The Effects of Irreversibility and Uncertainty on Capital Accumulation PDF
Preview The Effects of Irreversibility and Uncertainty on Capital Accumulation
UUnniivveerrssiittyy ooff PPeennnnssyyllvvaanniiaa SScchhoollaarrllyyCCoommmmoonnss Finance Papers Wharton Faculty Research 1999 TThhee EEffffeeccttss ooff IIrrrreevveerrssiibbiilliittyy aanndd UUnncceerrttaaiinnttyy oonn CCaappiittaall AAccccuummuullaattiioonn Andrew B. Abel University of Pennsylvania Janice C. Eberly Follow this and additional works at: https://repository.upenn.edu/fnce_papers Part of the Finance Commons, and the Finance and Financial Management Commons RReeccoommmmeennddeedd CCiittaattiioonn Abel, A. B., & Eberly, J. C. (1999). The Effects of Irreversibility and Uncertainty on Capital Accumulation. Journal of Monetary Economics, 44 (3), 339-377. http://dx.doi.org/10.1016/S0304-3932(99)00029-X This paper is posted at ScholarlyCommons. https://repository.upenn.edu/fnce_papers/353 For more information, please contact [email protected]. TThhee EEffffeeccttss ooff IIrrrreevveerrssiibbiilliittyy aanndd UUnncceerrttaaiinnttyy oonn CCaappiittaall AAccccuummuullaattiioonn AAbbssttrraacctt Irreversibility and uncertainty increase the user cost of capital which tends to reduce the capital stock. Working in the opposite direction is a hangover effect, which arises because irreversibility prevents the firm from selling capital even when the marginal revenue product of capital is low. Neither the user cost effect nor the hangover effect dominates globally, so that irreversibility may increase or decrease capital accumulation. Furthermore, an increase in uncertainty can either increase or decrease the long-run capital stock under irreversibility relative to that under reversibility. Other effects that we consider, however, have unambiguous effects on long-run capital accumulation. DDiisscciipplliinneess Finance | Finance and Financial Management This journal article is available at ScholarlyCommons: https://repository.upenn.edu/fnce_papers/353 ehT stceffE y tfiolibisre vdenrayrtIniatrecnU noitalumuc clAatip anCo leb A. BwerdnA ,ainavlysnn e fPyotisrevi neU h ftloooh cnSotra heWhT A S4U0 1 A 9,P1aihpledalihP ylreb E. CecinaJ * ytisrev innrUetsewht r,otNnemega nlfaooMo hectSaud agrgGol l.eLK.J ,no tLsInav E802A0S6U 5 9,9r1ebmevoN 8 9,9t1su gdueAsiver tcartsbA e hetcud eosrtdn ehtci hlwatip aftcos orce se uhetsaerc nyitniatrec nd unyatilibisreverrI esuac esbesi rhaci h,wtcef freevog n sanaihoitcer iedtisop pe o hngtini k.r kocWo tlsatipac euneve rlanigra meh tneh wnev elatipa cgnille smor fmri feh tstnever pytilibisreverri setani mtocde frfeevog n ea rhhtotcne ftf sero ec esrhuet h. t w lisoaeiltNi ptfacocudorp .noitalumuc claatip aecsaerc e rdeosaerc nyi aymtilibisrever rtia h ot,syllabolg latip ancur-gn oe lhetsaerc eredosaerc nrieht in eayctniatrec nneuisaerc nn,iaeromrehtruF etwa hsttcef freeh t.Oytilibisrev erred ntua h otetvital eyrtilibisrever