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PolicyResearchWorkingPaper10956

FadingAwayInformalitybyDevelopment

M.Naz?mTamko?

WORLDBANKGROUP

DevelopmentEconomicsGlobalIndicatorsGroupOctober2024

PolicyResearchWorkingPaper10956

Abstract

Thispaperfocusesontheroleofdevelopmentininfor-malitythroughhigherwagesandexpandedproductionpossibilities.First,itusesinformal,plant-levelsurveydataacrosscountriestodocumentthatonaverage,richercoun-trieshavesmallerinformal,unregisteredplantsintermsofemployment.Thisnegativerelationshipholdsevenaftercontrollingforplant-levelcharacteristics.Then,adynamicgeneralequilibriummodelwithincompletetaxenforcementisdevelopedsuchthatformalandinformalplantscoexistinequilibrium.Themodelallowsfortwogroupsofagentsoperatingintheinformalsector:thosewithlowerabilities

thanworkers,andthosewithabilitiesfallingbetweenworkersandformalmanagers.Inthemodel,whenplantsbecomemoreproductive,someagentsoperatinginformallychoosetobeworkersandsomeofthemtransitionintoformalityduetohigherwagesandbetterproductionpos-sibilities,whichdecreasesthemeansizeofinformalplants.Thequantitativeresultsindicatethataround30percentoftheincreaseinaggregateoutputduetohigherproductivityisassociatedwitharoughlyone-quarterdeclineinthemeansizeofinformalplants.

ThispaperisaproductoftheGlobalIndicatorsGroup,DevelopmentEconomics.ItispartofalargereffortbytheWorldBanktoprovideopenaccesstoitsresearchandmakeacontributiontodevelopmentpolicydiscussionsaroundtheworld.PolicyResearchWorkingPapersarealsopostedontheWebat

/prwp

.Theauthormaybecontactedatmtamkoc@.

ThePolicyResearchWorkingPaperSeriesdisseminatesthefindingsofworkinprogresstoencouragetheexchangeofideasaboutdevelopmentissues.Anobjectiveoftheseriesistogetthefindingsoutquickly,evenifthepresentationsarelessthanfullypolished.Thepaperscarrythenamesoftheauthorsandshouldbecitedaccordingly.Thefindings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.TheydonotnecessarilyrepresenttheviewsoftheInternationalBankforReconstructionandDevelopment/WorldBankanditsaffiliatedorganizations,orthoseoftheExecutiveDirectorsoftheWorldBankorthegovernmentstheyrepresent.

ProducedbytheResearchSupportTeam

FadingAwayInformalitybyDevelopment*

M.Naz?mTamko??

October2024

Forthelatestversion,pleaseclickhere

Keywords:Informality,EconomicDevelopment,PlantSize,Productivity

JELClassification:E23,J24,L25,O41,O33

*IwouldliketothankJuheeBae,FilipJolevski,NormanLoayza,HibretMaemir,JorgeRodriguezMeza,FurkanSarikayaandGustavoVenturafortheircommentsandsuggestions.Thefindings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.TheydonotnecessarilyrepresenttheviewsoftheWorldBankanditsaffiliatedorganizations,orthoseoftheExecutiveDirectorsoftheWorldBankorthegovernmentstheyrepresent.

?TheWorldBank,EnterpriseAnalysisUnitE-Mail:mtamkoc@

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1Introduction

Informality,economicactivityoutsideofformalregulationsandinstitutionalframeworks,isoftenseenasacommonfeatureofdevelopingcountries.1Theliteraturehasfocusedonreducinginformalitythroughstrengtheningenforcementofpoliciesandloweringthecostsofoperatingformally,suchastaxratesandentryfees.However,developedcountriesdon’thaveoversightofalleconomicactivities,andtheirtaxratescanbeashighasindevelopingcountries.2Thispaperarguesthathigherlevelofinformalityinpoorercountriesisnotonlytheresultofburdensomeregulationsorinadequateenforcement,butalsoabyproductofunderdevelopment.

