IMF-揭示城市地租对全要素生产率的隐性影响（英）-2023.8

UnveilingtheHidden

ImpactofUrbanLand

RentsonTFP

WhyTFPgrowthindenselypopulated

economieswithrapidlygrowingcapitol

stockshasbeenseverelyunderestimated

BasB.Bakker

WP/23/170

IMFWorkingpapersdescriberesearchin

progressbytheauthor(s)andarepublishedto

elicitcommentsandtoencouragedebate.

TheviewsexpressedinIMFWorkingPapersare

thoseoftheauthor(s)anddonotnecessarily

representtheviewsoftheIMF,itsExecutiveBoard,

orIMFmanagement.

2023

AUG

©2023InternationalMonetaryFund

WP/23/170

IMFWorkingPaper

WesternHemisphereDepartment

UnveilingtheHiddenImpactofUrbanLandRentsonTotalFactorProductivity:

WhyTFPgrowthindenselypopulatedeconomieswithrapidlygrowingcapitolstockshasbeen

severelyunderestimated

PreparedbyBasB.Bakker*

August2023

IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicit

commentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseofthe

author(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.

ABSTRACT:ThispaperaddressesthepuzzlingdeclineofTotalFactorProductivity(TFP)levelsinrapidly

growingeconomies,suchasSingapore,despiteadvancementsintechnologyandhighGDPpercapitagrowth.ThepaperproposesthatTFPgrowthisnotnegative;instead,standardgrowthdecompositionshave

underestimatedTFPgrowthbyoverestimatingthecontributionofcapital,failingtoaccountforthesubstantialpartofcapitalincomedirectedtourbanlandrents.Thisleadstoanoverestimationofchangesincapitalstock'scontributiontogrowthandtherebyanunderestimationofTFPgrowth.AreviseddecompositionsuggeststhatTFPgrowthineconomieswithhighlandrentsandrapidcapitalstockgrowth,suchasSingapore,hasbeen

considerablyunderestimated:TFPlevelshavenotdeclinedbutincreasedrapidly.

JELClassificationNumbers:D24,D33,E22,O47

Keywords:

TotalFactorProductivity;EconomicGrowth;CapitalStock,LandRents;GrowthDecomposition;UrbanEconomics;Population

Density;DiminishingReturnstoScale;TechnologicalProgress;Singapore

Author’sE-MailAddress:bbakker@

*ThepaperhasbenefitedfromcommentsbyNikolasFernandez-Arias,NirKlein,NanLi,LeslieLipschitz,

JimMorsink,SofiaPiresMendesAbranchesPessoa,FlavienMoreau,CedricOkou,CarlosvanHombeeck,WillemvanEeghen,RodrigoValdes,andTianxiaoZheng.

WORKINGPAPERS

UnveilingtheHiddenImpactof

UrbanLandRentsonTotalFactor

Productivity

WhyTFPgrowthindenselypopulatedeconomieswithrapidlygrowingcapitolstockshasbeen

severelyunderestimated

PreparedbyBasB.Bakker

5

Contents

1IntroductionandExecutiveSummary

6

2ExistingLiterature

12

3StandardGrowthDecompositionsoverstatetheContributionofCapital

16

3.1Standardgrowthdecomposition

16

3.2Growthdecompositionwhenlandisincludedasaproductionfactor

16

3.3CapitaldeepeningisassociatedwithadeclineinTFPgrowth

17

4DetermininglandrentsfromthevalueofLand

21

4.1Theory

21

4.2CalculatinglandrentsforOECDcountries

22

5DeterminingLandrentsfromPopulationDensity

23

5.1Populationperdevelopedareaandlandrents:EvidencefromUSstates

23

5.2Population-weighteddensityandLandRents:EvidencefromUSStates

25

5.3LandrentsandpopulationweighteddensityinOECDCountries

27

5.4DerivingalowerboundforHongKongSARandSingapore

27

6RevisitinglowTFPgrowth

29

6.1Re-estimatingTFPforHongKongSARandSingapore

29

6.2SensitivityAnalysis

30

6.3Othereconomies

31

7FurtherevidencethatTFPgrowthisunderestimatedineconomieswithrapidly

growingcapitalstocks:1994-2019

33

8PopulationgrowthandTFP

35

9Islandconstant?

