctionUtofthisconsumerisgivenby

Ut=

σ σ

^−1C

σ−1

Ntσ +

σ

σ

^−1C

σ−1

Ttσ ,

σ

^>0,

where

σ

^{isthe(constant)elasticityof}substitution.

Attimet,thetotalvalueofproductionintheeconomyisgivenbythesumofincomefromtheproductionofnon-traded andtradedgoods,plusthetotalincomefromoilextraction.ThetotalincomeYt oftheeconomymeasuredintradedsector goodsunitsattimetisgivenby

Yt=PtXNt+XTt+QtHTtRt, (7)

whereP_t istherealexchangerate, i.e.,thepriceofnon-tradedgoodsrelativetotradedgoods,andQ_t istheworldmarket realoilprice,i.e.thepriceofoilrelativetotradedgoods.In(7)wehaveincorporatedthattheincomefromtheoilservice sectorplustheremainingnetincomefromoilextraction,equalsgrossincomeQtH_TtRtinoilextraction.

The realexchange rate isendogenous, whilethe real oilprice is takenas exogenous by oursmall open economy, as both theoil priceand theprice oftraded goods are assumedto be givenat theworld market. Since there areno (net) financialnorrealassets,incomemustequal consumptionateachpoint intime, andthe demandfornon-traded goodsis, consequently,givenby

CNt= Yt

Pt+P_t^σ. (8)

3. Staticequilibrium

Inthissectionwesolvethemodel,determinethestaticequilibrium,andinvestigatetheeffectsofanincreaseintheoil priceQ_tandanincreaseintheoilactivitylevel,R_t.Thiswillclarifytheconnectionsto,andthedifferencesfrom,theexisting

3As in the earlier literature of learning by doing with heterogeneous productivity dynamics in different sectors, we abstract from real capital. The reason is, as in these papers, that we would then have too many differential equations for the system to be analytically possible to solve. Note, however, that this is less limiting than it might appear at first sight. Consider, for instance, sectoral production functions homogeneous of degree one in effective labour and real capital, and let the required rate of return on investments be given exogenously from the world market. Then, in steady state, the effective labour- capital ratio will be uniquely determined, implying that if productivity has increased, then real capital has increased by the same rate. Thus, taking into account real capital will, in steady state, imply that the effects of learning by doing become more important, as increased productivity also induces a proportional change in real capital. Thus, if anything, abstracting from real capital implies that the effects of learning by doing is stronger than our theory model predicts.

a b

Fig. 2. Static Equilibrium. (a) Shows the effect of: Increased oil price (A to B), increased oil activity (A to C), and higher productivity in traded versus non-traded production (A to C). (b) Shows the effect of higher productivity in traded versus oil service production (A to B).

literature.An oilpriceshock,aswe havemodeledit,isolates thespending effectofoil income.⁴ An oilactivityshock,on theother hand,alsointroducestheresourcemovement effectofoilincomeinthestaticmodel.Byhavingbothoilprices andoilactivityasexogenousvariablesinthemodel,thespendingeffectcanthusbeseparatedfromtheresourcemovement effectinatransparentway.Note,however,thatthisdoesnot precludethepossibilityofhavingoilactivityrespondtothe oilprice.Thiscanbestudiedinthemodelbyinvestigatingthecombinedeffectofanoilpriceandanoilactivityshock.⁵

Ateachpointintimet,thelevelsofproductivityinthethreesectorsaredeterminedbyhistory,andastaticequilibrium isdefinedasasetofrelative pricesandfactorallocationsthat satisfythefollowing constraints:thesupplyofnon-traded goodsequalsthedemandofnon-tradedgoods;thesupplyoflabourequalsthedemandforlabour(whichhasalreadybeen incorporatedsincelabourinthetradedsectorisgivenby1−n_t−l_t whichensuresfullemployment);consumersmaximize utilityandproducersmaximizeprofitsgiventhefactorpricesandpricesoffinalgoods.

Starting withtheconstraintthatdemand mustequalsupplyofnon-traded goodsX_Nt =C_Nt,we insertfrom(2)onthe lefthandside,andontherighthandsidefirstfrom(8),thenfrom(7)andfinallyfrom(3),(2)and(1)toyield

HNtf

(

ⁿt

)

=PtHNtf

(

ⁿt

)

+HTtg

1−nt−_H^α_StHTtRt

+QtHTtRt

Pt+P_t^σ .

