Prelmary Bas Are Where The Lquy Is Olver Har Harvar Uversy & NBER a Lug Zgales* Uversy of Chcago, NBER & CEPR February 04 Absrac Wha s so secal abou bas ha her emse ofe rggers goverme erveo? I hs aer we show ha, eve gorg ercoeceess ssues, he falure of a large ba causes a larger welfare loss ha he falure of oher suos The reaso s ha ages ee of lquy e o cocerae her holgs bas Thus, a shoc o bas srooroaely affecs he ages who ee lquy he mos, reucg aggregae ema a he level of ecoomc acvy We also show ha he goverme wll choose a larger fscal erveo whe a large ba fals Key Wors: lquy, balou, bag JEL Coes: E4 G, E5 * Olver Har graefully acowleges facal suor from he US Naoal Scece Fouao hrough he Naoal Bureau of Ecoomc Research Lug Zgales graefully acowleges facal suor from he Ceer for Research Secury Prces (CRSP) a he Iave o Global Mares a he Uversy of Chcago
Durg he 007-008 facal crss usral frms, clug maor oes le Geeral Moors, were allowe o go baru By coras, facal frms, wh he oable eceo of Lehma, were bale ou Oe ossble reaso for hs ffereal reame ca be fou he olcal clou of hese wo usres Facal frms were a are maor oors of rece amsraos May of he rece Treasury Secreares a Whe House Chefs of Saff came from he facal usry The greaer aeo show by he goverme owar he facal usry, hus, mgh be urely a maer of olcs o ecoomcs Whle o eyg hs ossbly, hs aer we elore a alerave erreao: ha goverme erveo s usfe by a rsc fferece he welfare cosequeces whe a ba, raher ha a equally-sze usral frm, fals A ofe-meoe raoal for hs fferece s he egree of ercoeceess of facal suos Bu whle here s o oub ha large facal suos e o be hghly ercoece, large usral frms le Geeral Moors a For are very ercoece oo, as s srogly suggese he followg esmoy of For s CEO Ala Mulally: The omesc auo usry s hghly ereee A collase of oe of our comeors woul o oly affec For a our rasformao la, bu woul have a evasag rle effec across he ecoomy Aoher oular erreao amog facal ecoomss for he fferece bewee large maufacurg frms a bas focuses o he ably of eosors o ru (eg, Damo a Dybvg, 983), rasg he ossbly of effce lquao Ye, f hs were he oly roblem, eos surace woul f Furhermore, sulers a cusomers of GM ca ru oo, as show by he fac ha 008 he Goverme ervee o guaraee GM warraes So wha maes bas ffere? I hs aer, we focus o a ffere meso: bas are uque because hey are where eole ee of lquy ee her wealh I a worl where he reur from huma caal s o fully legeable, he falure of ay frm mles wo losses: a rec loss of wealh a a rec loss lquy, ue o he reuco legeable asses Ths ual effec s rese boh for a ba a for a Ala Mulally s esmoy o he Ue Saes Seae Commee o Bag, Housg a Urba Affars, November 8, 008
usral frm Ye, he mac of a loss of legeable asses s ffere eeg o he lquy ees of he holers of hose asses We wll show ha ages who ee lquy for rasaco uroses wll srooroaely hol her wealh he form of ba eoss Hece a ba falure hs hese ages, who are lquy cosrae, more severely ha he falure of a usral frm, causg a larger ro ema for labor servces, whch was suore by ha lquy, a a larger fall GDP( Smlarly, a loss bore by eb-holers affecs GDP srooroaely more ha a equally-sze loss bore by equy vesors) Bulg o Har a Zgales (03), we coser a smle geeral equlbrum ecoomy where secury mares are comlee, bu fuure labor come s o legeable There are wo grous of ages, ocors a eachers, a he lac of a smulaeous ouble cocece of was bewee he wo grous geeraes he ee for a relavely safe asse for rasaco uroses I hs coe we show ha ages wh lquy ees (ocors) wll choose o hol a srooroae amou of (Arrow) secures ha ay off he low saes of he worl We also show ha hese Arrow secures ca be maufacure by rachg vesme ayoffs orer of seory If we bul Arrow secures hs way, he ages ee of lquy wll hol srooroaely more of he mos seor raches We he coser he macroecoomc effecs of