Inrichercountrieswithbetterproductiontechnologiesandeconomicenvironments,someworkerspreferformalwageemploymentoveroperatinganinformalbusiness,aswageratesarehigher.Likewise,somemanagersoptforformalfirmregistrationandoperationbe-causetheincomepotentialinrichermarketsmakesformalitymoreprofitabledespitethecostsoftaxesandregulations.

Inthispaper,Ifocusontheincidenceofinformalityattheextensivemargin,referringtounregisteredplants.Istartbydocumentingempiricalfactsrelatedwithinformalityinthedevelopingworld.Usingplant-leveldatafromtheWorldBankInformalSectorEnterpriseSurveys(ISES),Ishowthatinformalplantsinrichercountriestendtoemployfewerwork-ersonaveragethaninformalplantsinpoorercountries.Inotherwords,theinformalmeansizedecreaseswiththelevelofdevelopment.Forexample,informalplantsinGhanahave2.3workersonaverage,whereasinPeru,informalplantsaverageonly1.4workers.ThisnegativerelationshipbetweeninformalplantsizeandGDPpercapitapersistsevenaftercontrollingforplantcharacteristicssuchasmanagers’education,experience,andgender,sectorofac-tivity,andplantage.Moreover,whilesomeinformalplantsachieveproductivitylevels,mea-suredbyvalue-addedperworker,comparabletotheirformalcounterparts,mostoperateatverylowlevels.

Toquantifytheimpactofdevelopmentoninformality,Idevelopadynamic-generalequi-libriummodelofoccupationalchoicewhereagentsareoptimallyallocatedasworkersormanagersaccordingtotheirabilitiesinthespiritofLucas(1978)’sspan-of-controlmodelbasedonPoschke(2018).Inthemodel,whileworkers’earningsareproportionaltotheirabilities,managerialearningsareincreasinginreturnstotheirabilities.Iintroduceinfor-

1SeeDeSoto(1989),andLaPorta&Shleifer(2014),Ulyssea(2020)andOhnsorge&Yu(2022)forasurveyofinformalityliterature.

2SeeFriedmanetal.(2000)forthenegativerelationshipbetweentaxratesandinformality.

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malitybyallowingmanagerstooperateinformallytoavoidtaxationduetoincompleteen-forcement.Theyriskbeingcaughtiftheyusecapitaloveracertainthreshold,similartoDeSoto(1989)andLeal(2014).Inequilibrium,agentsatthelowerendoftheabilitydistribu-tionoperateasinformalmanagers.Agentswithabilitieshigherthanthoseofinformalman-agers,butnothighenoughtorunplants,becomeworkers.Ifenforcementlimitsortaxesarenotexcessivelylow,informalitymayalsoexistamongagentswithabilitiesexceedingthoseofworkers.Ofthesehigher-abilityagents,therelativelylessableoperateinformally,whilethemoreablerunformalplants.Informalmanagerswithabilitieslowerthanworkersarere-ferredtoasoperatinginsubsistenceinformality.Inthecasethatenforcementlimitsortaxesaresufficientlylow,allagentswithabilitieshigherthanworkersoperateintheformalsector.

Icalibratekeymodelparameterstomatchplantsizedistribution,includinginformalplantsinGhana.Themodelsuccessfullygeneratestheobservedmeanplantsizedifferencesbetweenformalandinformalsectors.Inthebenchmarkeconomy,while90.6%ofplantsareinformal,theyaccountfor34.2%ofaggregateoutput.Moreover,71.1%ofinformalplantsoperateatthesubsistenceinformalitylevel.Hence,theaverageinformalmanagerearnslessthantheaverageworker.

