Capital Requirement and the Financial Problem in the Macroeconomy

Transcription

1 Capial Requiremen and he Financial Problem in he Macroeconomy Bowornlux Kaewun 1 Absrac The 2008 financial crisis has revialized policymakers o find an appropriae policy o respond o he financial problem. The purpose of his paper is o invesigae he impacs of capial requiremen in response o shocks and o find ou how capial requiremen works in reducing he financial problem and sabilizes he balance shees. We consider a macroeconomic model wih a banking secor allowed o borrow funds from he inernaional and domesic markes. The resul shows ha he capial requiremen is efficien in responding o he financial problem. I increases he bank s ne worh and reduces a leverage raio. The less aggressive he policy produces he lower loss and sabilized he variaion of ne worh and bank leverage. Bu a high degree of responsiveness is required if auhoriies aim o accelerae a ne worh accumulaion and overcomes he banking crisis. However, he capial requiremen is less effecive in responding o he echnology shock. I canno sabilize ne worh and balance shees. Keywords: capial requiremen, financial problem, and macroeconomic model 1. Inroducion The 2008 financial crisis has shown ha macroeconomic sabiliy does no guaranee he banking secor sabilizaion. Since he financial problem is no always relaed o he policy ineres rae, i however depends on he banker behavior in making decisions on heir balance shees. A bank maximizes is profi by purchasing he asses and finances by borrowing from financial markes. However, many banks failed o inernalize heir balance shees and made decisions based on he aggregae asse prices. This conribued he financial effecs o he banking sysem and accumulaed he sysemic risk. Afer a subprime crisis, he devaluaion in he asses has sharply deerioraed banks balance shees and ne worh conracion. Thus, banks face high exernal finance premiums and induce o a reducion of invesmen and oupu. The 1 Faculy of Economics, Thammasa Universiy, Bangkok, Thailand. bwkaewun@gmail.com

2 2 impacs of financial problem become more severe and lead o a significan oupu loss. Moreover, i akes ime for policymakers o overcome such a banking crisis. The objecive of his paper is o find ou wheher he regulaory insrumen imposed by he Basel commiee helps o miigae he banking problem and improves banks balance shees. The capial requiremen is inroduced o regulae banks behavior and o limi he impacs of he financial problem. To end his quesion, we use a sandard open economy wih he banking secor following Gerler and Karadi (2011). In his se up, i shows he capial inflows from he agency problem beween domesic financial inermediaries and foreign invesors. The leverage raio can be deermined wihin he model and i will flucuae over he cycles. As a sequence, he amoun of credi supply ha he bank can exend from he exernal funds depends on endogenous bank capial (ne worh). In he presence of adverse shocks, namely a echnology shock and capial qualiy shock, a reducion in he bank capial leads o a self-enforcing financial acceleraor mechanism. Tha is banks will reduce heir domesic credi supply immediaely in order o resore accepable bank capial levels, hereby driving he asse prices down furher. Many papers invesigae he poenial benefi of capial requiremen on he financial crisis, such as Meh e al. (2008), Angeloni e al. (2009), Dib (2010), Chisensen e al. (2011), Gerler e al. (2012), and find ha he poenial gains of capial requiremen reduce he impacs of he financial crisis. Meh e al. (2008), uses a sandard dynamic sochasic general equilibrium (DSGE) model wih he bank o examine he effecs of bank capial and balance shees on he economy. The paper finds ha he bank s capial has a negaive relaion o he financial shock and helps sabilizing he financial crisis. The bank s capial shorage generaes double impacs during he economy downurn during crisis. Angeloni e al. (2009), using a DSGE model wih moneary policy reaches he similar conclusion. The key finding is ha a srong counercyclical capial requiremen improves economic losses when he economy is hi by he banking crisis. The gains of capial requiremen in responding o echnology shocks depend on he aggressive of he moneary policy. Dib (2010) analyzes he role of capial requiremen in propagaing he effecs of shocks in real economy under financial fricions environmen by using a DSGE model wih an acive role of banking secor, financial acceleraors, and financial fricions in he capial marke. The resul shows ha he financial fricions in he capial marke amplify he effecs of shocks on he economy and he capial requiremen reduces real impacs of shocks by sabilizing macroeconomic variables. Chisensen e al. (2011), exends furher by invesigaing he ineracion beween he moneary policy and counercyclical buffers. The sudy reveals ha a srong ineracion beween he capial requiremen and moneary policy are benefi. The counercyclical bank leverage regulaion is more beneficial if bank s capial shock arises. Gerler