mosg a loss o ffere raches There s a bul- correlao bewee eremely egave aggregae oucomes a losses bore by he mos seor raches To elmae he effec of hs surous correlao, we coser oly losses ue o a osycrac frau a secfc rache: a Maoff-ye loss If we o, he effec we observe woul be eve larger We show ha, whe a loss falls o seor raches, he macroecoomc effec of hs loss s more severe a so s he welfare loss assocae wh Losses bore by seor rache holers erve he ages who ee lquy, our moel he ocors, of collaeral I so og, hey reuce he effecve ema of hese ages for eachg servces, ecreasg he amou of come he eachers ca mae Uable o sell her labor servces o favorable erms, eachers wll cural her ow ema for ocors 3
servces, furher reucg he overall level of ecoomc acvy Ths effec s more lme or eve comleely abse whe a uor raches face a loss, because uor raches are hel srooroaely by ages wh low lquy ees The very seor raches hel by he ocors loo smlar o ba eoss Iee, bas ca be cosere muual fus ha o he asse se ves facal clams a o he lably se have a srooroae share of very seor clams (eoss) Accorg o hs vew, bas are ohg bu a cos-effecve way o maufacure Arrow secures eee for lquy uroses Ths smle heory of bag s able o ela why bas ee o have eoss ha o o flucuae value Deosors are he ages wh he hghes ee for lquy a hus hey ema surace agas ossble falls he value of her vesmes, eve f hey are rs eural I our moel hs surace s rove by he eachers, e, he ages less ee of lquy Ths very smle heory of bag s able o ela o oly why he efaul of a ba s worse ha he efaul of a smlarly-sze comay, bu also ha hese effecs are o uque o bas: hey are commo o all he mos seor secures Ths mgh ela why govermes are so reluca o mose losses o bos, esecally secure bos The reaso s he same: hey are hel srooroaely by eole ee of lquy The res of he aer rocees as follows Seco reses he framewor Seco 3 characerzes he o-legeable equlbrum for he case where here s suffce lquy each sae of he worl o susa he frs-bes level of rae (Oe of he sub-cases s relegae o a Ae) Seco 4 shows how hs ema ca be sasfe by secures raches a how he mos seor raches wll be srooroaely hel by ocors Seco 5 ees he aalyss o he case where here s suffce lquy he bes sae of he worl o susa he frs-bes level of rae Seco 6 cosers he role of fscal olcy Seco 7 elas how our very seor fus ca be erree as bas Fally, Seco 8 coclues The Framewor 4
There s a large umber of ages E ae each age s equally lely o be a ocor or a eacher; ages lear her ye a he begg of ero Docors wa o cosume eacher servces ero a eachers wa o cosume ocor servces ero 3 Docors a eachers ca also cosume whea ero 4 a here s o scoug Each ocor a eacher has a eowme of whea ero equal o e Whea ca be vese roecs; hese roecs yel whea ero 4 We wll assume ha e>0 The mele s as Fgure ---------------------------------------------------------------------3----------------------------------4 Ages lear wheher Sae of worl Trae of Trae of Ouu hey are ocors or eachers realze eacher servces ocor servces from Whea vese Secures rae roecs/ whea cosume Fgure We wre ages ules as: Docors: ( ) U w l Teachers: ( ) U w l where s he quay of eacher servces cosume by a ocor; l s he labor sule by a ocor; s he quay of ocor servces cosume by a eacher; l s he labor sule by a eacher; a s he quay of whea cosume by vual, ero 4 We assume cosa reurs o scale: oe u of eacher labor yels oe u of eacher servces a oe u of ocor labor yels oe u of ocor servces w 5