Motivatedbybetterbusinessenvironmentsandhigheryearsofschoolinginrichercoun-tries,developmentisintroducedintothemodelsuchthatallmanagers’productivityin-creases.Asaresult,relativelyhigher-abilityinformalplantmanagersstartoperatingformallysince,oncemoreproductive,theydemandmorelaborandcapital.Incontrast,relativelylower-abilityinformalplantmanagersswitchtobecomeworkersinthenewequilibrium,enjoyinghigherwages.Therefore,whileinformalitydecreaseswithdevelopment,theshareofsubsistenceinformalityincreasesamonginformalplants.

Quantitativelywhentheaggregateoutputincreasesbyabout29.5%duetoimprovementsinmanagers’productivity,theoverallaverageplantsizeincreasesby30%whereasthemeaninformalplantsizedeclinesbyabout26.1%.Whenthemodelisdisciplinedtoaccountfordifferencesininformalmeanplantsizeacrosscountries,itcanexplain32.8%ofincomepercapitadifferencesonaverage.Moreover,whenonlytheformalsectorbenefitsfrompropor-tionalandskill-biasedimprovementsinthemanagers’productivity,theshareofinformalplantsshrinks,andtheoverallmeansizegrowsfastercomparedtothecasewhereallman-agersbenefitfromdevelopment.Thepaperconcludesbycomparingthegainsfromformal-izationpolicies,suchasbetterenforcementandlowertaxes:whileformalizationpolicieshavethepotentialtodecreaseinformality,theirgainsarelimitedcomparedtothegainsfromhigherproductivityassociatedwithimprovingthebusinessenvironmentandimprovinged-ucationlevels.

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BackgroundTheinformalityliteraturegrewextensivelyfollowingDeSoto(1989).First,LaPorta&Shleifer(2008)andLaPorta&Shleifer(2014)areamongtheearlieststudiesthatutilizesISEStodocumentdifferencesbetweenformalandinformalplants.Amin&Okou(2020)extendstheircomparisontoabroadersetofcountries.Icontributetothisliteraturebysystematicallyshowingthatinformalplantstendtobelargerinpoorercountries.

Second,Rauch(1991),Loayza(1996),Amaral&Quintin(2006),D’Erasmo&Boedo(2012),Leal(2014),Meghiretal.(2015),Ulyssea(2018)andFranjoetal.(2022)developenviron-mentswhereinformalityexistsduetotheminimumwages,incompleteenforcementandfrictionsinaccessingfinance.IextendthemodelofPoschke(2018)byallowinginformalitytoexistendogenouslyduetotheincompleteenforcementoftaxes.Inthemodel,agentssortintobeingworkers,informalmanagers,andformalmanagers.Mycontributionisprovidinganenvironmentwhereagentswithabilitieslowerthanworkers(subsistenceinformality)aswellasthosewithhigherabilitiesbecomeinformalmanagers.

Third,theaboveliteraturefocusesontheformalizationpoliciessuchasreducingthecostofbeingformalortaxes,motivatedbyJohnsonetal.(1998),Fajnzylberetal.(2011),DeMeletal.(2013),Bruhn&McKenzie(2014),DeAndradeetal.(2016)andRochaetal.(2018)amongmanyothers;andincreasingenforcementasinKuehn(2014),Orsietal.(2014),Leal(2014)andUlyssea(2018).However,inthispaper,Iquantifytheroleofdevelopmentinre-ducinginformality.Loayza(2016)studieshowgrowthratesandmigrationaffectinformalityinagrowth-accountingsetup,andprojectslaborinformalityovertwodecades.Thispaperdiffersbydevelopingaspan-of-controlmodelwithheterogeneousproductionunitsanddis-cipliningthemodelusingaplantsizedistributionincludinginformality.