3 3 e al.(2012) invesigaes he impacs of capial requiremen wheher i discourages he bank o issue shor-erm debs and encourages he bank o increase he ne worh. The sudy finds ha he capial requiremen can sabilize he bank s balance shees and he poenial benefi is high when economy faces a financial crisis. This paper differs from he previous sudies in wo key aspecs. Firs, he model is analyzed under a neoclassical perspecive of a small open economy ha he bank is allowed o borrow from an inernaional financial marke. Second, he model is calibraed based on he Thai economic parameers. This paper is organized as follows. Secion 2 briefly presens he baseline model descripion. Secion 3 is he quaniaive model analysis. The las secion offers some conclusions and remarks. 2. The baseline model The core framework is a small open economy neoclassical model. We modify his model wih a financial secor based on Gerler and Karadi (2011) and Seffen (2011). A financial inermediary is allowed o borrow from wo financial sources, namely domesic deposis and inernaional financial markes. There are four ypes of agens in he economy: households, financial inermediaries, non-financial firms and capial producers. The capial producers producion is subjec o he capial adjusmen coss, oherwise he capial can change easily. The financial inermediaries are owned by domesic households and inves mainly by purchasing asses of non-financial domesic firms. An agency problem beween financial inermediaries and lenders generaes an endogenous borrowing consrain on he leverage raio in he financial secor and inroduces he financial acceleraor mechanism following Bernanke e al. (1999). We also include a disurbance o he quaniy of capial. Wih a financial fricions process, he shock induces a significan capial loss in he banking secor, which in urns increases a ighening credi and a significan downurn. The real aciviy of he economy depends on he financial conrac, and he banks balance shees consrain limis domesic producion. Nex, we will characerize he basic ingrediens of he model. 2.1 Households Assuming ha here is measure one coninuum of idenical households in he economy, each household engages in consumpion, savings, and labor supply. A household saves by lending funds o compeiive financial inermediaries. Wihin each household, here is a fracion 1 f of workers and a fracion f of bankers. Workers supply labor o non-financial firms and reurn he wage hey earn o he household. Bankers manage financial inermediaries and conribue o he household s income by ransferring heir earnings back o he household. Wihin each household, here is perfec

4 4 consumpion insurance. Bankers face a finie horizon o insure ha over ime hey will no accumulae capial unil hey can fund all invesmen projecs from heir own capial. In paricular, bankers have probabiliy 1 o exi from he financial secor, which is independen of hisory. The average survival ime for he bankers o work in he financial secor is 1 1 and leads o he amoun f 1 of bankers ha exi he financial secor and become workers in each period. To keep a consan raio of workers and bankers, a similar amoun of workers moves o he financial secor. Bankers who exi finally ransfer heir reained earnings o heir household. The new enry bankers will be provided wih some sar-up funds from heir family which will be described laer. Households maximize expeced lifeime uiliy funcion by choosing a level of consumpion C, labor supply given as follows: H, and nex period deposi level D H 1. The household preferences are 1 1 C H max E, (1) wih 0,1 denoes he subjecive discoun facor and,, 0 represen he degree of risk aversion, he elasiciy of labor supply and disuiliy weigh, respecively. The inermediaries deposi is a one period deposi which pays a real gross reurn d R from H period 1 o. In equilibrium, i is considered as a riskless asse. Le D 1 be he oal demand for deposis he household acquires, W be he real wage, and be he ne payous o he household from he ownership of boh non-financial firms and financial inermediaries. The household budge consrain is given as follows: C D W H R D (2) H d H 1 The household s correspondingly opimal condiions for consumpion, labor supply, and saving are, respecively, given by C 1, 1 E C (3) H C W (4) (5) d E, 1R 1 1 where, 1 is he marginal rae of subsiuion of consumpion beween he period and 1. Equaion (4) ses he marginal rae of subsiuion beween consumpion and leisure equal o he