Ages are rs eural The mares for eacher a ocor servces are erfecly comeve I s crucal for our aalyss ha here s o smulaeous ouble cocece of was: a eacher oes o wa o cosume ocor servces ero from he ocor who s buyg hs eacher servces Coser ow rouco There s a rsy echology ha rasfers eowme bewee eros a 4 There are (aggregae) saes of he worl Wh robably >0, oe u of ero whea s rasforme o R us of ero 4 whea (=, ) Whou loss of geeraly we label he saes so ha 0 R R R Ages lear abou he sae of he worl bewee eros a All ages are rs eural We also assume ha here s free ery of frms ossessg he echology escrbe a ha hese frms face cosa reurs o scale (he frms echologes are erfecly correlae) Ths framewor s smlar o Har a Zgales (03), ece hree resecs Oe (mor) s ha here are saes sea of us The seco (more mora) s ha we o o assume ha a age ca sure agas becomg a ocor raher ha a eacher before ero ; a usfcao s ha ero eowme cao be lege avace Thr, a mos mora, hs moel here s o rsless sorage As we show Har a Zgales (03), he resece of mulle vesme choces creaes a soro bewee rvae a socal ceves Sce hs soro has alreay bee aalyze our oher aer, we wa o elmae here I se of hese ffereces, some of he basc resuls are he same For eamle, he absece of ay legeably roblem he ecoomy has a uque Arrow-Debreu (or sequeal Arrow) equlbrum I hs equlbrum, here s a searao bewee cosumo a rouco The rces of ocor a eacher servces, he wage raes of ocors a eachers, a he rce of whea wll be he same, a we ca ormalze hem o be each sae of he worl A hese rces each ocor a eacher rouces a cosumes oe u of servces, curs a labor cos of /, a receves a cosumer surlus of ½ Ages also receve eece surlus e R from vesg her eowme, a so he uly of each 6
age s e å R + Fally, he equlbrum rce of a Arrow secury, whch ays off oe u of whea sae, s / R, where R= å R 3 No-legeable Equlbrum for he case where er Coser ow he case where fuure labor come cao be lege (e, worers ca he her come from leers) Suose, however, ha roec reurs ca be lege Tha s, frms ca ves ero whea he rsy roec a ssue secures collaeralze by he roec reurs (roec reurs cao be sole by frms maagers) These secures wll be urchase ero by ocors a eachers a use as a meas of ayme for servces eros a 3 Sce here are o furher frcos s aural o assume ha frms ssue a full se of Arrow secures bace by her roecs (where secury, =,,, ays off a u of whea f a oly f sae occurs) Le us revew he mg Ages lear her ye a he begg of ero Arrow secury mares oe, a frms ves The sae of he worl, sae say, s leare a he e of ero A hs o Arrow secury has value ( erms of ero 4 whea) a all oher Arrow secures have value zero I ero ocors use her holgs of Arrow secury o buy eachg servces I ero 3 eachers use her holgs of secury acqure ero, lus wha hey have accumulae from ocors reur for eacher servces ero, o buy ocor servces I ero 4 vesmes ay off a whea s cosume I hs seco we suose ha er ; we coser he case er > Seco 5 To comue he o-legeable equlbrum, ormalze so ha he rces of whea ero, whea ero 4, Arrow secury ero, a Arrow secury ero 3, are all oe (f sae occurs) Coser a ocor s uly mamzao roblem I equlbrum he rce of eacher servces ero cao ecee sce oherwse ocors woul srcly refer o use her secures o urchase ero 4 7
whea raher ha eacher servces, a so he eacher mare woul o clear (Docors are ffere bewee eacher servces a whea) Thus, we ca assume for he urose of calculag uly ha ocors use all her Arrow secures o buy eacher servces (By a arallel argume he rce of ocor servces ero 3 cao ecee a so for uroses of calculag uly we ca assume ha eachers se all her Arrow secures o ocor servces) Ne coser a ocor s labor suly ecso ero 3 Igore he subscr o he sae The a ocor wll choose hs labor suly l o mamze l ( ) l, e, se l =, where s he rce of ocor servces Noe ha s oo lae for he ocor o buy more eacher servces a so hs margal reur from wor s (he wll use he rocees o buy whea ero 4) A ocor s labor yels reveue ( ), whch he reeems for whea ero 4; ao he curs a effor cos of ( ), a so hs e uly from wor s ( ) I follows ha ero a ocor chooses hs holgs of Arrow secures (, =, ) o solve: (*) Ma s q e, where, are he rces of ocor a eacher servces, resecvely, sae a q s he ero rce of he h Arrow secury Noe ha frm rofs are zero equlbrum gve cosa reurs o scale, a so we o o ee o ee rac of ay ves receve by cosumers A smlar calculao ales o eachers The fferece s ha a eacher ero chooses her labor suly l o mamze l - (l ), where s he rce of eacher servces The reaso s 8