Lastly,thispapercontributestotheliteraturestudyingplant-levelproductivity,size,andaggregateproductivity,advancedbyHsieh&Klenow(2009),Bartelsmanetal.(2013)andHsieh&Klenow(2014).Bento&Restuccia(2017)andBento&Restuccia(2021)documentthatrichercountrieshavelargerplantsintermsofemploymentonaverage.Restuccia&Rogerson(2008),Guneretal.(2008),Garcia-Santana&Pijoan-Mas(2014)andGourio&Roys(2014)havefocusedontheroleofsize-dependentdistortionsasoneofthemainreasonsforsmallerplantsinpoorercountries.Tamko?&Ventura(2024)studytimetaxes–rulesandregulationsthatdistortmanagers’productivetime–asadeterminantofsmallerplantsinpoorercountries,onaverage.Inthispaper,Istudytheprevalenceoflargerinformalplantsinunderdevelopedcountriesasonereasonforthesmalleroverallmeanplantsizeinthesecountries.

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2Data

ThemaindatasourceofthispaperistheWorldBank’sISESwhichconsistsofface-to-faceinterviewswithownersormanagersofinformalplants.3Itusesanarea-basedsamplingmethodologythatgeneratesaprobabilisticsampleofinformalfirmswhereinterviewersenu-merateallplantsinarandomlyselecteduniformblocksinagivenregionorcitytodetermineregistrationstatus.Ifaplantisnotregisteredinthelocalregistrationinstitution,itiscon-sideredinformal.Withinselectedinformalplantsarerandomlyselectedinrealtimeforadeeperinterview.Varioustopicssuchasworkforce,sales,sectorandbackgroundofman-agersarecoveredinthequestionnaire.4ISESincludes25,995plant-levelobservationsfrom78regions/citiesin26countriessince2008.5ThePPPadjustedrealGDPpercapita,RGDP,andemploymentdatacomefromWorldDevelopmentIndicators(WDI).Thesamplecoverscountriesatdifferentlevelsofdevelopment:therichestcountryinthesampleisArgentinawhereasDemocraticRepublicoftheCongohasthelowestRGDPpercapitacomparedtoothercountriesinthesample.

Thenumberofworkersinaninformalplantisthetotalnumberofpaidandunpaidwork-ers.Figure1presentsthemainmotivatingfactofthepaper:richercountriestendtohavesmallerinformalplantsonaverage.Inthefigure,eachdotrepresentsacountry.They-axisandx-axisaretheaveragenumberofworkersininformalplantsandtheRGDPpercapitaineachcountryrespectively.Forexample,theaverageinformalplantinArgentinahas1.6workers,whileinGhanaandNepal,theaveragesare2.3and4.1workersperinformalplant,respectively.

ThesolidlineinFigure1isthesimplelinearregressionlinewherethelog-informalmeansizeisregressedonthelog-RGDPpercapitawhereobservationsareweightedaccordingtotheiremploymentsize.Despitethesmallsamplesize,theelasticityoftheinformalmeansizewithrespecttoRGDPpercapitaisnegativeandstatisticallysignificant.ItimpliesthatdoublingRGDPpercapitaisassociatedwith29.3%declineininformalmeansize.

ThefollowingregressionequationisestimatedtotestwhetherthenegativerelationshipbetweentheinformalmeansizeandtheRGDPpercapitapersistsaftercontrollingforplant

3Forplant-leveldatasetsandfurtherinformationaboutthemethodology,pleasevisit

4After2015,ISESusesanadaptiveclustersamplingmethodologywhichenablesthecomputationoftheprobabilityofselectionofaplantwithinablock,thusallowingtheuseofsamplingweightstomakeinferencestothepopulationofinformalbusinesseswiththeregion/city.SeeAgaetal.(2023)andAberraetal.(2022).

5PleaseseeAppendixBforthelistofcountriesandthenumberofobservations.

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characteristics.

log?Sizei,c￠=β0+β1log(RGDPc)+Xi,c+?i,c(1)

whereSizei,cisthenumberofworkersinplantiincountrycandRGDPcistheRGDPpercapitaincountryc.Xi,cincludesplantcharacteristicvariablesinplantiincountryc.Itconsistsofamanufacturingdummy;aneducationofamanagerdummywhichis1ifthehighestlevelofamanagerisatleastsecondaryschool;experienceofamanagerinthesector(inyears);afemaledummywhichtakesvalue1ifthemanagerisfemale;andtheageoftheplant(inyears,asofthedateofinterview).