rried nkucots .noitalumuc claatip ancur-gn o nlsotcef fseuougibma neuv a,hrevew o,hredisnoc 2 2:Enoitacifissa lLCEJ ytniatrec n,Uytilibisrever r,Itnemtsev n:IsdrowyeK * gnidnopserroC :rohtua rosseforP ecinaJ ,ylrebE ecnaniF ,tnemtrapeD .L.J ggolleK etaudarG loohcSfo Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208-2001. The authors ,mddonlraafn ot wDr ,e cedor,MbnLdo oancoRAocuiCn ehsmtnoioDwissu cmdsoeirtdfifeneb correspondence with Giuseppe Bertola and Ricardo Caballero. We thank seminar participants at the NBER, Northwestern University, and the Penn Macro Lunch Group for helpful comments, and the lanoitaN ecneicS noitadnuoF rof laicnanif .troppus eW osla knaht na suomynona eerefer rofstnemmoc taht del su ot etirw noitceS .2.4 sihT krow saw detaitini elihw ylrebE saw gnitisiv dravraH ytisrevinUdna ;ainav lyyt si lfen sdyool n nretoi fen oetlhhfo Po eetveuc wo,eh hrilcSeRhtdtanpahEtnhUmftBaWoNc rieht troppus si yllu f,edteagrdgelwonkca sa si a naolS noitadnuo Fhcraese.RpihswolleF 1 1. noitcudortnI ytniatrec nrued ntunemtsev neilbisrever r nieorutaret ielgr ael h fttolus erroj aemhT ylbatifo r e pobrted r noriae ltcs usmtcejo rtpa hetldr ueh hstesaerc nyitilibisrever rtia hsti ese hhtguo h.t yltAniatrec nsruiehg ie hhdtesaerc nseiildr ue hh,tnoiti d. dnnaeIkatrednu e ryae h,tsnoisic egdnitegd ulbatip agcnik asmregan a omltufpl eyhlsuomro nee rsatluser fnooitalumuc cnaur-gn oe lhttuo bd antanemtsev nftionuo mlaamit pe ohttuo btanelis koo blanime ss’kcydni Pdn atixi Df oweive rsi hn idrabbu Hy bdebircs e .ds lAatipac ytniatrec nrUed ntUnemtsevnI snoitcide rcpifice prsef fto o ons…dled owme iwv eenh t,“ about the level larutcu rnftoositacific e epshsetriu qpe eratrs tsx ie.oohtTgtnemtse vfnoi .)p4991 (”[.kco tlsatip adceris eed hdt nlaatip a fcyotilibatifo rlpanigr aem hnteewt esbknil larutcu retss oghntidiv opyr ebpatrs t exsheet kr ae.t p] ralupaOnig isriosah p,m8e281 e h ntyotniatrec ndu nyatilibisrever r fisotcap mei hettalucl ayclticilp x oe ntsoe odg nsaknil .k cloatts inpuarc- gdneotlcepxe oltaicu re crsatlus eerse h,tsezisahp mderabb usHA yllacipy ts iflest ielu rtnemtsevn ieh tecn i .Sledo meh tf onoitaulav elaciripme odte syulnomm oecr oe mrkaco tlsatip ae chd tntanemtsev nnaiot a,delbavresbonu e h ttkaco tlsatip aec hdt ntanemtsev n niaot aedl i. hsWled otmnemtsev neitaulave tnemom em iet raat aed h ft,iel utrnemtsev nei hetcud e oddte s eutbhg itmnemtsev n fio .elbiss ot p ossnii hnte h)tat addevres byoletercs ifed ose uhmto rgfnisir ad(etagergga .tnemtsev noir ed zneavitis ohpt ofsbodoir erpe vdoetagerg gstainemtsev ndievresbO -em ihatc urs oyftniatrec ndu nyatilibisrever r fisonoitacilp mei hetv isgtlus erruO , ed,renut us arrafgo-eo egm l.rneakgohtcgltioaptasc 2 ytilibisreve rhti wledo mlacissalcoe ndradnat seh tn ignitegdu blatipa clamitpO 1 ydbevir etds orce seu h otltau qleatip a fctocudo repunev elranigr aem hstniatniam tnemtsev nliamit peo h,telbisrever r sitinemtsev nnie