5 5 real wage. The las equaion denoes he opimal savings decision which implies ha he household smoohs consumpion over ime. 2.2 Financial inermediaries The financial inermediaries are owned by domesic households. Banks lend funds obained from households and inernaional financial markes o non-financial firms. Bankers ac as specialiss ha assis in ransferring funds from savers o invesors. They engage in he mauriy ransformaion by holding long erm asses and fund hese asses wih shor erm liabiliies. The financial inermediaries capure he enire banking secor including invesmen banks and commercial banks. The represenaive financial inermediary j is separaed ino wo subunis, a liabiliies uni and operaion uni. The liabiliy uni obains wo sources of funding, namely deposiors and foreign lenders, and hen sells hem as liabiliies o he operaion uni. The operaion uni acs as a commercial bank and uses liabiliies o expand is balance shee by purchasing he asses. B d * The liabiliy uni obains deposis Dj 1 wih an ineres rae R and foreign debsb j wih an ineres rae * R. Then hey sell liabiliies L j o an operaion uni wih an ineres rae B b However, o obain he foreign debs, bank faces a convex adjusmen cos, 2 L * j j 2 L R.. is a desire level of foreign deb o liabiliies raio. I coss o he liabiliy uni if he srucure of deb over he desired level. The purpose o inroduce his fricion is o wedge beween a domesic ineres rae and foreign ineres rae. The liabiliy uni maximizaion problem is specified as follows: B max ( ( ) ) (6) * i L d B * * b j 2 E B *, i R 1Lj 1 R Dj R Bj D j 1, B j 1 i0 2 Lj subjec o he liabiliies consrain given by L D B (7) B * j1 j1 j1 The liabiliy uni chooses opimal deposis o maximize heir profi as follows: R * * B j1 Bj1 Lj 1 Lj1 R L d 1 1 b 2 The liabiliy uni chooses opimal foreign debs o maximize heir profi as follows: (8)

6 6 R * B L * j1 Dj 1 1 R 1 b 2 Lj 1 Lj 1 B Dividing equaion (8) by equaion (9), we ge he reurn o liabiliies as follows: B * D j 1 B L d * j1 R 1 R 1 R 1 L j1 L j1 Noe ha he reurn on liabiliies is a sum average of he ineres raes. The operaion uni maximizes he expeced erminal values of ne worh. Le (9) (10) N j be he amoun of ne worh ha he inermediary j holds a he end of period, Lj 1 be he liabiliies B * composing of domesic deposis Dj 1 and he non-coningen debsbj 1 ha banks issue o inernaional financial markes, banks hold, and Z j be he quaniy of financial claims on non-financial firms ha Q denoes he relaive price of each claim. The relaionship beween asses and liabiliies of balance shee of financial inermediary j a ime is given by Q Z j N j Lj 1 (11) The Lj 1 can be hough as he inermediary s debs and N j as is equiy capial. The bank asses K K L earn he sochasic reurn R 1over his period. Noe ha boh R 1and R 1 are deermined endogenously. Over ime, he financial inermediary s ne worh evolves as he difference beween earnings on he asses and ineres repaymens on is liabiliies, which is given by L N R Q Z R L K j1 1 j 1 j1 R R Q Z R N (12) K L L 1 1 j 1 j The growh of ne worh above he riskless reurn is increasing in he oal quaniy of K L asses, QZ j, and depends on he ineres rae premium R1 R 1. When he bankers receive a paymen on is asses, he repays o he lenders. earnings a i Le, i denoe he sochasic discoun facor ha he banker, a, applies o he i. In order o se an incenive for he financial inermediary o engage in financial inermediaion, he risk adjused ineres rae premium mus be posiive a all imes and given as follows: i K L i, 1i 1 i 1 i 0 E R R, i 0 (13) The raional banker will no fund he asses if a discouned reurn less han he discouned borrowing cos. Under perfec capial markes, his relaionship always holds a equaliy, he risk

