論商業(yè)建筑活動(dòng)的長(zhǎng)期可變滯后 On Commercial Construction Activity's Long and Variable Lags

FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

OnCommercialConstructionActivity’sLongandVariableLags

DavidGlancy,RobertJ.Kurtzman,andLaraLoewenstein

2024-016

Pleasecitethispaperas:

Glancy,David,RobertJ.Kurtzman,andLaraLoewenstein(2024).“OnCommer-cialConstructionActivity’sLongandVariableLags,”FinanceandEconomicsDiscus-sionSeries2024-016.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2024.016

.

NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

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OnCommercialConstructionActivity’sLongandVariableLags*

DavidGlancyyRobertKurtzmanzandLaraLoewensteinx2

1FederalReserveBoard

2FederalReserveBankofCleveland

March27,2024

Abstract

Weusemicrodataonthephasesofcommercialconstructionprojectstodocumentthreefactsregardingtime-to-planlags:(1)plantimesarelong—about1.5yearsonaverage—andhighlyvariable,(2)roughlyone-thirdofprojectsareabandonedinplanning,(3)propertypriceappreciationreducesthelikelihoodofabandonment.Weconstructamodelwithendogenousplanningstartsandabandonmentthatmatchesthesefacts.Endogenousabandonmentmakesshort-termbuildingsupplymoreelastic,aspriceshocksimmediatelyaffecttheexerciseofconstructionoptionsratherthanjustplanningstarts.Themodelhasthetestableimplicationthatsupplyismoreelasticwhentherearemore“shovelready”projectsavailabletoadvancetoconstruction.Weuselocalprojectionstovalidatethatthispredictionholdsinthecross-sectionforU.S.cities.

Keywords:commercialrealestate,construction,timetoplan

JELClassi?cation:R33,E22,E32,L74

*ThankstotheaudienceattheFederalReserveBoardR&Sworkshopfortheirhelpfulcommentsandsuggestions.Theviewsexpressedinthispaperaresolelythoseoftheauthorsanddonotnecessarilyre?ecttheopinionsoftheFederalReserveBoard,theFederalReserveBankofCleveland,ortheFederalReserveSystem.

yPrincipalEconomist,DivisionofMonetaryAffairs,FederalReserveBoard,david.p.glancy@

zPrincipalEconomist,DivisionofResearch&Statistics,FederalReserveBoard,robert.j.kurtzman@xResearchEconomistII,FederalReserveBankofCleveland,lara.loewenstein@

2

1.INTRODUCTION

Commercialconstructionaccountsforasizableportionofprivatedomesticinvestment

(about20%)andisanimportantdriverofinvestment?uctuations.1

Commercialcon-structioninvestmentisalsowellknowntorespondslowlytoeconomicshocks(

Edge,

2007

),dueinparttoitslongplanninghorizons(

Millaretal.,

2016

).Indeed,Figure

1

plotsyear-over-yearchangesincommercialandtotalgrossprivatedomestic?xedinvestmentandshowsthatcommercialconstructionisbothmorevolatileandslowertorespondtobusinesscycle?uctuations.Ifeconomicconditionsdeteriorateoverthecourseoftheselongplanninghorizons,developersmayabandonprojectsbeforestartingconstruction.Existingworkonsucheffectsislimited,dueinparttodif?cultiesmeasuringconstructionactivitythatdoesnotoccur.

Inthispaper,weuseuniquemicrodataonthephasesofconstructionformorethan200,000U.S.commercialconstructionprojectstodisciplineatractabletime-to-planmodelofbuildingproductionwithendogenousabandonment.Ourdataincludesbothcompletedandabandonedprojects,anditincludesapanelofthephasehistoryforeachproject,allowingustoobservetheextentofandtimevariationinabandonmentfromplanning.Wedevelopthemodeltomatchthreefactsfromthemicrodata.First,commercialconstructionprojectshavelongplanninghorizons.Theaveragetimespentinplanningforprojectsthatmakeittoconstructionisabout1.5years,roughlysimilartoaverageconstructiontimes.Second,asigni?cantnumberofprojectsinplanning(around40percentonavalue-weightedbasis)areabandonedbeforebeginningconstruction.Almostallabandonmentshappenduringtheplanningstage:oftheprojectsthatmakeittotheconstructionphase,over99percentarecompleted.Third,whetherprojectsadvancefromplanningtoconstructionisstatedependent.Speci?cally,highercommercialpropertypricegrowthattheonsetofaprojectincreasestheprobabilityoftheprojectbeingcompleted.