h,wreve w. o)H369 1n(osnegroJ ftocudo repunev elranigr ae mhttneve rodptede esynal nloatip aecsahcr u ospyticilop ts orce seu h sthici h,weldr ush i. heTldr udhevired-yllamit p noeavo bganis imro rlfatipac rehg i sh,iytniatrec ndu nyatilibisrever r fitonuoc ceak a otdtenif eydletairporp plaatip afco saec adf nlaatip a ocsn ayhltnerr umcr ief h ft,is u. htTs orce snuainosnegr oeJ hntaht ,)kco tlsatip ae c hfntooitcn ugfnisaer c se aade(ludeh ctscudo repunev elranigr anmevig kco tlsatip alcamit peo hnta hrtella m ssyitilibisrever rried nkuco tlsatip alcamit peoht .ytilibisreve rrednu esua2c esbruc c,otcef f"etsoc-res ue" hltl alcl i ewhwci h,wtlus es ri hT ssiu hdt nearut uef h ntdin iyb atmniartsn oyctilibisrever rei htta hstetapicit nmar iefht ,)889 1a(lotr e yBdbezisahp mnee esb aghnidn isfi h;tyad ottsev n oittnatcul eerrom ntaa hsttilus edret a. l) e4Ar99 1k(cydn id Pntaix id Dn,a)989 1t(ix i,D)889 1k(cydniP red ntus orce se uhetsaerc nositdn emtr ie fhgtnic asfkco he s hfetocnair ae v hnetisaercni esaerc nsi i. heTs aeclbisrev edrradna tes h nttis orce seu hgtnitcef ftauoht iywtilibisreverri lati plaacmi teephcotu dreerh t srodu tnfyettniatre cdneusae r ecto unstrdi o eecnshiut .ytilibisrever rried nkucots shac u,slatip aocr es zayhltnerr utca hmt r oiyatflp peavo bdaebircs esdtlus eerhT desaerc ndi nyatilibisrever r fisotcef fee het rtaa ht.w udBetra tgsnitt etgs umjr iwf ean 1 Throughout this paper we will use the term "reversibility" to refer to the situation in which the firm can purchase and sell capital at the same price without any transactions costs or adjustment costs. 2 It is important for this result that the marginal revenue product of the firm is a decreasing function of the latipa c,kcots sa deton yb kcydni P)3991( dna lebA dna ylreb E.)7991( fI eht lanig reaumnevetrcudorp does not depend on the capital stock, then current and future marginal revenue products are unaffected by today's investment, so the link from today's investment to future returns is broken. The firm is then no more reluctant to invest under irreversibility than with reversible investment. Caballero (1991) also 3 nur-gn oe l hnstouc oenfwoitse usqi hstser d? dmoarT igfniog nnro aoyftniatrecnu ts oeknoc doltasti peyahtctniatr e ecfcnonue s ,.eenekrhis c ptr oluftaoOstcipac eg rote tnv nan not o ai ise cf,gtnh.oe na otnrsotec uoulcw trfce nneo poerfexreherhtuTc k cloatt siephatc K at a future date gnittte ly broivahe bnur-gno lenimax eneh tdn a t t .ytinifn ihcaorppa ottnatrop mst,iiin ugrn oe lhnktico tlsatip ae chfrtooivah ee bhetnima xoeT et aedrut uyf n taeavir rlal imwr itafa hetzingocer t eghntitneser pkecr oltast ih p taaicw d n.a) mnfeoIditaicer ptfenoduo cgcnaik aet t(ta adrohott itrnpemtse vnfnooiitalumuc et a tdwa oylllausu n sutiupt uso'mr ief hrtof ts t fieom olsl e osetk idllu omwr ief h,t d n,alatip alcl etsonn amcr ief h,tytilibisrever rried n,ureve w. oeHci repvitis o taplaatipac stia hktco tlsati p