37

10Conclusion

38

Bibliography

39

ADataSources

41

6

1IntroductionandExecutiveSummary

Inanumberofveryrapidlygrowingeconomies,TFPlevelshavedeclinedinthepasthalfcentury.Forexample,inSingapore,GDPpercapitain2019was81/2timesthelevelin1970s,butTFPwasalmost10percentlower(Figure1.1).InMalaysia,Türkiye,andPanama,TFPlevelswerealsolower,eventhoughGDPpercapitagrowthhasbeenrapid.

LowerTFPisapuzzle,asitwouldimplythatittakesmoreinputstoproduceagivenlevelofGDPthanitdiditthepast.Butweknowtechnologicalprogresshasbeenspectacular.ItwouldseembizarretoarguethattechnologyinSingaporein1970wasmoreadvancedthanitwasin2019.

ThereisalsoapuzzlethatTFPgrowthinseeminglysimilareconomieshasbeenstrik-inglydifferent.SingaporehasseennoTFPgrowthinthelastfiftyyears,whileTFPgrowthinHongKongSARhasbeenconsiderable(Figure1.2)

.1

Thispaperproposesasolutionforthispuzzle.TFPgrowthhasnotbeennegative;rather,standardgrowthdecompositionshaveunderestimatedTFPgrowthbyoverestimat-ingthecontributionofcapital.

●Theyassumethatthecontributionofcapitaltogrowthisequaltothegrowthrateofthecapitalstocktimesthecapitalincomeshare—whichiscalculatedasas1-laborincomeshare.

●Butaconsiderablepartofcapitalincomegoestolandrentsratherthantotheownersofthephysicalcapitalstock

.2

●Aproperdecompositionshouldincludenotonlycapitalandlabor,butalsoland,withthecontributionsofeachfactordeterminedbythegrowthrateoftheproductionfactortimestheshareoftherewardsoftheproductionfactorinGDP.NOte

●Thismeansthatgrowthdecompositionsshouldusealowercoefficientforthecapitalstock—theyshouldusethecapitalincomeshareexcludinglandrentsratherthanthe

totalcapitalincomeshare.

●Thatmeansthatstandardgrowthdecompositionsoverestimatethecontributionofchangesinthecapitalstocktogrowth—andtherebyunderestimateTFPgrowth.

●Theoverestimationcanbesignificantineconomieswherelandrentsarehighandthecapitalstockhasgrownveryrapidly—whichincludesSingapore

.3

1See,forexample,

Young

(1992)

.

2Notethatinthepaperwedonotfocusontheshareoflandrentsforagricultureornaturalresources,butonurbanlandrents—capitalincomegoingtolandownersinurbanareas.

3TheincreaseinthecapitalstockinSingaporehavebeentrulydramatic:thecapitalstockin2019was39timesashighasin1970.Toputthisintoperspective,intheUnitedStatesthecapitalstockwas4.7timesashigh.

7

WedonothavedatafortheshareoflandrentsinGDPinSingaporeandHongKongSAR,nordowehavedataontheiraggregatelandvalue.Wethereforetrytoderiveaplausibleestimate.WeshowthattheshareoflandrentsinGDPisnotconstant—itishigherinmoredenselypopulatedareas.WederivealowerboundfortheshareoflandrentsinGDPofSingaporeandHongKongSARbylookingatlandrentsincountrieswherepopulationdensityislowerthaninHongKongSARandSingapore.