Inthemodel,developersoptimallychoosehowmuchtoinvestinplanningstartsandwhetherprojectsthatcompleteplanningproceedtoconstruction.Projectsinplanning

1ThesourceistheBureauofEconomicAnalysis.Thenumeratoristhesumofnonresidentialandmultifamilystructuresinvestment(FREDseriesB009RC1Q027SBEAandC292RC1Q027SBEA),whilethedenominatorisFREDseriesGPDI.Notethatnonresidentialstructuresincludesotherstructuretypesthanthoseinthemicrodatainthispaper,suchasmanufacturingandpower.

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areoptionstoengageinconstructionthatdeveloperschoosetoexercisebasedonpre-vailingpropertyvaluesandbuildingcostsattheconclusionofplanning.Themodelmatchesthefactsfromthemicrodataandalsohasanimportantimplicationforthesupplyofcommercialbuildings:thenear-termresponseofconstructionactivitytopriceappreciationdependsontheavailabilityofprojectsinplanning.Priceappreciationcanaffectconstructionactivitybybothstimulatingplanningstartsandbycausingmoreprojectsinplanningtoadvancetoconstruction.Becauseplanningstartsareslowtotranslateintoconstructionactivity,thissecondchannelisthemaindriverofshort-termsupplyelasticitiesandisdependentontheavailabilityof“shovelready”projectsthatcanimmediatelybeginconstruction.

Wetestthismodelimplicationbyempiricallyexaminingcross-sectionaldifferencesintheresponseofconstructionactivitytopriceappreciation.Speci?cally,weuselocalprojec-tionstotraceouttheresponseofconstructionstartstocommercialpriceappreciationfor

metropolitanstatisticalareas(MSAs)withdifferentinitialstocksofprojectsinplanning.2

Wedemonstratethatconstructionstartsareincreasinginpricegrowth,andthisresponsedependsimportantlyonthestockofprojectsinplanning,aspredictedbythemodel.Asfurthervalidation,we?ndsimilarresultsforemploymentgrowthforthesectorsmostengagedincommercialconstructionactivity.

Inthe?nalpartofthepaper,wecalibrateandsolveastandardDSGEmodelextendedtoincludethecommercialplanningandconstructionenvironmentfromourearliersetup.Relativetothepartialequilibriummodel,theDSGEmodelallowsustoendogenizecommercialpricesandtoquantitativelyexaminethemodel’sdynamics.Weshowthatendogenousabandonmentspeedsuptheresponseofconstructionactivitytoshocks(comparedtoanequivalentmodelwithexogenousabandonment).Thishighlightshow,eventhoughplantimesarelong,investmentmaystillrespondquicklytoshocksifthereareprojectsalreadyunderwaythatareonthemarginofadvancingtoconstruction.Additionally,wedemonstratethestate-dependentnatureofhowconstructionactivityrespondstoshocks.Ifaneconomyhasalowstockofprojectsinplanning,itisless

2WeconstructthemeasuresofpriceappreciationandconstructionstartsrelativetothebuildingstockbypropertytypeandMSAsusingacombinationofdatafromCostar,RealCapitalAnalytics(RCA),andCBRESupplytrack.

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responsivetoeconomicshocksthananotherwisesimilareconomystartingatsteady-state

planninglevels.Namely,theresponseofconstructionactivityqualitativelymatchestheimpulsesfromthelocalprojectionsanalysis.

Thequantitativeworkinthispapermostcloselybelongstotheliteratureontimetobuild.Inseminalworkinthisarea,

KydlandandPrescott

(1982)layoutaninvestment

technologythatincorporatestimetobuildandintegrateitintoamacroeconomicmodel,demonstratingtherelevanceofthistechnologyformatchingkeybusinesscyclefacts.

Christianoetal.

(1996)extendthemodeltoincorporateaplanningphase—aperiodof

less-resource-intensiveinvestment—anddiscussitsroleinexplainingbusinesscyclefacts.Morerecentworkbuildson

MajdandPindyck

(1987)toanalyzehowtheoptionvalueof

delayinginvestment(OhandYoon,

2020)ordiscountrateshocks(

FernandesandRigato,

2023

)affectbuildtimes.Additionally,contemporaneousworkby

Ohetal.

(2024)shows

thatlongdevelopmenttimelinesinresidentialhousingmatterforthebusinesscyclepropertiesofhousing.Ourworkdevelopsfactsthatdisciplinetheroleofendogenousabandonmentintheplanningphaseina“timetoplan”model;inturn,constructionsrespondsmoreswiftlytoeconomicshocksinourmodelbecauseofchangesinwhetherprojectsthatcompleteplanningadvancetoconstruction.