ha a eacher s margal reur from wor s, sce she wll use her come o buy ocor servces Thus a eacher s e uly from wor s Hece ero a eacher chooses her holgs of Arrow secures (, =, ) o solve: (**) Ma subec o q e As oe, rof mamzao a cosa reur o scale mly zero rof: (3) qr Sce all he whea s vese, he suly of he h Arrow secury s er Hece, he secures mare clearg coos are (3) er, for =, I s easy o see ha equlbrum 0 for all : f 0, he rce of he eachg servces sae woul be zero a he reur o a ocor of urchasg a Arrow secury ha sae woul be fe Also, sce we have assume ha er, eve he bes sae he suly of lquy s o eough o suor he Arrow-Debreu level of rae a so rces of ocor a eacher servces wll be srcly below I follows ha ocors a eachers wll se all her avalable wealh o each oher s servces eros a 3 Gve he suly fucos for ocor a eacher servces obae earler, we ca wre he mare clearg coos for ocor a eacher servces sae as (33), 9
(34), for =, (*), (**), (3) - (34) characerze a o-legeable equlbrum Alhough 0 for all, s less clear ha 0 for all I he e we wll cocerae o he case where 0 for all : we show ha a suffce coo for hs s R R I he ae we esablsh ha our resuls geeralze o he case where 0 for some Prooso : Le S R J, a suose ha S R The here s a uque o-legeable equlbrum characerze by q, RS er S, er er S 0, ( er ) = 4 R 3 e 4 S for all Proof: Suose 0 The, he frs orer coos for (*) a (**) are: (35) q (36), q for all, for some, 0
From (3) (34), (37) ( er ) a 4 ( ) ( ) er a so (38) 4 q ( ) ( er ) (39) q ( er ) I ur, hs mles (30) ( ) ( ) 4 er From (3) a (39) (3) å R = = S (er ) (e) Subsug (3) o (39), we have (3) q = (R ) S From (30)- (3) a he buge cosra å q = e, we have (33) = S a so we ca wre 3 e, (34) er S (35) = 4 (R ) 3 e 4 S
We have esablshe he formulae Prooso The oly remag hg o chec s ha 0, e, er Ths wll be rue as log as (36) er S er for all, e, S R I s clear ha he above s a o legeable equlbrum The argume he ae esablshes uqueess Prooso ells us ha a ocor s ema for Arrow secures QED s srcly creasg I s also easy o see ha a eacher s ema for Arrow secures, er er S, s srcly creasg (gve R S) Boh of hese resuls are uve I beer saes he suly of Arrow secures s greaer, her rce lower, a ares wll hol more of hem The e rooso ells us ha a ocor s ema for Arrow secures ecees a eacher s ema he lowes sae = a he reverse s he case he hghes sae = Also he emas cross oly oce Prooso :,, a here ess a * such ha for * a for * Proof: Coser (35) e[ R S R ] Ths s osve for = sce R J R a egave for = sce RJ R Also f * * 0, e, R* RJ, he for * R RJ a so 0
QED Prooso s also uve Lquy s more mora for ocors ha for eachers, a s relavely more hs way low saes of he worl 4 Trachg of Secures So far we have show ha ocors wa relavely more Arrow secures he low saes a eachers he hgh saes Gve he umber of saes of he worl, s worhwhle o coser wheher hs ema ca be sasfe by smler secures I hs seco we wll rove ha boh yes of ages ema for secures ca be sasfe by rachg he ayoff of a vesme he esg echology o he bass of seory, smlar o he rachg of collaeralze eb oblgaos ha was so oular before he 008 facal crss (For a ffere elaao of rachg, base o asymmerc formao, see DeMarzo (005))We wll also argue ha hs way o maufacure secures s less roe o e os maulao by he facal ermeares Fally, we wll aalyze he welfare effecs of losses curre by secures wh ffere levels of seory 4 Traches as a vable subsue for Arrow secures Le s sar by rovg ha boh he ocors a he eachers ema for Arrow secures ca be sasfe by raches o he ecoomy s reur sream ( R, R, R ) A rache corresos o a eb level of a cera seory If he raches are,, 3,, esceg orer of seory, he sae he frs rache receves M(, R), he seco rache M(, R M(, R) ), he hr rache M( 3, R M(, R) M(, R M(, R)) ), a so o Prooso 3: The ema for Arrow secures by ocors ( ) a eachers ( ) ca be sasfe by raches,, 3,, of he rsy roec reur R, R, R 3