Definingtherelativeproductivities

λ

^t≡_H^HTt

Nt, and

γ

^t≡ HTt

H_St,

thenon-tradedmarketbalanceequationmayberewrittenasafunctionofrelative(andnotabsolute)productivities:⁶ Pt=

_g

₍

_1−n

t−

αγ

tRt

)

^+QtRt f

(

^nt

)

_σ¹

λ

t^1σ. (9)

Since therelativeproductivities arepredetermined, thisequationis oneequation inthetwo endogenousvariablesPt and nt,depictedasthedownwardslopingsolidcurvedenotedNNinFig.2(a).

Toseetheunderlyingintuition,startout withsupplyequaltodemandinthenon-tradedsector.From suchanequilib- rium,assumethat employmentinthe non-tradedsector increases.Forequilibriumtobe reestablishedatthisnewlabour

4The property that an oil price shock has no resource movement effect holds in our static model, since in the static model an increased oil price (for a given level of activity in the oil sector) only affects income, not employment, in the oil service sector. As we discuss below when we study transitional dynamics, however, there is an endogenous dynamic resource movement effect from an oil price shock.

5In most resource rich countries, and in Norway, research extraction is mainly a political decision. Moreover, when an oil platform is in operation, it operates under full capacity. In such settings, it seems realistic to assume that the oil price and oil activity are both exogenous. However, the recent shale boom in the U.S. is very different, for two reasons. First, the production is more flexible (due to the technology used), see Bjørnland et al. (2017a) . Second, unlike in other countries the property rights to subsoil assets in the U.S. are not public, but private. As a consequence, oil activity can be increased without active political decisions. Thus, in the economic and institutional setting in the U.S., a higher oil price is likely to affect oil activity. That said, in the empirical model applied in Section 6 , we allow oil activity to respond to oil price shocks with a lag of one period.

6Also, note for later reference that with these definitions, it follows that the productivity in the oil service sector relative to the non-traded sector is given by ^H_HNt^St = ^λ_γ^t_t.

allocation,arealexchangeratedepreciation(lowerP_t)musttakeplace,sincehigherdemandisrequiredtobringthemarket backtobalanceatthenewandhighersupply.Therealdepreciationachievesthisbyshiftingdemandtowards non-traded goods.

Astaticequilibriumalsorequiresfirmstomaximizeprofitsandthelabourmarkettobeinequilibrium.Thisimpliesthat thevalueofthemarginalproductivityoflabourmustbeequal(tothewage)intradedandnon-tradedproduction:

PtH_Ntf

(

^nt

)

=H_Ttg

(

¹−nt−

αγ

^tRt

)

. Thisconditioncanberewrittenas

Pt=g

(

¹−nt−

αγ

^tRt

)

f

(

^nt

) λ

^t. (10)

Ateachpointintime,thelabourmarketequilibrium(10)canberepresentedbyapositiverelationshipbetweenthereal exchangerateP_tandtheemploymentshareinthenon-tradedsectorn_t,asdepictedbythesolidcurveLLinFig.2(a).Tosee theintuitionforthis,startoutinlabourmarketequilibrium, andthenallowtherealexchangeratePttoappreciate.Atthe newrealexchangerateproductioninthenon-tradedsectorhasbecomemoreprofitablerelativetoproductioninthetraded sector.Toagainequalizethevaluesofthemarginalproductivitiesatfullemployment,employmentinthenon-tradedsector hasto increaseandemployment in thetraded sectordecrease. Thisdecreases themarginal productivityoflabourin the non-tradedsector,andincreasesthemarginalproductivityinthetradedsector,againequalizingthevaluesofthemarginal productivitiesoflabouratthenewrealexchangerate.

TheinitialuniquestaticequilibriumisrepresentedbytheintersectionofthetwosolidcurvesatpointAinFig.2(a).⁷

3.1. StaticDutchdisease– increasedoilpriceandoilactivity

Wenow investigatetheresponseofthe staticequilibriumtoan increasedoilpriceandoilactivity. Westart withthe former.Whatisoftenreferred toasDutchdiseaseisshowninFig.2(a),asthemovementfromtheinitialequilibriumAto thenewstaticequilibriumB.Asseen from(9)and(10),Qt affectstheNNcurve, butnottheLL curve.Ahigheroilprice increasesincome, pushing demandfor non-traded goods up, andthus for anygiven labourallocation, the priceof non- tradedgoods hastobehighertoensuremarketbalance.TheupwardshiftintheNNcurvetothedottedcurveinFig.2(a) producesthetwocommonsymptomsassociatedwiththeDutchdisease:higheremploymentinthenon-tradedsectorand arealexchangerateappreciation.