●Wearguethatlandvaluesarehigherinmoredenselypopulatedareas.GDPishighertoo,butthedifferencesarelesspronouncedthatthedifferenceinlandvalues.Asaresult,theratiooflandvaluestoGDPishigherinmoredenselypopulatedareas.

●Assumingthereturnonlandisthesameeverywhere,thisimpliesthattheratiooflandrentstoGDPishigherinmoredenselypopulatedareas.

●WeshowthatforUSstatesthereisastronglinkbetweenpopulationperdevelopedareaandtheratioofthevalueofdevelopedlandtoGDP:thehigherthepopulationdensity,thehigherthevalueoflandrelativetoGDP.AssumingthatthereturnonlandisequalacrossUSstates,thisimpliesthatshareoflandrentsinGDPdependsonpopulationdensityaswell.

●WethenshowthatasimilarlinkexistsforUSstatesbetweenweightedpopulation

density4

andlandrents.

●WeshowthatforOECDcountriesforwhichtheOECDhasdataontheaggregatevalueofland,thereisastronglinkbetweenweightedpopulationdensityandtheshareoflandrentsinGDP.

●WeusethislinktoderivealowerboundfortheshareoflandrentstoGDPinSingaporeandHongKongSAR—twoeconomiesforwhichwedonothavedataoneitherlandrentsorlandvalues.InKorea,whereweightedpopulationdensityisthehighestamongallOECDeconomiesforwhichtheOECDhasdataonaggregateland

values,landrentsareslightlylessthan25percentofGDP.AsHongKongSARandSingaporehaveamuchhigherweightedpopulationdensity,theyshouldhaveahigherlandrentratio.Wethereforeassume,veryconservatively,thatlandrentsinHongKongSARandSingaporeare25percentofGDP.

ThatwouldimplythatTFPgrowthinSingaporehasbeensubstantiallyunderestimated.InSingapore,thecapitalstockhasgrownby7.5percentannuallybetween1970and2019.Theaveragecapitalincomeshareduringthisperiodwas56percentofGDP.Iflandrentswere25percentofGDP,TFPwasunderestimatedby0.25*7.5=1.75percentannually.This

4Population-weighteddensityisthemeanofthedensitiesofsubareasofalargerareaweightedbythepopulationsofthosesubareas(

Ottensmann

(2018))

8

wouldimplythatTFPdidnotdeclineby0.2percentannuallybetween1970and2019,butincreasedby1.55percent

.5

WealsoshowthatSingaporeandHongKongSARaremuchmoresimilarthanstandardTFPestimatessuggest.ThecapitalstockinSingaporehasgrownmorerapidlythaninHongKongSAR,whichimpliesthatTFPgrowthhasbeenmoreunderestimated

.6

Krugman

(1994)inhisfamouspapernotedthat‘Economicgrowththatisbasedon

expansionofinputs,ratherthanongrowthinoutputperunitofinput,isinevitablysubjecttodiminishingreturns.’Yetstandardgrowthdecompositionsassumethatdiminishingreturnstoscaledonotexist.Theyassumethatveryrapidgrowthofinputsshouldleadtoanequallylargegrowthofoutput.Totheextentoutputgrowsbyless,theyattributethistodecliningTFP.

ThepapershowsthatSingaporehasnotsufferedfromnegativeTFPgrowth.Rather,withonefixedproductionfactor(land),therehavebeendecliningreturnstoscalefromincreasingcapitalandlabor.

●ThecapitalstockinSingaporein2019was39timesashighasin1970whilehumancapitalwas15timesashigh.WithunchangedTFP,constantreturnstoscaleincapitalandlabor,andacapitalincomeshareof60percent,thisshouldhaveledtoanoutputlevelthatis27timesashigh.Asoutputwasonly24timesashigh,growthdecomposersconcludethatTFPgrowthwasnegative.