Thispaperalsocontributestotheliteratureexaminingthecommercialconstructionsector.TheU.S.CensustracksconstructiontrendsthroughtheBuildingPermitsSurveyandtheSurveyofConstructiontoassesstheevolutionofthetimeittakestocompletetheconstructionprocessintheUnitedStates.ThesesurveysprovideimportantinsightsintotheevolutionofconstructionintheUnitedStates,withthecaveatthattheyarefocusedon

onlyresidential(asopposedtocommercial)construction.3

Thenonresidentialcommercialrealestate(CRE)constructionprocessislesswellunderstoodgiventhereishistoricallylessqualitydatainthespace.GiventhatnonresidentialCREisalargeandimportantassetclass(

Ghentetal.,

2019

),thisisasigni?cantgapintheliterature.

Theclosestcounterparttoourempiricalworkisthatof

Millaretal.

(2016).Theauthors

usesimilardatatoexaminethedeterminantsofplanninglagsforcompletedprojects,

3NotallsurveysrelatedtoconstructionfromtheCensusfocusonresidentialconstructiononly.Forexample,theValueofConstructionPutinPlaceSurveyincludesinformationonnonresidentialCREconstructionspending.Thedatausedinthispaperareusedinparttodevelopthestatisticsinthatsurvey.

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highlightingtheroleofregionaldifferencesinlanduseregulation.

DelBocaetal.

(2008)

provide?rm-levelevidencethatstructuresinvestmentissubjecttolongertime-to-planandtime-to-buildeffectsthanequipmentinvestment.Inotherwork,

Bischoff

(1970)

examinesmodelsofnonresidentialinvestmentandtheirrelationtothedata.Ourworkdemonstratesthekeyroleabandonmentplaysinthedynamicsofthesector.

Theremainderofthepaperproceedsasfollows.InSection

2,wedescribethedataand

establishthefactsoncommercialconstructionthatwewillusetodisciplinethemodel.InSection

3,wepresentapartialequilibriummodelofthecommercialconstructionprocess

thatcanmatchthesefactsandderivehowtheshort-termelasticityofbuildingsupplydependsonthestockofprojectsinplanning.InSection

4,wetestthispredictionand

demonstratethattheresponsivenessofconstructionactivitytochangesinpricesisindeedafunctionoftheplanningstock.InSection

5,weembedthePEmodelfromSection

3

inacalibratedDSGEmodelandexaminethequantitativeimplicationsofthemodel.InSection

6,weconclude.

2.FACTSONCOMMERCIALBUILDINGCONSTRUCTION

Inthissection,we?rstdescribethedata.4

Wethenprovideanoverviewoftypicalplanningandconstructiontimelinesincludinghowoftenandunderwhatcircumstancesprojectsareabandoned.Finally,wesummarizethekeystylizedfactsthatwilldisciplinethemodel.

2.1.ConstructionPhaseDataandOtherDataDetails

ThedatafromCBRE-EA/SupplyTrackrelyoninformationcollectedfromDodgeData&Analytics(DD&A).ConstructionstartsfromDD&AareusedbytheU.S.Censusaspart

oftheirmethodologyforestimatingmonthlyconstructionspending.5

Millaretal.

(2016)

4AdditionaldetailsonthedataareavailableinAppendix

A.

5Ourdataincludesdataonconstructionstartsalongwiththepre-andpost-startphasesformultifamily,hotel,of?ce,retail,andwarehouseproperties.ThemonthlyconstructionspendingdatafromtheCensusprovidesestimatesofallconstructionspendingintheU.S.,notjustthepropertytypesconsideredinthispaper.NotethattheCensususesotherdatasourcesandmethodsaswell.Themethodologyforthesurvey

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documenttimetoplaninthisdatasetthrough2010;oursamplegoesthroughtheendof2022.