Proof: The roof wll be by cosruco Le R, R R, 3 R3 R,, R R be raches esceg orer of seory The he reur vecors of he raches,, 3,, across ffere saes of he worl are gve by = [ R, R, R ], =[ 0, R - R, R - R R - R ], a =[ 0, 0, R3 R, R3 R R3 R], 3 = [ 0, 0, 0, 0 R R ] A ocor s orfolo yels he reur vecor (, ) Sce s mooocally creasg, f he ocor buys R of he frs rache, R R of he seco rache, R R 3 3 of he hr rache u o R R of he las rache we ca relcae he same ayoff he ocors woul have obae wh he Arrow secures Tha s, R R R R R R R 3 3 3 (,0,0,0) (0,,0,0) 3 (0,0,,0,0) (0,0,0,) The same logc ales o eachers QED Whle here are may ways o maufacure he Arrow secures eee, rachg s arcularly aracve because s robus o maagers esroyg some of he ayoff o favor oe se or aoher Coser a secury ha ays oly f he sae of he worl s For he ower of ha secury here s a srog ceve o clam ha he sae of he worl s, eve whe he rue sae s +, sce oe case 4
he wll be a a lo, he oher ohg We have assume ha maagers cao seal ay ayoff, bu hey may be able o esroy some Thus, f he rue sae s above may be ossble for he ower of secury o brbe he maager o esroy ouu a ree he rue sae of he worl s The same roblem oes o arse wh raches, sce he ayoff of hese secures s mooocally creasg he rue sae of he worl a so here s o ceve o falsfy he sae of aure by esroyg ayoff 4 Dsrbuo of owersh of he varous raches Havg esablshe ha raches are a covee way o acheve he same ayoff as ha obae by Arrow secures, we as e how he varous raches wll be allocae across vesors Prooso 4 says ha ocors wll ves more seor raches a eachers wll ves more uor raches Prooso 4: The amou vese by a ocor rache R R s srcly ecreasg =, (where 0 = R 0 =0) The amou vese by a eacher rache R R s srcly creasg =, (where 0 =0) Proof: Usg Prooso we ca wre (4) e( R R ) S, R R R R whch s srcly ecreasg sce R s a srcly cocave fuco Also from (3), (4) R R R R e, 5
a so R R mus be srcly creasg QED 43 Welfare effecs of losses ffere raches Now we wa o suy he ffereal macroecoomc a welfare effecs of losses ffere raches There s a obvous reaso why a loss suffere by a very seor rache has worse welfare cosequeces: sce he rache s seor, s mare oly whe he loss he uerlyg vesme s so severe as o go hrough all he oher layers Hece, a loss a very seor rache s a caor of a very egave realzao of he sae of he worl To elmae hs effec, we assume ha each rache s maage by a searae fu a ha oe of hese fus faces a ueece loss ue o a accoug frau (a Maoff-ye shoc), e, a oally osycrac eve I s ow legmae o as whch fu s losses wll have he wors mac o he ecoomy To be recse, suose ha he ecoomy has arrve a he begg of ero, a s ow ha sae has occurre A hs o he fu maagg rache eereces a shoc: a small (fesmal) ueece chage s wealh equal o (We are assumg ha sae s such ha rache s worh a srcly osve amou, e, ) Ths wealh shoc s srbue amog ocors a eachers accorg o her relave holgs of rache Recall ha a ocor hols R R us a a eacher sasfy (43) (44) R R us These sum o e, a so he wealh chages he realze sae wll = =, R R e R R e 6
If we efe (45) = we ca rewre hs more comacly as, R R e (46), = ( ) As Har a Zgales (03), we use he sum of ules of ocors a eachers as our measure of welfare Ths s reasoable sce e ae each age s equally lely o be a ocor or a eacher From (*) a (**), he sum of ules sae s (47) W = Usg (33)-(34) o solve for,, we ca wre (47) as (48) ( ) 4 W = ( ) ( ) ( ) Noe ha he absece of he shoc er Dffereag (48) wh resec o a usg (46), we oba, a =0, (49) W = 3 4 4 4 ( er ) ( ) ( ) ( er ) ( er ) ( ) ( ) 4 er ( er ) ( er ) 4 ( er ) = 5 3 4 4 ( ) ( er ) ( ) ( er ) ( )( er ) ( er ) ( er ) 4 4 4 The coeffce of (49) s 7