eaav c aorhtoivah etbnemtsev ntis an pws otydibeniartsn oedcblu otwi e thtasad etrrf adtls ueftosiico odhlc unto aiwrhethgih te hnteewt eebcnanoss is di. hT y ntacelf et rosne oddl ooehtsoo hdclu ottwia hltev ee lhd tnkaco tlsatip alcaut csa'mrif elbarov a ofetsnops elramit pso'mr ief hsttcelf e trdiaet s. nyItilanoit a freoruliaf e hettacid notitcef f"erevogna he "hsttacef fsei hort te.f tees rWae phnstiecnatsmucric e hrtet atla hrtoivah eybllaicep s,eroivah etbs ankpoco tlsatip atcnerr ue chfetocnedneped .esrev e oretk idllu omwrif 3red nkuco tlsatip arceh g odiata hen latccef freevog n ae hhT .ytilibisreve rredn unah tytilibisreverri tnerr ue chr tosfnoitacilp mginisop peov ashtcef freevogn ad hntasoc-re seuhT sodt ntecte ftfseoc-r e es,huyttilibisreve r.hrk tici oWltasti pnaucr-g n eonfhlootitatcepxe eehstae r scod ntntiecte frfeevog nesahahter ekhc woltasti pdaectce peexhcetuder sezisahpme eht ecnatropmi fo gnisaerced lanigram eunever tcudorp fo latipac ni sih sisylana fo ehttceffe of uncertainty on investment. 4 tfcoe f efghentidra gserrew sgnnaiso pep vooi sgsltace f. ofk ewecht oTltasti pdaectcepxe e h,tdessucs iedv aes.hwAkco tlsatip ancur-gn odletcep xe ehnytotniatrec nduesaercni nur-g ndoeltce p exehectu dsoedtr nyettniatre cdneusaer ctn aishetil ptmcie ftfseoc-resu desaerc ntia hsteilp mticef freevogn aeh h,treve w. oyHtilibisrever rried nkuco tlsatipac ezyl arenewa p.sak ipcnh oItltasti pnaucr-g ndoeltce p exehestaer csondti nyettniatrecnu gnik aktco tlsatip ancur-gn odletcep xee h ntyotniatrec ndu nyatilibisrever r fisotcef feeht tnuocca fo ethstoc-r ed snruae vs.otrgcenehafthfeegot suoir a nvdietpmet tsa ayhtniatrec nrued ntunemtsev neilbisrever r nieorutaret ielhT .kco tlsatip ae c hnytotilibisrever rfsiotcef feegare vrnaour-gn oe lhstses sosatyaw 4 )0 9a9l1o( tadrlneiaBlo t)dn8ne 8aBa9l1o(treB 5e h ftnooitubirts indur-gn oel hetnima xe snioitubirts isdi h ftnoa eem htta hetdulcn odc nlaatip a fctocudo repunev elranigram .ytniatrec n suriehg ieh hrtehtr udfecud edr n -ay-tilibisrever r fieocnese rep h ytdbecuder latip ae chfetoul advetcep xe ehstelbmes etra hctitsita trsalucit r taaa phwto hoss lyaehT skac( oltasti p eeafhuco tldaevtce p e xt,hseoytinltnatro p,mtiub-- ngu n rekonhclitots )399 1o(rella b. ayCtilibisrever r fieocnese rep h ytdbesaerc nsii -,- )n3oitc e nSwio hesw ,tcef freevogn ae hhd tntacef ftesoc-re se uhltl aetcwa hsttcef fgenisop pe ohstebircsed egar elnvaoati psa scere rolsodm lmo rh eirhfethte htw a“fhot otrupoh tsitwre sdsnaa eta t)s499 1o(rellab ad Cnaalo t.r )e8B8. p”(suougib mskairowema rsfselnoitc i nnraiafht tnemtsev nried nnuoitcudo rfypotisnet nliatip ae ch,tegar e fvn oaOo “rtpuohtiw 3 d e rst tesc envuey h.eocfb t T)mgsfsie2tnie ixl9sad"ib9 ehsD i1evins(lns arpienem rivafeexotresryih" Dixit emphasizes the finding that with irreversibility past events affect current investment behavior. 