Consider now theeffect ofincreased oil activityRt, due, forinstance, tonew discoveries ofoil, ornewtechnological opportunitiesmakingnewformsofextractionpossible(suchasdeepseadrillingintheNorthSea,theshalerevolutionin theUS,orimprovements enablingnotonly verticaldrilling buthorizontaltoo).Throughout weconsider thenaturalcase wherethesepossibilitiesareprofitable,i.e.,thattheoilpriceissufficientlyhighthatQt−g

αγ

^t>0.Ifthiswasnotthecase, theoilisofsolittlevaluethattheincomelostbecausealternativeproductiondecreasesishigherthantheincomegained byextractingtheoil.Insuchacase,incomeishigherbynotusingthenewopportunities,andthusthestaticequilibriumis notaffected.Theonlyinterestingcasetostudyisthereforethatinwhichthenewoilactivityisactuallyprofitable.

Consider first theNN curve. When oil extractionRt increases,again the demandfor non-traded goods increases,and againthisspendingeffectofoilincomeshiftstheNNcurveup,asinFig.2(a).⁸ThesizeoftheverticalshiftintheNNcurve isfoundfrom(9),andgivenby

1

σ

Qt−g

αγ

^t

f

(

^nt

)

_g

₍

_1−nt−

αγ

^tRt

)

+QtRt

f

(

^nt

)

σ¹−1

λ

t^1σ = 1

σ

Qt−g

αγ

^t

g+QtRt

Pt>0.

Turningnext to the LLcurve, a higherRt alsoshifts thiscurve up;higher oilactivity requiresmore labourinthe oil servicesector.Foragivenemploymentshareinthenon-tradedsectorn_t,therealexchangerate(andthewagelevel)must increase,makingproductioninthetradedsectorlessprofitable,andtherebyenablingincreasedlabouruseintheoilservice sector.TheshifttothedottedLLcurve inFig.2(a)representstheresourcemovementeffectofhigheroilactivity.Thesize oftheverticalshiftintheLLcurveisfoundfrom(10),andgivenby

−

αγ

^tg

f

(

^nt

) λ

^t=−

αγ

^tg

g Pt>0.

7Note that the same static equilibrium applies with an infinite number of possible distributions of income, profits and wages between oil extraction income and the oil service sector. The only relevant variable for the mechanisms we are studying is the total income from the oil service industry plus the remaining income from oil extraction (after they have purchased their inputs from the oil service industry). Thus, without any loss of generality, we do not need to specify the interactions between the oil service industry and oil extraction. One possibility, among many, is that there is full mobility of labour into and out of the oil service sector, implying that the wage in this sector equals the wage in the other sectors. The price of the output from the oil service sector then determines how much profit will remain in the sector (possibly zero), and how much income will remain from oil extraction after purchasing services from the oil service industry. In any case, the sum of income from the oil service sector and oil extraction measured in traded goods units is given by Q tH TtR t.

8In Fig. 2 (a), for simplicity, we have drawn the same size of the shift in the NN curve as when we studied a higher oil price above, although, in general, the size of the shifts differ.

ThetotaleffectisanewstaticequilibriumatpointCinFig.2(a).Thespendingeffectandtheresourcemovementeffectboth contribute toa realexchangerateappreciation. Asa consequence,employmentinthe tradedsector mustunambiguously fall,againbothasaresultofthespendingeffectandtheresourcemovement effect.Employmentintheoilservicesector increases,andemploymentinthenon-tradedsectorincreasesifthespendingeffectdominates,butdecreasesiftheresource movement effect dominates. Which ofthese effects dominates is determined by the size ofthe vertical shift in the NN andLLcurves.Ifthe formeristhelargest,then thespending effectdominatesandemployment inthenon-traded sector increases.Ascanbeseenfromtheexpression,thespendingeffectdominateswhen(andonlywhen)

σ

^<Qt−g

αγ

^t

−

αγ

^tg

g g+QtRt

Thus, thespendingeffectwillalways dominateprovidedtheelasticityofsubstitution

σ

^{and/or thelabour}requirementin theoilservicesector

α

^{issufficientlysmall,whiletheresourcemovementeffectwillalwaysdominateiftheoppositeisthe}

case.