(40) 4 ( ) ( er ) ( er ), a hs s easly see o be srcly osve, sce (4) er ( er ), gve ha er Hece, we have esablshe ha he effec o welfare of a small shoc o rache s greaer f s large Bu we ow from Prooso 4 ha s ecreasg Therefore, we have esablshe ha he welfare loss from a small egave shoc o a rache wll be greaer he more seor he rache s The uo s smle Each ollar los has wo effecs: a rec effec o welfare (equal o a ollar sce ages have lear uly) lus a rec effec o welfare rouce by he reuce level of rae (whch geeraes a osve surlus), cause by a reuce level of lquy The ocors are he ages more ee of lquy Thus, a loss ha falls srooroaely o he shoulers of he ocors wll have srooroaely large welfare cosequeces As Prooso 4 shows he eole who ee lquy he mos ( our moel he ocors) ves more of her wealh seor fus I fac, he more so, he more seor hey are Thus, a loss he more seor fus wll fall srooroaely o he shoulers of he ocors a hus wll have a srooroaely large effec o he level of ecoomc acvy a a srooroaely large loss aggregae welfare I s aural o as how large W s Oe s frs hough s ha W >, e, he effec of a wealh shoc wll be mulle, gve lquy cosras However, hs oes o have o be he case I fac, s eve ossble ha W <0! The reaso s ha a osve wealh shoc ha affecs maly eachers ( close o zero) wll rve u he rce of ocors servces (see (34)) a herefore reuce he suly a crease he rce of eacher servces (see (33)) Ths ca mae he ocors so much worse off ha he sum of he ocor a he eacher ules falls 8
However, hs cao hae for very seor raches, arcular, = For =, er er sce er S s cocave R Therefore, a lower bou for W s gve by (49) wh relace by er Subsug er o (49) yels (4) 5 3 4 ( ) ( ), 4 4 ( er ) ( er ) ( er ) whch ecees sce (43) er ( er ) mles ha 5 3 4 er ( ) ( ) 0 4 4 ( er ) ( ) The cocluso s ha a egave shoc o he mos seor rache causes a welfare loss ha s greaer ha he shoc self 5 No-legeable Equlbrum whe er a R s large We ow coser how he aalyss chages whe he bes sae here s eough lquy, so ha a he level of rae s effce Ths case s acually much smler a wll erm a suy of fscal olcy Seco 6 To smlfy maers we coue o assume ha er for all Much of he aalyss of Seco 3 coues o aly Frs, 0 for all a so he frs orer coo for (*) s (5) for all q O he oher ha, he frs orer coo for (**) s 9
(5) for all, q wh equaly f 0 We also ow ha sae, rces wll be srcly less ha a so (33)- (34) escrbe he equlbrum he goos mare Hece, by (3), (53) ( er ) (54) for ( er ) 4, We ow show ha he above mles 0 for all Suose o: 0 for some < The, (5)-(5) a = mly: (55), sce O he oher ha, (5)-(5) a = mly: (56) 4 er Hece, 4 (57) er whch s mossble sce, from (3),, er er, gve ha er Therefore, 0 for all, a, sce eachers have he wealh o buy some secures, 0 I follows ha (58) er for all, a so we ca rewre (54) as 0
(59) 3 ( er ) 4 for all Combg (5) wh (59), a usg, yels (50) q q er 3 4 Fally, we ca subsue (50) o (3) o oba (5) q R 3 4 er R (53), (59), (50), (5), a (58) (lus he sasfaco of ocor a eacher buge cosras) escrbe a o-legeable equlbrum where rces are he hghes sae There s a furher feasbly coo:, e, a ocor mus be able o affor a leas oe u of Arrow secury orer o be able o urchase oe u of eacher servces a rce sae Usg (58), we requre (5) q er q e, whch, from (50) a (5), ca be smlfe o (53) I oher wors er er 4 3 4 R mus be large ( arcular, er a so er ) I s easy o ee he rachg resul of Seco 4 o hs case A ocor s holg of rache, gve by R R, s cosa a equal o e for =, - from (58); whle for =, sce 0, er a so