●ButwithunchangedTFP,decliningreturnstoscaleincapitalandlabor,andacoefficientoncapitalthatis35percentratherthan60,thesameincreaseininputswouldonlyleadtoanoutputlevelthatis11timesashigh.ThatmeansthatmorethanhalftheincreaseinoutputwastheresultofTFP!

Finally,bothdecliningreturnstoscaleandnegativeTFPgrowthleadtooutputgrowingbylessthaninputs.Butthedifferencebetweenthetwoismorethansemantics.

●DecliningTFPimpliesthatmoreinputsareneededtoproducethesamelevelofoutput,whichsuggeststhatefficiencyisdecliningortechnologyisregressing

.7

●Decliningreturnstoscalemeansthatanincreaseininputsleadstoalessthanpropor-tionateincreaseinoutput.Itdoesnotmeanthatefficiencyisdecliningortechnologyisregressing

.8

5Wederiveamoreprecisecalculationinthepaper,usingannualdataforthegrowthofthecapitalstockandthecapitalincomeshare.Themorepreciseestimateis1.70percent.

6TheunderestimationofTFPgrowthhasalsotakenplaceinadvancedeconomies,butthemagnitudeoftheunderestimationhasbeenmuchsmaller.TaketheUnitedStates.Theaverageannualgrowthrateofthecapitalstockbetween1970and2019hasbeen3.2percent,whiletheaveragecapitalincomesharebetween1970and2019was39percent.Assumingthatlandrentswere15percentofGDP,theunderestimationofTFPwas0.15*3.2=0.5percentperyear.

7TFPisusuallyinterpretedasameasureoftechnology,summarizinghowintensivelyandefficiently

9

10

11

inputsareusedinproduction.(

CraftsandWoltjer

(2021),page672)

.

8Itistruethattheabsenceoflandavailablefordevelopmentwilleventuallyreduceoutputgrowthandpercapitaincome.Thismaybemitigatedtosomeextentbyashiftintolessland-intensivesectorsandsuchashiftwillbeincentivizedbyrelativecostdevelopments.

12

2ExistingLiterature

Theroleofland

Landplayedapivotalroleinclassicaleconomictheory.Agriculture,asthedominantsectorduringthatera,underscoredthesignificanceofland.

HansenandPrescott

(2002)

arguedthatthepre-industrialerausedaMalthustechnology—aland-intensivetechnologywherelandisafixedfactorandtherearedecreasingreturnstolabor.Thetheoryofrent,particularlyemphasizedbyeconomistslikeRicardo,exploredtheincomeearnedbylandownersduetoitsscarcityandproductivity.

Incontrast,moderneconomicgrowththeorylimitstheroleofland.

HansenandPrescott

(2002)arguethatthemoderneraoperatesonacalled"Solow"technology,whichexhibits

constantreturnstoscalewithcapitalandlaborasinputs.Iflandstillhasarole,itisprimarilyasasourceofnaturalresourcesornaturalcapitalthatcanbedepleted(

Brandt

etal.

(2017))

.

Thesignificantdecreaseinthevalueofagriculturallandhascontributedtoashiftineconomists’productionfunctions.

PikettyandZucman

(2014)observethatthevalueof

agriculturallandinFranceandtheUnitedStates,whichonceamountedtofourtofiveyearsofnationalincomearound1700,isnow"negligible."

Butwhilethevalueofagriculturallandhasdeclinedsharply,thevalueofurbanlandhasincreasedsharply.

Knolletal.

(2017)presentsannualhousepricesfor14advanced

economiessince1870.Theyshowthatrealhousepricesstayedconstantfromthenineteenthtothemid-twentiethcentury,butrosestronglyandwithsubstantialcross-countryvariationinthesecondhalfofthetwentiethcentury.Risinglandpricesexplainabout80percentoftheglobalhousepriceboom.

Thelandpriceincreasehasbeenparticularlypronouncedindenselypopulatedareas.

Barretal.