4 alotreB )2991( sredisnoc a citsinimreted ledom fo tnemyolpme htiw gnirih dna gnirif .stsoc eHsdnif that with positive discounting and/or attrition, hiring costs tend to reduce average employment, while .ytnia tsr te fc croeene fhud,f t iy es eslte.hnsootoundnco eimvybo Olepgma ereesvaae rs ctgnsnioicrif 5 nI alilotneB dna alotreB ,)0991( eht rotcaf fo noitcudorp taht si yltsoc ot tsujda si ,robal tub tisi straightforward to interpret this factor as capital and to treat investment as irreversible. 5 yllautc as iytilibisreverri rehgih hcih w)[ 7n(oitau q fe eidblu o twnia h]tlanigi r nosicilat i[ l l tadaeilp p]aytilibisrev esrselts o fceos aec h ntliatip a fctonuo mlaamit peo hstebircsed e hodtteilp pnae hewu rsmtiia lsci htt a nh3otitc enwSio he.s W). 4n,f922. p”(semit robal-latipac oitar , t utbo no tleeh. vtklfeca olotetihsptac .tnemtsev n niyotniatrec n futocef fee hdtenima xoes lsa aehrutaret ielhT f It“a hstedulcn otcnemtsev n niyotniatrec n futocef fee h ftsoisyla n)a199 1s(’orellabaC e hdt neagr a slsits otcnemtsuj d fayortemmy sea h,t.e. ig(nor tysltneiciff u ssticef fseiht s ilatipa cf oleve leh tn olatipa cf oytilibatifor planigra meh tf oecnednepe devitagen -elbisrever re.i heTvitag esnemoc epbihsnoital eyrtniatrecnu-tnemtsev nei h,t)gnorts . p”[.es asci h otdtnopserr oycllacip yetrutaret iel h ntdiezyla nsatnemug rtanemtsevni laiti noir ehzt iswnig embr ief htta hgtnimus s yadbeniat b sotilus egrnor tss i. h]T682 kcydn id Pntaix i.Devitarepo nstiicef freevogn ae hhltl aetcwa htwa ho,ts]3 8. 2pl[atipac ytniatre ctfncoue f efsnheuot c dosnf rarouatoli mli esr deaodmis n)o3c73-27 3,.4p991( e h ftmohtirag oel h nteigna hdcetcep xee hettalucl ayce h,tyllacific e. ptSnemtsev nnio d ek t clc roaeeott phsin xtpuee ar udc- flegeoat nhvc nroteeaelphhh xttt,eak rcl(oattsipac ntia hetdulcn o yc.e )hkTco tlsatip ancur-gn oe l hn)tiem itti n ruee gpn(a he c hfetoulav regr a ale"s asciht s ,dkn caloat ts e ihtfeptaoha wrtceograg rneuvra- gsrn n eoaawleoml er e,h)w 3 .7"p3e(gar etnvnoaemtse vsn siseulht s nwio h. esyWtniatrec nsuerusa em detaluc lksacic oltasti pnaucr-g n eoefhluot ldaevtce p exnhe et thn awo4hittceS .desrev e ernb akccydn idP ntaix idD noarellab a fCsotlus eer h,tylticilpxe mr ira fokfco tlsatip aecrut uef h fteoul advetcep xee hytltcer iedtalucl aecW tcef ftesoc-re seu h,tkco tlsatip aocr ehazt igwnitra tmsr ir.a foyFtilibisrever rginicaf s itah ttceff en a,ytilibisreve rredn unah tlatipa csse letalumucc ao tmri feh tsesua cyllaitini 6 semoc e tb,irevew o,hlatip ascetalumuc cmar ief h. styAtniatrec nduesaerc n yidbeifingam t fi,ilatip alcl e osetk idllu omwr ief hetdosi pdenamed-w ogalnir utda hytlek ielrom red nkuco tlsatip ae chgtnisaerc n,ievitare pnoe hstticef freevog n .ae dhhlTuoc hcih wn isesa cdni fe w,nu rgno leh tn .Iytilibisreve rredn utah to tevitale rytilibisreverri .setanim otdcef freevogn ae hhhtci hnswireh td on,asetanim otdcef ftesoc-re seuht w o .h etssWinepe eddaets nti u,bytiugib msai hetvlos etr osne oydtniatrec ngunisaercnI red nkuco