(54) R R e I oher wors, a ocor hols equal amous of all raches ece he mos uor oe a srcly less of ha I s also easy o ee he welfare resuls of Seco 4 o show ha a egave shoc o a seor rache wll creae a larger welfare loss ha a equvale shoc o he mos uor rache We wll o rove he eals here, bu sea carry ou a smlar calculao whe we scuss fscal olcy he e seco 6 Fscal Polcy So far we have o cosere how he goverme mgh reso o he lquy roblems ha we have hghlghe I hs seco we aalyze fscal olcy alog he les of Har a Zgales (03) Secfcally, we assume ha here s a mllg echology ero 4 ha allows ocors a eachers o cover whea o flour, a ha hey eoy cosumg flour as well as whea The goverme ca mose a er u sales a o flour somehg ha he rvae secor cao o a ca ssue bos ero, afer he sae of he worl s realze, bace by hs sales a As Har a Zgales (03), we suose ha he goverme bos (b us of hem) are hae recly o ocors (ohg our aalyss reles o he ea ha he ey of a age s overfable) The eals of he mllg echology a refereces for flour versus whea ca be fou Har a Zgales (03) For our uroses s eough o rely o he followg resul from ha aer: he goverme ca crease he lquy of a ocor ero sae from o b, bu hs moses a loss o he ecoomy ero 4 of b () b, where he frs erm reflecs he bo reayme a () b s he eawegh loss of he sales a requre o rase b Here () b sasfes (6) (0) 0, '(0) 0, ( b) 0 for all b 0
I oher wors, he margal eawegh loss s zero whe he a rae s zero bu s srcly osve a creasg whe he a rae s osve We wll be arcularly erese how he goverme shoul reso o a Maoff shoc However, gve ha here s a shorage of lquy he ecoomy, he goverme wll wa o reso eve he absece of such a shoc Thus, we wll aalyze he omal fscal olcy wh a whou a shoc Aalyzg fscal olcy he moel of Seco 3 ur ou o be har, a so we wll focus o he moel of seco 5 where er a R s large We wll suose ha he goverme chooses fscal olcy sae ero o mamze he sum of ocor a eacher ules We wll also assume ha he goverme cao comm o s fscal olcy avace: he goverme wll choose b sae o mamze he sum of ocor a eacher ules afer, are eerme Le s coser he case here s o shoc a ae he o-erveo equlbrum as a sarg o Clearly, here s o ee for erveo sae sce he effce level of rae s realze here Coser < If he goverme ssues b us of bos o a ocor (each bo ays oe u of whea ero 4 sae ), he sce er, 0, he ew equlbrum he goos mare s gve by (6) (63) er b, er b, for =, - Tha s, (64) er b, er b 3 4 From (*) a (**), he sum of ocor a eacher ules sae s (65) b b b W = ( ) 3
The goverme wll choose b o mamze frs orer coo s ecessary a suffce: 4 er b er b er b b ( b ) = W Sce 3 er 4 b er b '( b ) 4 4 (66) W s srcly cocave b, he followg Noe ha he lef-ha se of (66) s srcly osve whe b 0 a zero whe er b, a so he omal b wll sasfy 0 b er Now suose ha ages acae ha he goverme wll choose b each sae < o sasfy (66) Wll hey chage her e-ae behavor? We argue ha hey wll o: he raoal eecaos equlbrum er, 0 To see hs se he ew rce sae o be as (64) Also le (67) q q er b 3 4, (68) q R 3 4 er b R The, s easy o see ha (5) s sasfe, whle (5) hols wh src equaly for < So 0 for sae < Hece, f we se er, (3) s sasfe for < Fally, he feasbly coo (53) becomes (69) er er, 3 4 ( er b ) whch s mle by (53) 4
Thus, we have cosruce a ew equlbrum wh goverme erveo where ocors coue o hol all he Arrow secures sae =, -, a he goverme omzes accorgly Noe ha sce er for all =, -, a er, he rachg resuls of Seco 4 a 5 coue o hol Le us ow coser how he goverme wll reso o a uacae Maoff shoc Noe ha sae < oly seor raches are he moey (raches ), a sce ocors hol all hese raches ( 0 for all <), oes o maer whch rache s h by he Maoff shoc Thus, f we are cocere wh how goverme erveo ees o he seory of he rache h, he eresg case s whe we are sae I sae a small Maoff shoc wll have o effec f So le s assume ha he ocors are us o he marg erms of lquy: Noe ha hs mles, so ha for small shocs here wll be eough lquy he mare for ocor servces o susa Suose ha here s a small (egave) shoc o he aggregae amou of lquy, whch s ve amog ocors a eachers as (46) Before he shoc he goverme ha a zero fscal olcy sae ( b 0 ), bu afer he shoc wll ervee As we have us argue, afer he shoc, a so he equlbrum he eacher mare s gve by (60) e, b, We coue o assume ha he goverme mamzes he sum of ocor a eacher ules eve hough hs welfare crero may o be so comellg he case of a uacae shoc 5