Table1presentstheestimatedcoefficientsoftheEquation(1).Theelasticityoftheinfor-malmeansizewithrespecttoRGDPpercapitais-0.16andsignificantevenaftercontrollingforallplantcharacteristics.Inaddition,theestimationresultsindicatethatinformalplantsoperatinginthemanufacturingsectorsignificantlyemploymoreworkersthanthoseoper-atingintheservicessectoronaverage.Moreover,theexperienceandeducationofmanagersispositivelycorrelatedwiththesizeofinformalplants.Ontheotherhand,plantsmanagedbyafemalemanageraresignificantlysmallercomparedtoplantsmanagedbyamale.

Next,Icompareinformalplantsvis-a-visformalplantsinGhana.6WorldBankEnterpriseSurveys(WBES)conductedtwoothersurveysinGhanain2013alongwithISES:Micro-WBESandWBES.Onlyformal(registered)plantsarecoveredinbothsurveys.Micro-WBESinter-viewsplantswithfewerthan5workers,whileWBESinterviewsplantswithatleast5workers.IrefertoplantsinbothMicro-WBESandWBESasformalplants.

Table2presentsthecomparisonofinformalandformalplantsinGhana.Themeansizeofinformalplantsissmallerthanformalplants:thereare2.3workersininformalplantswhereas3and34.7workersareinvolvedinproductionintheMicro-WBESandWBESre-spectively.7Moreover,informalmanagershavelessexperienceinthesectortheyoperateincomparedtoformalmanagers.While42.8%ofinformalmanagershaveatleastasecondaryschooldegree,around65%ofworkersinformalplantshaveatleastasecondaryschoolde-gree.Tosumup,onaverage,informalplantsaresmallerandyoungercomparedtoformalplants;theirmanagershavefewerexperienceandlesseducation;thefractionoffemaleman-agersishigheramonginformalplants.

6SimilaranalysisisdonebyLaPorta&Shleifer(2014)acrossafewcountriesusingthesamedataset,andMeghiretal.(2015)andUlyssea(2018)inBrazil.

7AsSection4discussesindetail,theGhanaStatisticalService’sIntegratedBusinessEstablishmentSurveyreportsthemeansizeofinformalplantsas2.3workersandthemeansizeofformalplantsas33.8.SimilarmeansizesoftheWorldBank’splantlevelsurveydatasetswiththatoftheGhanaStatisticalService’scensusbuildconfidenceintheusageofISESandWBEStocompareinformalandformalplantsinGhana.

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Finally,IfocusonproductivitydifferencesbetweeninformalandformalplantsinGhana.8Figure2plotsthedistributionofLog-VAperworkerinISES,Micro-WBESandWBES.Therearethreeobservationsrelatedwiththeproductivitydifferencesbetweeninformalandformalplants.First,asTable2alsoshows,informalplantsarelessproductivecomparedtoformalplants.Secondly,whilemostproductiveinformalplantsaresimilartomostunproductiveformalplantsintermsofproductivitylevels,therearesomeinformalplantsthatoperateatverylowlevels.Third,informalplantshavelongleft-tailproductivitywhereasformalplantshavelongright-tailproductivity.

3Model

ThemodelisbasedonPoschke(2018).Theinnovationinthispaperisthatmanagerscanoperateintheinformalsectortoavoiddistortions.

3.1Environment

Thereisahouseholdwithacontinuumofhouseholdmembers.Eachhouseholdmemberisbornwithaunitofefficiency,zandaunitoftimesuppliedinelastically.TheunitofefficiencyisdistributedaccordingtoacdfG(z)over[0,]andisreferredasabilityinthispaper.Thehouseholdhasapreferenceoveraconsumptiongoodanddiscountsthefutureattherate

β<1:

∞

βtlog(2)

Ateachperiod,householdmembersareassignedtobeworkersormanagersbasedontheirabilities.Workerssupplytheirabilitytocollectwages.Managersrunplantstoproducethesinglefinalgoodoftheeconomybyhiringworkersandrentingcapital.Productionofthefinalgoodrequiresrunningdifferentiatedactivitiesi.e.,usingintermediategoods.FollowingPoschke(2018),thenumberofactivitiesthatamanagerwithabilityzcanperform,M(z),

equalstozwhere>1representstheaggregatetechnologylevel.Irefertothenumber

ofactivitiesamanagercanperformasproductivitythroughoutthepaper.