Thedataincludesmonthlyinformationontheconstructionphaseforeachproject,wherethephasesare:pre-planning,planning,?nalplanning,bidding,underway,completed,deferred,andabandoned.AccordingtoCBRE,thesephasesaregenerallyde?nedasfollows.Planningstageprojectshavegenerallyalreadyhiredanarchitectthathasstartedtodrawupplans.The?rstmonthoftheunder-constructionphase(thestart)occursafteracontracthasbeensignedbetweenageneralcontractorandthedeveloper.Atthispoint,permitswouldtypicallybepulledandtheprojectshouldbreakgroundwithinafewmonths.Aprojectcanbedeferredinde?nitelyfromanyphaseinthedata.Thedatadonotincludeinformationonthereasonforthedeferral,butpossiblereasonsincludegoingoverbudget,marketconditionsworsening,or?nancingbeingpulled.A?nalstateforaprojectiseithercompletedorabandoned.Forouranalysis,wegroupprojectsin

pre-planning,planning,?nalplanning,andbiddingtogether.6

Wetreatdeferredprojectsasaseparatecategoryunlesswestateotherwise.

Alongwiththephases,thedataincludeinformationontheproperty’stype,itssquarefootage,thetotalcostofconstructionfortheproject(oranestimateforthatspendforprojectsinplanningorbidding),anddetailedgeographicinformation.

Toexaminecommercialrealestatesupplyelasticities,wealsouseinformationoncom-mercialpropertypriceappreciationfromCoStar.ThedatauseCREtransactionstoestimatepriceindexesattheproperty-typeCBSAlevel.Sincesomeofouroutcomes(e.g.,constructionemploymentgrowth)areatthemarketlevel,wetaketheaveragepriceappreciationacrosspropertytypes,weightingbytheirrespectivebuildingstockinthemarket.Afewlargecitieshavepricesreportedbymetropolitandivision;inthesecases,wetaketheaveragepriceappreciationinanMSA,weightingbythebuildingstockineachsubmarket.

canbefoundat

/construction/c30/methodology.html.

6Pre-planningprojectshavenotyethiredanarchitect,buttherehastypicallybeensomeconceptforthebuildthathasbeenannounced,while?nalplanningprojectsaretypicallyveryclosetoapprovalformovingtoconstruction.Biddingoccursaftertheplansareapprovedandtheprojectislookingforacontractwithageneralcontractor.

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2.2.Project-levelsummarystatistics

InTable

1,weshowinformationontheroughly260,000projectsinoursample.Thetop

panelpresentsinformationforthewholesample,whilethelowerpanelsdisaggregatebypropertytype.

Westartbyreportinginformationontime-to-plan(timefromplanningstarttoconstruc-tionstart),time-to-build(timefromconstructionstarttocompletion)andtime-to-complete

(timefromplanningstarttoconstructioncompletion).7

Thedatashowthatplantimesareroughlycomparabletoconstructiontimes.Onavalueweightedbasis,theaveragetimeinconstructionandinplanning(forprojectsthatmakeittoconstruction)areabout1.5yearseach.Thesetimelinestendtobelongerforlargerprojects,causingtheaveragetimetoplanandtimetobuildtobeabitunderayeareachonanunweightedbasis.Plantimesarealsomuchmorevariablethanbuildtimes.Thestandarddeviationoftime-to-planisabout16months,comparedwithabout12monthsfortime-to-buildonavalue-weightedbasis.Planningphasesforprojectsthatareultimatelyabandoned(planningstarttoabandonment)arelongeratabitabovetwoyears,likelyre?ectingtheoptionvalueofdelaysforprojectswhoseeconomicviabilityisinquestion.

Wehavetwofurtherpiecesofinformationontheproject:itsestimatedcostandsquarefootage.Themedianrealprojectcostisabout3million(2012)dollarsandthemedianbuildingsizeabout32,000squarefeet,withtheaveragesbeinghigher(atabout13milliondollarsand107,000squarefeet,respectively)duetotheright-skewednatureofthedistributionsofprojectsizesandvaluations.

Averageplantimesvarymoderatelyacrosspropertytypes,largelyre?ectingdifferencesintypicalprojectsizes.Retailandwarehousepropertieshavetheshortestaverageplanninghorizonsat11and12months,whilehotelandmultifamilypropertieshavethelongestat18and19months.Of?cepropertieshaveaverageplantimesthatareinthemiddle,withanaveragehorizonof15months.Theotherbroadpatternsdiscussedforthefullsamplealsoholdacrosspropertytypes:theaverageconstructiontimeisalwayswithin4monthsoftheaverageplanningtime,andtheaverageplantimeforabandonedprojectsisalwayslongerthanforthosethatadvancetoconstruction.

7Here,wejustcollectallplanningphasestogetherintoplanning.