tlsatip adcetcep xe ehstesaerc nyitniatrec nduesaerc n,in ugrn oe lhnttiaht e hrtehte h,ws u. hyTtilibisrev erred neur onme v teeisaerc nni atc u,bytilibisreverri red n ruyotilibisrev erred nruegr a slkico tlsatip ancur-gn odletcep xee h nteisaercni .seul arvetemar a fpeocio hec h ntsodnep eydtilibisreverri nhat imw r filaofed oemlp m tiacsurtsn oe,cwrep ae p hfntooitc etsx ee nhntI dn aytilibisreverr ihti wnoisice dtnemtsevn ilamitp ost ieziretcarah cdn anoziro hetinifni gnirap m,okcc oltasti p eaefhcuot ldaevtce p exehettaluc ln,eao3wc i.ty ctnenISiatrecnu -re seu hgtniyfitne ddi neas atcnemtsev neilbisrev eer h otets atcnemtsev neilbisrever reiht detce p eyxnhteotniatre csfntouce f esfnheeots un co 4oi.fts ctecSe frfeevog n datnhsaoc ,e ttasrere te,nhhitt w softrocge fesfhreted ins on5iot cceel Si,hkwc oltasti pnaucr-gnol ref fne6oowit c. ednSnIam efydoticitsa leeci re phd tn,anoitcudo rnepira hlsatip aecht .skram egrnidulcnoc 2. melb onroPitazimi tsp'Om reihFT fsotneme lye eek h ntsouc o ofrted r nomir ief h ftloed oemlpm ipasolev eedW s :tfncoo eiefthf stereuuoq ytilibisreverri d na ytniatrecnu e h ntnioitalumuc claatip a nco 7 gnolnur e rlaatip a ocstnrut e,relbisrever r sitinemtsev ntia hetmus s ea,wylgnidro c. cA r onfeso hec rea s euswmr olfanoitcn u ef. hnTozir oehtinif n nisa amhr ief hdt n,aniatrecnu tix i,D)099 1a(lotr ed Bnaalilotn e,B)889 1a(lotr eydBbe sous le ard an,aytilibatca rrtieht .)69 9y1l(r e dblnE ea db,nA)a49 9o1r(ella b daanClaot r,e)B1991( evr udcnam ecditsaleo s nisaec atfa hmtr irafedisnoC Q = X P -e (1) t t t erehw Q ,dedna mteud p ytftuoiotn aesuhiqt P si eh tecirp f,otuptuo X citsahc o stais t t t d n,akco hdsnamed eelbarotsn osnecudo rmpr ief h.Tdnam e fdyoticitsa leeci rep h st>1i output Q noit cnnouiftcu dsoarlpguo Dg -n obietbdhort Cocca t Q = L 1 -bK b (2) t t t erehw L ,rob a sli K era hlsatip ae chd tn,akco tlsatip ae chsti b <0seifsita s b < 1. At t t sesoo hmcr ief hetm i fttoni ohpcae L tifo rgpnitare pso teizimix a omt P Q - Lw er ehw w t t t t stiifo rgpnitare p foeoul advezimix a em. htTnatsn odcemus s sahici h,wet aerg aew hsti y bnevig 6 h p( K , X ) = X gK 1 - g 1 - g t t erehw (3) (cid:230) 1 (cid:246) ge 1 1 h ” (1 - g)(cid:231)(cid:231) (cid:247)(cid:247) (ge - 1 )ge- 1 w 1 - ge > 0 dna 0 < <g ” ( ) <1 . Ł ge ł e 1 + b e - 1 latip asc'mr ief h ntsodnep emdr ief h fttoifo rgpnitare psouoenatnats nei hetsuaceB stock K dna mtfenodenop mcoictsahc o e tdnhsnota X gnit an rofeeiohpttou l,eohvte t t [ ] 6 gen hitTtiafroerpp osi nevigyb p(K , X )= max X 1 /eL (1- b)(1- 1 /e)K b(1- 1/e) - wL = L { [ ]} max (X / K )1 /el1- 1 /(ge) - w l K erehw l” L / K and g is defined in equation (3). Solving this l maximization yields l= w - ge(cid:230)(cid:231) ge (cid:246)(cid:247) - ge(cid:230)(cid:231) X (cid:246)(cid:247) g and p(K , X )= w lK which is equivalent to equation (3) Ł ge - 1 ł Ł K ł ge- 1 in the text.
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