The Effects of Irreversibility and Uncertainty on Capital Accumulation

53 Pages·2017·0.54 MB·English

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Finance Papers Wharton Faculty Research
1999
TThhee EEffffeeccttss ooff IIrrrreevveerrssiibbiilliittyy aanndd UUnncceerrttaaiinnttyy oonn CCaappiittaall
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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
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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
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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
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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
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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
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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
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kcydn id Pntaix i.Devitarepo nstiicef freevogn ae hhltl aetcwa htwa ho,ts]3 8. 2pl[atipac
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e h ftmohtirag oel h nteigna hdcetcep xee hettalucl ayce h,tyllacific e. ptSnemtsev nnio
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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
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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
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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
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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.