8

Figure

2

showstheshareofplansthatareabandonedbypropertytype.Forthesample

ofprojectsthatconcludebytheendofthesample(i.e.,either?nishconstructionorgetabandoned),37percentareabandoned(31percentonanunweightedbasis).Acrosspropertytypes,theabandonmentraterangesfrom30percentforwarehousesto50percentforhotels.Thisresultdemonstratesthattheinitiationofacommercialconstructionprojectshouldnotbeviewedasaninvestmentthatwillinvariablyaddtothebuildingstock(withsomeuncertaindelay).Instead,enteringtheplanningphaseisanoptionthatdevelopersmaychoosetonotexercisedependingonwhattheylearnabouteitherthespeci?cprojectorbroadermarketconditionsoverthecourseoftheplanningperiod.

Figure

3

presentsadecompositionoffactorschangingthestockofprojectsacrosstime.Thenumberofprojectsinplanninginagivenyearisincreasedbythenumberofnewplanstartsanddecreasedbythenumberofprojectsthatleaveplanningduetoconstructionorabandonment.The?gureshowsthatthenumberofprojectsfellnotablyduringthe?nancialcrisisduetoacontractioninplanningstarts(whichfellbyoverhalf)andariseinabandonments(whichexceededconstructionstartsin2009and2010).TheplanningstockthenrosethroughmostoftherecoveryduetoasteadyincreaseinplanningstartsbeforecontractingduringtheCOVID-19pandemicastherateofplanningstartsslowed.

2.3.PhaseTransitionsfortheFullSampleAcrossPhases

Table

2

providesmoredetailonthedynamicswithwhichprojectsadvancethroughvariousphasesofconstruction.Speci?cally,itshowsatransitionmatrixwhereeachcell(i,j)givestheprobabilitythataprojectthatstartsinphaseiinmonthttransitionstophasejinmontht+1.Thestatisticspertaintothefullsampleofprojectsthatstartin2004orlater.Thestatisticsareunweighted,sotheycorrespondwithaprobabilitythataparticularprojectchangesstatus.Consequently,theimpliedplanspellsdiffersomewhatfromtheweightedsummarystatisticsemphasizedfromTable

1.

The?rstrowshowsthetransitionsforprojectsthatentertheperiodintheplanningphase.About93percentofprojectsinplanninginagivenmonthremaininplanningthefollowingmonth.Thisimpliesthatprojectsonaverageremainintheplanningstagefor

9

overayear,about15monthsinexpectation.8

About4percentofprojectsinplanning

advancetounderconstructioninthefollowingmonth,withabout2percentofprojectsinplanningbeingdeferredorabandonedeachmonth.

Thetransitionmatrixshowsthatoutcomesintheplanningstageareuncertain;morethanathirdofprojectsexitingplanningaredeferredorabandonedinsteadofproceedingwithconstruction.Constructionoutcomesaremuchmorecertain;only0.1percentofprojectsunderconstructionaredeferredthenextmonthandnexttononeareabandoned.About11percentofprojectstransitionfromunderconstructionpermonth,withalmostallofthoseprojectsgettingmarkedascompleted.Thisimpliesatypicaltime-to-buildofabout9months,closetotheunweightedaverageconstructiontimeinTable

1.

Deferredprojectstendtoremaindeferred,though1percentofprojectseventuallyreturntoplanning,construction,orareeventuallycompleted.Thatsaid,about3percentofdeferredprojectsareabandoned,meaningthatdeferralisnormallyaprecursortoabandonment.

2.4.DeterminantsofAbandonment

Tostudywhatcausesprojectstofailtoadvancetoconstruction,wecollapsethedatatotheprojectlevelandcreateanindicatorforwhethertheprojectevermovesfromplanningtoconstruction.Wethenlookathowcommercialpropertypriceappreciationoverthe?rstyearoftheprojectaffectsthelikelihoodofadvancingtoconstruction.

Speci?cally,werunthefollowinglinearregression:

EverCompletedi,m,t=βln(C1)+gXi,m,t+ei,(1)

whereEverCompletediisanindicatorforwhetherprojectiisevercompleted,ln(C1)

isgrowthinCostar’scommercialpropertypriceindexfortheproject’smarketmintheyearfollowingthestartofplanningt.Xiisavectorofproject-levelcontrolsincludingthelogofthebuildingsquarefootageandtherealprojectcost,aswellasMSA,property

8Theexpectedtimeremaininginagivenstagecanbeobtainedbytaking1/(1-.932).

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type,andyear-quarter?xedeffects.StandarderrorsareclusteredbyMSA.