(6) b Welfare sae afer he shoc s herefore gve by (6) b b b W = = ( ) b b b ( b ) W s srcly cocave b a so he followg frs orer coo s ecessary a suffce: (63) We ca use (63) o comue alyg (46), yels (64) 3 b '( b ) b b b b ''( b ), 4 Dffereag (63) wh resec o, a (65) b 4 ''( b ) b 4 3 b 3 Calculag hs a 0, where b 0 a, we have (66) b 4 0 ''(0) 4 I follows from (66) ha he omal fscal resose sae o a uacae Maoff shoc (e, a egave ) s: a) osve; b) wll be bgger f he shoc hs a seor rache (where e ) ha f hs he mos uor rache (where ) e 6
7 Very Seor Fus a Bas So far, we have cosere oly absrac secures Ye, he mos seor raches hel by he ocors ca be erree as ba eoss O he asse se bas ves facal clams a o he lably se hey have a srooroae share of very seor clams (eoss) Thus, bas are a cos-effecve way o maufacure he Arrow secures eee by ocors a eachers I arcular, ba eoss lay he role of he mos seor secury hel by he ages wh he hghes lquy ees (ocors) I real-worl bas here s a aoal feaure (o coae our moel) ha gves eoss a hghly seor saus: her callably o ema If we coser callably o ema as a form of suer seory, moey mare fus e o have hs feaure oo, esecally f hey are (mlcly) guaraee by he equy of he sosorg orgazao (Kacerczy a Schabl (03)) a ossbly by he goverme Accorg o hs vew, wha maes bas secal s o he aure of her vesmes (e, formao-sesve ba loas, as Share (990) a Raa (99)) or her ercoeceess (as Alle a Gale, (000)), bu he eole who eos hem Bas are secal because her eoss are hel by eole wh he hghes lquy ees As a resul, losses amog eosors have eremely egave macroecoomc cosequeces because hey erve of lquy he ages who ee lquy he mos o suor her urchases A loss her lquy buffer wll lea hese ages o cural her ema for goos a servces, reucg he come (a he ably o ay) of oher ages he ecoomy Ths effec may reuce he level of ecoomc acvy a he aggregae welfare by a mulle of he loss bore Ths feaure s o uque o bas, bu s share by moey mare fus, sce hey rove a almos erfec subsue for eoss for ages who ee lquy As a resul, losses 7
bore by moey mare fu vesors woul have smlarly sruve effecs o he ecoomy Cosse wh hs erreao, 008 moey mare fus were bale ou a way smlar o bas, eve hough her leg was o secal a hey were o hghly ercoece The same logc ha ales o bas a moey mare muual fus ales o a lesser ee o bos geeral, arcular secure a hghly rae bos These bos are also hel hgher rooro by eole who ee lquy he mos Hece, losses bor by boholers ca have some of he same macroecoomc cosequeces (albe less severe) as losses bore by eosors Ths resul mgh ela why govermes are so reluca o le boholers suffer a loss Ths smle heory of bag s also able o ela why bas (a moey mare muual fus) ee o have eoss ha o o flucuae value Deosors are he ages wh he hghes ee for lquy a hus hey ema surace agas ossble falls he value of her vesmes, eve f hey are rs eural Ths surace s rove by he ages less ee of lquy ( our moel he eachers) Ths surace comoe ca ela why he yel of eoss a of very shor-erm US reasury blls s lower ha he curve of rs a reur woul rec (Krshamurhy a Vssg- Jorgese, 0) 8 Coclusos Ths aer elas why a comlee mare framewor wh legeably cosras -- here s a ema for relavely safe asses for rasaco uroses I also elas why ages ee of lquy ves srooroaely hs asse a why losses mose o hs ye of asse have a srooroae mac o he ecoomy The characersc of hs relavely safe asse s ha s very seor, us le eoss a moer ba Our argume s ha he essece of bas s ha ba eoss are hel srooroaely by eole ee of lquy I oher wors, bas are where he lquy s 8