(2018)estimatesthatthevalueofalllandinManhattan(28squaremiles)was

US$1.74trillion.Thelinkbetweenurbandensityandlandpriceshasbeenextensivelydiscussedintheliterature.See,forexample,

DurantonandPuga

(2020)and

Glaeserand

Gyourko

(2018)

.

Therehavebeenpapersthathavefocusedontheeconomicimpactofthelandpriceincreases.

Rognlie

(2015)arguesthattheincreaseinthe(net)capitalincomesharein

recentdecadesisentirelytheresultofanincreaseincapitalincomeofthehousingsector.

GanongandShoag

(2017)arguesthatrisinghousingpricesinhigh-incomeareasintheUS

hasdeteredlow-skillmigrationandslowedincomeconvergence.

Toourknowledge,thereisnopaperthatdiscussesthesharpincreaseinlandpricesforgrowthaccounting.

LowTFPgrowthinsomeAsianTigers

Krugman

(1994),inhisfamouspaper‘TheMythofAsia’sMiracle‘,popularizedtheidea

thateconomicgrowthinSingaporeandotherrapidlygrowingAsianecononomieswassolely

13

theresultofanincreaseininputsandthattotalfactorproductivityhadnotincreasedatall:

‘Butitisonlywhenoneactuallydoesthequantitativeaccountingthattheastonishingresultemerges:allofSingapore’sgrowthcanbeexplainedbyincreasesinmeasuredinputs.Thereisnosignatallofincreasedefficiency.Inthissense,thegrowthofLeeKuanYew’sSingaporeisaneconomictwinofthegrowthofStalin’sSovietUnion—growthachievedpurelythroughmobilizationofresources.‘

Young

(1992)comparedHongKongandSingapore

.Henotedthat‘whiletheHongKonggovernmenthasemphasizedapolicyoflaissezfaire,theSingaporeangovernmenthas,sincetheearly1960s,pursuedtheaccumulationofphysicalcapitalviaforcednationalsavingandthesolicitationofaveritabledelugeofforeigninvestment.‘Hefoundthat‘WhiletotalfactorproductivitygrowthhascontributedsubstantiallytoeconomicgrowthinHongKong,itscontributiontogrowthinSingaporeisnexttonil.‘HesuggestedthiscouldbeexplainedbySingapore’sindustrialpolicies:‘Singaporeisavictimofitsowntargetingpolicies,whichareincreasinglydrivingtheeconomyaheadofitslearningmaturityintotheproductionofgoodsinwhichithaslowerandlowerproductivity.’

InanoverviewarticleaboutTFPgrowthinAsia,

Felipe

(1999)arguesthatattributing

lowTFPgrowthtoindustrialpolicyisnotwarranted:

‘Performingagrowthaccountingexercisewiththeaimofdecomposingover-allgrowthorfittingaproductionfunctionisnotthesameasexplainingtheul-timatecausesofgrowth.Therefore,mostexplanationsaboutthegrowthofthecountriesunderstudy,advancedex-post,areunwarranted,andthus,fallacious.Inotherwords,thereisanunfilledgapbetweencalculatingzeroproductivitygrowthandattributingittothefailureofindustrialpolicy.’

TFPandIncomeDifferentials

Itiswellestablishedintheliteraturethatcross-countrydifferentialsinincomelevelsarelargelyduetodifferencesinTFP.Seeforexample,theoverviewin

Jones

(2016)

.9

Similarly,inthelongerrun,differencesinpercapitaGDPgrowthtendtobeassociatedwithdifferencesinTFPgrowth(Figure1.1).DifferencesinlaborproductivitygrowthalsotendtobeassociatedwithdifferencesinTFPgrowth(Figure2.1).

However,therearesomeimportantexceptions.Panama,Türkiye,MalaysiaandSin-gaporearealleconomieswithrapidlaborproductivitygrowthgrowthbutnegativeTFPgrowth.