Themainobjectofinterestistherelationshipbetweenpriceappreciationandtheproba-bilitytheprojectisevercompleted.Weseeapositiveandsigni?cantrelationshiphere.InColumn(1),weseethata10percentagepointincreaseinpropertypricesattheonsetoftheplanstartleadstoa5.7percentincreaseintheprobabilitythataprojecteventuallyadvancestoconstruction.Column(2)addsinthepropertytype,MSA,andquarter?xedeffects,whichincreasestheestimatedcoef?cientfrom5.7to10.4percent.Column(3)addsthecontrolsforprojectsizeandcost,whichresultsintheestimatetorisingto11.8percent.Theseresultsareconsistentwithadvancementtoconstruction(andconverselyabandonment)varyingwitheconomicconditions.

2.5.ASummaryoftheFacts

Althoughtheconstructiondatacontainanarrayofinterestingpatternsandinformation,weseethefollowingfactsasmostrelevantfordiscipliningamodelwherebuildingacommercialbuildingrequiresplanningandconstruction.

.Projectsspendabout1.5yearsinplanningbeforeconstructionbegins.

.Projectsarefrequentlyabandoned,typicallyduringtheplanningphase.

–About60percentofprojectseventuallyadvancetoconstructionwhileabout40percentareabandoned.

–99percentofprojectsunderconstructionarecompleted.

.Abandonmentsvarywitheconomicconditions.

3.PLANNINGMODELWITHABANDONMENTS

OurgoalistobuildamodelconsistentwiththefactsoutlinedinSection

2.5.

Inthemodel,timeisdiscrete,labeledast=0,1,2,....Thereisarepresentativebuildingproducerwhooptimallydecideshowmuchtoinvestinplanningandconstructionstarts.

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Fornow,thebuildertakesasgivenaparticularsequenceofinterestrates(rt),rental

ratesofbuildings(r),andcostsofplanningstarts(it).InSection

5,wewillembedthis

section’smodelintoageneralequilibriumbusinesscyclemodel,andthesevariableswillbeendogenouslydeterminedbyhouseholds’consumption/savingsdecisions,thesupplyanddemandforspace,andplanningstockadjustmentcosts,respectively.

Theproductionofbuildingsissubjecttotwofrictions.First,thereisastochastictimelagbeforebuildingconstructionoccurs.Speci?cally,?rmscaninvestinplanningprojects,butonlyashareλoftheseprojectscanadvancetoconstructioninagivenperiod.Whentheplanninghorizoniscompleted,?rmsdrawacostκFandcanchoosewhetherornottopayκtoproduceaunitofbuilding.Firmschoosethemaximumamountthey

arewillingtopayforaprojectκ,resultingintheconstructionofλPt__1F(κ)buildings,

wherePt_1istheplanningstockchoseninthepreviousperiod.Projectswithcostsabovethisthresholdareabandoned.

Second,?rmsfaceadjustmentcostsinstartingprojects.Thecostofinitiatingaplanning

startattimet,denotedit,isincreasingintheamountofplanninginvestment,denotedI.

Weassumetheseadjustmentcostsareexternaltothe?rm(re?ectingfactorssuchasthesupplyofpermitsratherthaninternalcapacityconstraints)andthusre?ectedinthecostofplanningstarts,whicharetakenasexogenoustothedeveloper.

Consequently,theproblemofthedeveloperisasfollows:

max

fIs,κ+s0

s

EtΣ(?si=0

κ+s

)+ss__it+sIs_λPt+s_1ZκdF(κ)),

RentalIncomelanning&Cons

subjecttothelawsofmotionfortheplanningandbuildingstock:

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Pt+s=(1-δp-λ)Pt+s-1+Is

(2)

{z

Bt+s=(1-δb)Bt+s-1+s-1F(κ+s,

I+s

whereδpandδbarethedepreciationratesfortheplanningandbuildingsstock,respec-tively.Thisproblemhasthesolution:

κ=q

q=Et(r+1+(1-δb)q+1)

(3)

it(I)=q

q=Etλ+1(q+1-κ)dF(κ)+q+1(1-δp-λ),

whereqpandqbaretheLagrangemultipliersontheplanningandbuildingaccumulationconstraints,re?ectingthevaluesofaunitoftheplanningandbuildingstock.

The?rstlineshowsthatdevelopersproceedwithconstructionwhenthecostofconstruc-

tionislessthanq,whichisde?nedinthesecondlinetobethepresentdiscountedvalue

offuturerentalincome(i.e.,thevalueofaunitofBt).Thethirdlinesaysthatdevelopers

willinvestinplanningstartsuntilthevalueofaunitoftheplann