8Productivityismeasuredbythelogofvalueadded(Log-VA)perworkerandVAisdefinedassalesminusexpendituresonrawmaterialsandenergyfollowingLaPorta&Shleifer(2008).

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Thefinaloutputofaplant,y,withamanagerofabilityzcanbedefinedasfollows:

wherejdenotesdifferentactivities,njandkjaretheamountofabilityandcapitalusedinactivityjrespectively,1>α>0istheimportanceoflaborinproduction,1>γ>0isthespan-of-controlparameterandσ>1istheelasticityofsubstitutionbetweendifferentiatedproducts.

Governmentcollectstaxesfromoutputattherateτ.EnforcementoftaxcollectionisincompleteinthesensethatmanagerscanoperateinformallytoavoidtaxesinlinewithLeal(2014).However,thereisapossibilitythataninformalmanagercangetcaughtwithprobability,p(kj):

whereBrepresentstheenforcementlevelsuchthatifamanagerusesmorecapitalthanBintheproductionofthefinalgood,shewillbecaught.Therefore,managerscanavoidtaxesbylimitingtheircapitaltolessthanorequaltoBintotal.Ifamanageriscaughtwhileoperatinginformally,shelosesallprofits.

ProblemofanInformalManagerAmanagerwithabilityzwhooperatesinformallychoosestheamountofcapitalandlabortomaximizeherprofit,πI(z):

whereWandRarewagesandrentalrateofcapitalrespectively.

ProblemofaFormalManagerAmanagerwithabilityzwhooperatesformallychoosestheamountofcapitalandlabortomaximizeherprofit,πF(z).Sincethemanageroperatesformally,itsoutputissubjecttoatax,τ.

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Thegovernmentcollectstaxesfromformalmanagersandreturnsthemtothehouseholdasalump-sumtransfereveryperiod:

Tt=Gt?t(7)

whereTtdenotesthetransferstothehouseholdandGtisthegovernmentrevenuefromtaxation.

ProblemoftheHouseholdThehouseholdassignsitsmemberstothreeoccupations:work-ers,informalmanagersandformalmanagers,andchoosesitsconsumption,Ctandhowmuchcapitaltocarryouttothenextperiod,Kt+1inordertomaximizeitslife-timeutility:

s.t.

Ct+Kt+1=It(SW,t,SI,t,SF,t,Wt,Rt)+(1?δ+Rt)Kt+Tt

whereSW,t,SI,t,SF,tdenotethesetofworkers,informalmanagersandformalmanagersre-spectively,δisthedepreciationrateofthecapital,TtisthetransferfromgovernmentandIt(SW,t,SI,t,SF,t,Wt,Rt)isthetotalincomeofhouseholdmembers:

wherethefirstitemoftheright-handsideisthewageincomeofworkersandthesecondandthethirditemsrepresentthetotalprofitoftheinformalandformalmanagersrespectively.9

3.2PropertiesoftheEquilibrium

Thissectionfocusesonastationaryequilibriumanddiscussesitskeyfeatures.Profitofaformalmanagerwithabilityz,πF(z),canbewrittenasafunctionofparametersandinputpricesusingequations(A.3)and(A.4):

9AppendixAprovidesthefirst-orderconditionsofmanagers’problemsandthedefinitionofequilibrium.