9ItisalsowellestablishedthatdifferencesinTFPareduetodifferencesinhumancapitalandgovernanceandotherinstitutions(seeforexample,

Jones

(2016)and

Bakkeretal.

(2020))

.

14

Therearealsosomepuzzles.WhyhasSingapore,wherelaborproductivityhastripledsince1970,hadvirtuallythesameTFPgrowthasJamaica—wherelaborproductivityislowerthanin1970(Figure2.2)?

15

16

3StandardGrowthDecompositionsoverstatetheContributionofCapital

3.1Standardgrowthdecomposition

Standardgrowthdecompositionsassumethatthereareconstantreturnstoscale;andthatthereisperfectcompetitionwhichinturnimpliesthatfactorsgetpaidtheirmarginalproducts.Theproductionfunctionis:

Y=AF(K,L)(3.1.1)

Ifwetotallydifferentiatetheaboveproductionfunctionweget;

dY=F(K,L)dA＋AFKdK＋AFLdL(3.1.2)

Withperfectcompetitionthisequationbecomes:

dY=F(K,L)dA＋rdK＋wdL(3.1.3)

IfwedividebyYweget:

=＋＋(3.1.4)Ifwedefineαastheshareoftotalincomethatgoestocapitalwecanrewritethisas:

=+α＋(l−α)(3.1.5)

ThisequationistypicallyusedtoestimateTFPgrowth:

=−α−(l−α)(3.1.6)

isestimatedTFPgrowth.

3.2Growthdecompositionwhenlandisincludedasaproductionfactor

Assumethattherealproductionfunctionis:

Y=AF(K,L,T)(3.2.1)

whereT

island.10

Theonlydifferencebetweenthisproductionfunctionandthepreviousfunctionistheinclusionofland.Asbeforeweassumethatthereareconstantreturnstoscale;andthatthereisperfectcompetitionwhichinturnimpliesthatfactorsgettheirmarginalproducts.

10FromtheLatinwordterra.

17

DefineγastheshareofGDPgoingtolandrents.Wecandeducethat

=−(α−γ)−γ−(l−α)(3.2.2)

Assumingthattheamountoflandisfixedwecanwritethisas

=−(α−γ)−(l−α)(3.2.3)

Ifwecompareequation(3.2.3)with(3.1.6)weseethatstandardgrowthdecompositions

assumethatthecoefficientforthecapitalstockisequaltothecapitalincomeshare,whereasthedecompositionwithaproductionfunctionthatincludeslandusesacoefficientthatisequaltothecapitalincomeshareminustheshareoflandrentsinGDP.

Theresultisthatthemorethecapitalstockgrows,themoreestimatedTFPgrowth

d

=

−γ

(3.2.4)

InSingapore,thecapitalstockhasbeengrowingveryrapidly(Figure3.1).ThissuggeststhatTFPgrowthmayhavebeensubstantiallyunderestimated.

3.3CapitaldeepeningisassociatedwithadeclineinTFPgrowth

TofurthersupporttheideathatthenegativeTFPgrowthestimatesinPennWorldTablesaretheresultofanoverestimationofthecontributionofcapital,wewillshowthatcapitaldeepening(anincreaseinthecapital-outputratio)isassociatedwithadeclineinTFPgrowthasestimatedbyPennWorldTables.Figure3.2showsthatthereisastrongnegativelinkbetweenchangesinthecapital-outputratioandchangesinTFP.

Intheory,thelinkbetweenthechangeinthecapital-outputratioandthechangeinTFPcouldalsogotheotherway.LowTFPgrowthcouldleadtolowGDPgrowthandanincreaseinthecapitaloutputratio.Inpractice,however,thisdoesnotseemtobethecase.ThelinkbetweenchangesinthecapitaloutputratioandGDPgrowthispositivesuggestingthatcapitaldeepeningisassociatedwithfastergrowth(Figure3.3).