Tosummarizetheeffectsinthestaticmodel,ahigheroilpricemeanshigheremploymentinthenon-tradedsector,lower employmentinthetradedsector, anda realexchange rateappreciation.Higher oilactivityalsomeanslower employment inthetradedsectorandarealexchangerateappreciation.Employmentintheoilservicesector increases,whiletheeffect onemploymentinthenon-tradedsectorisambiguous.

3.2. Effectsofrelativeproductivity

Before turningto the dynamicsofthe model,we needto findout how thestaticequilibrium respondsto changesin relativeproductivities.Considerfirstthecaseofahigher

λ

^t,i.e.higherproductivityinthetradedrelativetothenon-traded sector.Asseenfrom(9)theverticalshiftinNNisgivenby

1

σ

_g

₍

_1−nt−

αγ

^tRt

)

+QtRt

f

(

^nt

)

_σ¹

λ

t^1σ−1= Pt

σλ

^{t >0,}

whilefrom(10)theverticalshiftinLLisgivenby g

(

^1−nt−

αγ

^tRt

)

f

(

ⁿt

)

⁼ Pt

λ

^{t >0.}

Thus,theshiftsdepictedinFig.2(a)canalsorepresentthiscase.Asseen,higherproductivityinthetradedversusthenon- tradedsectorappreciatestherealexchangerate(theBalassa–Samuelsoneffect)and,whentheelasticityofsubstitutionfalls shortofunity,increasesemploymentinthenon-tradedsectorwhiledecreasingitinthetradedsector.Whentheelasticity ofsubstitution exceedsunity, thisshiftdecreasesemployment inthenon-traded sectorwhileit increasesemploymentin thetradedsector.

Consider nextthe caseofa higher

γ

t,i.e.higherproductivityinthetraded sectorrelative totheoilservicesector. As seenfrom(9)theverticalshiftinNN,depictedbythedottedcurveinFig.2(b),isgivenby

1

σ

−g

α

^Rt

f

(

ⁿt

)

_g

₍

_1−n

t−

αγ

^tRt

)

^+QtRt f

(

ⁿt

)

¹_σ−1

λ

t^1σ = 1

σ

−g

α

^Rt

g+QtRt

Pt<0,

whilefrom(10)theverticalshiftinLL,againdepictedbythedottedcurveinFig.2(b),isgivenby

−

α

^Rtg

f

(

ⁿt

) λ

t= −

α

^Rtg

g Pt>0.

TheintuitionunderlyingthedownwardshiftintheNNcurveisthatahigher

γ

^t(foragiven

λ

^{t)meansthattheoilservice}

industry hasbecome lessproductive relativeto therest oftheeconomy, increasing theamount oflabourneededin this sector, andthusreducing productionintherestoftheeconomyaslesslabourisavailable.Inturn,thisimpliesdecreased income,adropindemand,andlowerrelativepricesofnon-tradedgoods.TheintuitionfortheupwardshiftintheLLcurve isthatwhentheoilserviceindustryneedsmorelabourrelativetotheother sectors,thentheincreaseddemandforlabour pusheswagesup,andtherefore,foragivenemploymentshareinthenon-tradedsector,thepriceP_t mustincrease.

AsseenbycomparingtheinitialpointAtothenewpointBinFig.2(b),theresultofahigher

γ

^{tisaloweremployment}

sharein thenon-traded sector, while theeffect onthe realexchange rateisuncertain, reflectingopposite forces derived fromthemarketbalancefornon-tradedgoodsandfromtheequilibriumconditionforthelabourmarket.

Wecansummarizetheemploymentresponseinthestaticmodelby

nt =n

(

^Qt,Rt,

λ

^t,

γ

^t

)

,with dn

dQt >0, dn

dRt >0iff

σ

^{< Qt−g}

αγ

^t

−

αγ

^tg

g g+QtRt, dn

d

λ

^{t >0iff}

σ

^<1,_d^dn

γ

^{t <0. (11)}

Fig. 3. Phase diagram for relative productivities.