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AllinformalmanagerslimittheircapitalusagetoBorlessintheirplants,astheywouldbecaughtoperatinginformallyotherwise.Then,theprofitofaninformalmanagerwithabilityz,πI(z),canbewrittenasafunctionofparametersusingequations(A.5),(A.6),(A.7)and(A.8):

(11)

Iassumethatγ>>αsuchthatprofitfunctionsofbothtypesofmanagersarein-creasingandconvexinz.Thisassumptionalsoguaranteestheexistenceanduniquenessoftheequilibriumwhereinformalandformalmanagerscoexist(givenhighτandB).Ifthe

totalamountofcapitalusedinaninformalplantislessthanB,theπIisstrictlygreaterthan

πFdueto<1.ThehighestamountofcapitalthataninformalmanageruseisB.IrefertoinformalmanagerswhouseexactlyBamountofcapitalasconstrainedinformalmanagers.Theycanstillincreasetheirprofitbyhiringmorelaborgiventheirconstrainedcapital.Asaresult,theslopeofinformalmanagers’profit,πI(z),isaffected.Whentheop-timalamountofcapitalforaninformalmanagerisequaltoB,theslopeoftheinformalmanager’sprofitwithrespecttozbecomessmallerthanthatoftheformalmanager’sprofitfunction.Then,πIcancrossπFatmostoncebecausebothfunctionsarestrictlyincreasing.Sinceworkers’earningsincreaseproportionaltotheirability,thisestablishestheexistenceanduniqueness.

Figure3describesanequilibriumassignmentofhouseholdmemberstodifferentoc-cupations.Thehorizontalaxisrepresentsabilitiesandtheverticalaxisistheearningsofhouseholdmembers.WhileπI(z),thesolidline,andπF(z),thedash-dottedline,areincreas-ingandconvexwheretheycrosseachotheronlyonce,theearningsofworkers,thedashedline,islinearandincreasingwithaslopeofW.Householdmemberswithz∈[0,z)andz∈[z,z)becomeinformalmanagers,householdmemberswithabilityz∈[z,]becomeformalmanagersandremaininghouseholdmemberswithabilityz∈[z,z)assignedtobeworkersinthisequilibrium.Thesubsistenceinformalityexistswherez∈[0,z).Iftaxesarelowortheenforcementisstricter(i.e.lowB)inaneconomy,theremaybeonlysubsistenceinformalityintheequilibrium.Inotherwords,z,theabilitylevelwheretheinformalprofitfunctioncrossestheformalprofitfunction,canbesmallerthanz,thethresholdlevelwheretheearningslineofworkerscrossestheprofitofmanagersfromabove.

Thesolutiontothemanagers’probleminAppendixAshowsthattheamountofcapital

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andlabordevotedtoeachactivityisthesameacrossactivitiesforagivenmanager.There-fore,Iexpressthecapital-laborratioattheactivitylevelwithoutlossofgenerality.Usingequations(A.3)and(A.4),thecapital-laborratioofformalmanagerscanbewrittenasfol-lows:

(12)

Similarly,thecapital-laborratioofinformalmanagerscanalsobederivedusingequations(A.5),(A.6),(A.7)and(A.8)asfollows:

Noticethatcapital-laborratiosofformalandinformalmanagersareconstantandequaltoeachotherifinformalmanagersoptimallychooselesscapitalthanB.However,moreable,constrained,informalmanagershaveasmallercapital-laborratiocomparedtoothermanagersandtheratiodecreaseswiththeabilityofinformalmanagersasγ>.

Sincemanagershireefficiencyunits,IdefinethesizeofaplantrelativetotheaverageabilityofworkersasinPoschke(2018).LetFPbethefractionofplants,i.e.thefractionofmanagers,whichisthesumofthefractionofformalmanagers,FF,andinformalmanagers,FI.Hence,themeansizeofinformalplantscanbedefinedastheratiooftheaverageabilitydemandedininformalplantsandtheaverageabilityofworkersininformalplants.Usingthemarketclearingcondition,itcanbewrittenasfollows

whereFWIistheshareofinformalworkersamongworkerssuchthatFWI(1?