18

19

20

21

4DetermininglandrentsfromthevalueofLand

4.1Theory

TheshareoflandrentsinGDP,γ,isequalto:

γ=

rTPTT

PYY

(4.1.1)

whererTisthereturnonland,PTisthepriceofland,Tistheamountofland,YisrealGDPandPYistheGDPdeflator.

Weassumethatthenetreturnonthecapitalstock,rK,isthesameasthenetreturn

onland:11

rT=rK−δ=r(4.1.2)

Itfollowsthat:

rPTT＋(r+δ)PKK=αPYY(4.1.3)

whereαisthecapital-incomeincomeshare(i.e.,theshareofGDPthatdoesnotgotolabor)andδisthedepreciationrateofthecapitalstock.Itfollowsthat

r=

TheshareoflandrentsinGDPis:

αPYY−δPKK

PTT＋PKK

γ=

(4.1.4)

(4.1.5)

Wethusneedfivevariablestocalculatelandrents:

●Thevalueofland(PTT)

●Thevalueofthecapitalstock(PKK)

●NominalGDP(PYY)

●Thecapitalincomeshare(α)

●Thedepreciationrateonthecapitalstock(δ)

11Notethatthenetreturnonthecapitalstockisequaltothegrossreturnminusdepreciation.Thenetreturnonlandisequaltothegrossreturn—thereisnodepreciation.

22

4.2CalculatinglandrentsforOECDcountries

TocalculatelandrentsforanumberofOECDcountrieswecombineOECDdataanddatafromPennWorldTables:

●WeuseOECDdataonthevalueofthecapitalstock,thevalueofland,andGDP.

●WeusePennWorldTables10.0dataonthecapitalincomeshareandthedepreciationrate

Wefirstcalculaterusingequation(4.1.4)

.WethencalculatethelandrenttoGDP

ratiofromequation(4.1.5)

.

TheresultsareinFigure4.1.LandrentsarehighestinKorea,atabout24percentofGDP.InGreatBritain,theyare21percentofGDP.TheyarelowestinGermany,atabout

10percentofGDP.12

12TheseestimatesforAustraliaaresimilarto

Putland

(2018),whoestimateslandrentsinAustraliain

2018atslightlyover20percentofGDP.

23

5DeterminingLandrentsfromPopulationDensity

Unfortunately,wedonothavedataontheaggregatevalueoflandinSingaporeorHongKongSARthatwecouldusetodeterminetheratiooflandrentstoGDPinthoseeconomies.WewillthereforeestimatethelandrentstoGDPratiobylookingatotherdenselypopulatedeconomiesforwhichwehavelandrentsestimates.

Itiswellknownthatlandvaluesindenselypopulatedareasaremuchhigherthaninlessdenselypopulatedareas.Accordingto

Albouyetal.

(2018),fiveurbanagglomerations

(NewYork,LosAngeles,SanFrancisco,Washington,DC,andChicago)accountfor48%ofallurbanlandvalueintheUnitedStates.Accordingto

Barretal.

(2018)theentire

amountofdevelopablelandonManhattanin2014wasworthapproximately$1.74trillion.

MoredenselypopulatedareaalsoproducemoreGDP,butthedifferenceislesspro-nouncedthanthedifferenceinlandvalues.In2018,theshareofthefiveurbanagglomer-ationsinUSGDPwas22.3percent—lessthanhalftheshareinUSlandvalues.

ThissuggeststhattheratiooflandvaluestoGDPishigherinmoredenselypopulatedareas.Andassumingthatthereturnonlandisconstant,thisimpliesthattheshareoflandrentsinGDPisalsohigherinmoredenselypopulatedareas.

5.1Populationperdevelopedareaandlandrents:EvidencefromUSstates

Larson

(2015)hascalculatedlandvaluesandareasfordevelopedland,agriculturalland

andfederallandforeachofthe48contiguousUnitedStates.Developedlandisworthanaverageof$106,000peracre,versusnon-developedland,whichisestimatedtobe