4. Dynamicequilibrium

Havingexamined thestaticversion ofthemodel, we nowstudythe dynamicpropertiesof themodel. Westart with fivedifferentialequationsanddiscusshowthemodelcanneverthelessbesolved analytically,beforeexploringthestability propertiesofthedynamicsysteminAppendixA.Wethereafterdiscussthesteadystateofthemodel.

Byinsertingfortheemploymentresponseinthestaticmodel,thedynamicmodelcanberepresentedbyfivedifferential equations:

λ

˙^t

λ

t = H˙Tt

HTt −H˙Nt

HNt, (12)

γ

˙^t

γ

^{t =}

H˙_Tt HTt −H˙_St

HSt, (13)

H˙St

HSt =q

αγ

^tRt+u

δ

^Nn

(

^Qt,Rt,

λ

^t,

γ

^t

)

+

v δ

^T

(

¹−n

(

^Qt,Rt,

λ

^t,

γ

^t

)

−

αγ

^tRt

)

, (14)

H˙Nt

HNt =un

(

^Qt,Rt,

λ

t,

γ

t

)

+q

δ

S

αγ

tRt+

v δ

T

(

¹−n

(

^Qt,Rt,

λ

t,

γ

t

)

−

αγ

tRt

)

, (15)

H˙Tt

H_Tt =

v ₍

1−n

(

^Qt,Rt,

λ

^t,

γ

^t

)

−

αγ

^tRt

)

+q

δ

S

αγ

^tRt+u

δ

Nn

(

^Qt,Rt,

λ

^t,

γ

^t

)

, (16) Althoughwehavefivedifferentialequations,wewillseethatitisentirelypossibletoinvestigatethedynamicsanalytically withoutresortingto simulations.To studythedynamicequilibrium, aswell asthetransitional dynamics,we firstreduce thedimensionsofthissystembystudyingthedynamicsofrelativeproductivities.Afterfindingthesteadystate,aswellas thetransitionaldynamicsoftheserelativeproductivities,wecanthen,aswewillsee,backouttheremainingdynamicsfor absoluteproductivityandincomegrowth.

Inserting(14),(15)and(16)in(12)and(13)thedifferentialequationsforrelativeproductivitiesread

λ

˙^t

λ

^{t =}

v ₍

1−

δ

^T

) (

¹⁻ⁿ

(

^Qt,Rt,

λ

^t,

γ

^t

)

⁻

αγ

^tRt

)

^−u

(

¹⁻

δ

^N

)

ⁿ

(

^Qt,Rt,

λ

^t,

γ

^t

)

^{, (17)}

and

γ

˙t

γ

^{t =}

v ₍

1−

δ

T

) (

¹−n

(

^Qt,Rt,

λ

^t,

γ

^t

)

−

αγ

^tRt

)

−q

(

¹−

δ

S

) αγ

^tRt. (18) Asteadystate ofthissystemisdefinedasasituationinwhich ^λ_λ^˙t

t = ^γ_γ^˙t_t =0,andthus,byimplication,thatproductivity growthisbalancedbetweensectors.

InAppendix A, we show that the phase diagram maybe represented asin Fig.3. The dynamicequilibriumis estab- lished attheintersection ofthe two curvesin Fig.3. Here,both

λ

^{t and}

γ

^{t are constantover time, andthus all sectoral}

productivitiesgrowbythesame(yetunknown)rate.

Considernowthecaseinwhichtheeconomyhasarrivedatasteadystate.Inserting

λ

˙^t=0in(17),andsolvingfor

αγ

^tRt

yields

αγ

^tRt =1−n

(

^Qt,Rt,

λ

^t,

γ

^t

)

−u

(

¹⁻

δ

N

)

ⁿ

(

^Qt,Rt,

λ

t,

γ

t

)

v ₍

1−

δ

T

)

^{. (19)}

Inserting

γ

˙^t=0 in(18), then substituting for

αγ

^{tRt from(19), andsolving for n(Qt, Rt,}

λ

^t,

γ

^{t), provides the non-traded}

steadystateemploymentshare,whichwedenotebyn^∗,as n^∗=

v ₍

1−

δ

^T

)

v ₍

1−

δ

^T

)

^+u

(

¹⁻

δ

^N

)

⁺¹q

v(¹−δT)^u(¹−δN) (¹−δS)

. (20)

Notethat thesteadystateemployment shareisconstant,and, inparticularthatitis increasinginq,i.e.,thestrongerthe learning by doing effect inthe oil service sector. The intuition is that stronger learning inthe oil service sector pushes productivity up, reducing the labour requirementin the sector. The increased productivity inthe oil service sector thus allowsforincreasedproductionandincomeintherestoftheeconomy.Someofthisincreasedincomepotentialisusedto consumemorenon-tradedgoods.Tobringforwardthesegoods,employmentinthenon-tradedsectorincreases.

Wearenowequippedtofindsteadystategrowth.First,notethat insteadystatetheemploymentshareisgivenbyn^∗, andthatin(17)and(18) ^λ_λ^˙t

t = ^γ_γ^˙t_t =0.Insertingthisimpliesthatthe righthandside of(17)equalstherighthandside of (18),whichimpliesthatinsteadystate

q

αγ

^{tRt= u}

⁽

¹⁻

δ

^N

)

^n∗

(

¹⁻

δ

^S

)

^.

Inserting this inone ofthe equations (14),(15) or(16) provides the steady state growth rateof productivity,which we denotebyg^∗,as

g^∗=n^∗

u

(

¹⁻

δ

^N

)

(

¹⁻

δ

^S

)

^+u

δ

^N+

v δ

^Tu

⁽

¹⁻

δ

^N

) v ₍

1−

δ

^T

)

.

Notethat,aslabourallocationsareconstantinsteadystate,g^∗isalsothegrowthrateofincome.

Since n^∗ is increasing inq,it followsthat thesteady state growthis increasing in thelearningspillover from theoil servicesector.Thus,thestrongerthelearningpotentialintheoilservicesector,themorethissectorservesasanengineof growth.Italsofollows,asn^∗isindependentofbothQ_t andR_t,thatthesteadystategrowthrateisindependentofresource abundance,whetheritismeasuredbythepriceoftheresourceorthequantityoftheresource.

Thus,anysteadystate effectoftheoilpriceQt ortheoilactivityRt mustcomeviathelevelofincome,notits growth rate.

5. DynamicDutchdisease

Wenowinvestigatethesteadystateeffectsofahigheroilpriceandofincreasedoilactivity.InSection5.1wefirstana- lyzehowanincreasedoilpriceaffectssteadystaterelativeproductivities,beforeturningtothemoreimportantquestionof howabsoluteproductivitiesandincomelevelsareaffected.Totraceoutthelatter,wemuststudythetransitionaldynamics fromtheold tothenewsteadystate.InSection 5.2we undertakethesameexercise forincreasedoilactivity. Aswewill see,thesteadystateeffectsofahigheroilpricedifferconsiderablyfromtheeffectsofincreasedoilactivity,and,moreover, the effectsofincreasedoil activitycontrastwiththe resultsinthe previous theoriesoflearningby doing andtheDutch disease.

Inasteadystatewithconstantoilpriceandoilextractionwehavefrom(18)andabovethat

γ

^∗R∗=u

⁽

¹⁻

δ

N

)

^n∗

q

α (

¹⁻

δ

S

)

^{. (21)}

Noteinparticularthatthisequationexplicitlydeterminesa uniquevalueof

γ

^{∗R∗that mustholdinanysteadystate,irre-}

spectiveofQ^∗,R^∗,and

λ

^{∗,sincen∗is}independentofallthesethreevariables.(Thesameresultcan,ofcourse,beestablished byusing(17)).

Next,combining(9)and(10),andinsertingthesteadystatelabourshare,weget

_g

₍

_1−n∗−

αγ

^∗R∗

)

+Q^∗R^∗ f

(

^n∗

)

σ¹

( λ

^∗

)

^σ1−1=g

(

¹−n^∗−

αγ

^∗R∗

)

f

(

^n∗

)

^.

Insertingfrom(21)for

γ

^{∗R∗wefindthat}

g

1−n^∗−

α

^uq⁽α(^1−1δ−^Nδ⁾Sⁿ)^∗

+Q^∗R^∗ f

(

^n∗

)

σ1

( λ

^∗

)

^σ1−1=g

1−n^∗−

α

^uq⁽α(^1−1δ−^Nδ⁾Sⁿ)^∗

f

(

^n∗

)

^{. (22)}