7 7 adjused premium is zero. However, wih imperfec capial markes, he premium mus be posiive due o limis on he bank s abiliy o receive funds. As long as he incenive consrain always holds, he bankers keep building asses unil hey exi from he financial secor. The financial inermediary uses he household s discoun facor, since i is owned by he laer. This moivaes he financial inermediary s objecive o maximize he erminal values of he ne worh which can be carried over o he household a he end of is lifeime. Formally, he bankers maximize he expeced erminal wealh, given by i i1 Vj max E 1, 1i N j1i (14) Z j i0 wih N R R Q Z R N K L L j1 i 1i 1i i ji 1i ji Given a posiive ineres rae premium, E i, 1 K L i i R 1 i R 1 i, he financial inermediary wans o exend is asses indefiniely by borrowing addiional funds from he financial markes. In so doing, we follow Gerler and Karadi (2011) by adoping a moral hazard problem beween inernaional invesors and domesic banks moivaes o limi he borrowing behavior of he bankers. Specifically, a he beginning of he period he banker has a possibiliy o diver he fracion of available funds from he projec and ransfers hem back o he household ha he or she is a member. The cos o he banker is ha lenders can force he inermediary ino bankrupcy and recover he remaining fracion 1 oo cosly for he lenders o recover he fracion of asses ha banker had divered. of asses. However, i is The lender is willing o supply he funds ino he banking sysem, if he following incenive consrain holds: V Q Z (15) j j Only if he value of he banker on he lef is higher han he value o diver funds on he righ, he lenders are insured ha hey will no going o be defrauded, and coninually lend heir capial o he domesic banks. The lef is wha bankers would lose if hey diver he asses, whereas he righ is he gain in doing so. Wih a profi maximizaion objecive, he bankers will expand he asses up o he poin ha he incenive compaibiliy consrain is binding, and if he ineres rae premium is always posiive. The soluion of he bank operaion maximizaion problem can be expressed in he following form: wih Vj lq Z j n N j (16)

8 8 K L 1 l E R R x l, 1 1 1, 1, 1 1 L 1, 1 1, 1, 1 1 n E R z n (17) where x, 1 Q 1Z j1 Q Z j is he gross growh rae of he asses from period o 1, and z N N, 1 j1 j is he gross growh rae of he ne worh. Thel denoes he expeced marginal gains of having addiional asse given he ne worh being consan and n is he expeced value of he bank of having addiional uni of he ne worh given he asse being consan. The value of l is relaed o he posiive ineres rae premium consrain. Wih he fricionless compeiive capial markes, he bank will expand borrowing up o he poin ha he rae of reurn will adjus unil l is zero. Thus, he agency problem ha is inroduced may pu limis on his arbirage. If he incenive consrain is binding, i can be shown ha he inermediary s asses are consrained by is ne worh. The incenive consrain can be expressed as follows: l Q Z n N Q Z (18) j j j Given a binding consrain, he asse holding by financial inermediaries can be expressed in he erm of ne worh posiion as follows: Q Z n N j j l Given ne worh N j being consan, an increase in asse quaniy (19) Z j would break his balance and raises an incenive for he banker o diver funds. Rearranging he previous equaion yields he bank j s leverage raio as he relaion of he asse over he ne worh, given by Q Z N (20) j j wih n l where is he raio of asse o capial, which refers o he individual financial inermediary s leverage raio. This consrain limis bank s leverage raio o he poin where he banker has incenive o chea exacly balanced by he cos. Hence, he agency problem leads o an endogenous consrained bank s balance shees (he ne worh) o acquire more asses. The asse divering process is increasing in he ne worh and asses growhs, bu decreasing in he leverage raio. We can hink ha he bank divers he fracion of asses for a personal purpose (e.g. payou a large bonus), which can be wrien in he following from:

9 9 n l (21) Given N j 0, he consrain is binding only if 0 l. In his insance, i is profiable for he banker o expand asses since l is greaer han zero. The larger is l, he greaer is he opporuniy cos o he banker from being forced ino bankrupcy. This is because of an increase in he asse growh and opporuniy o diver asses o saisfy he banks maximizaion problem. If l rises above, he incenive consrain does no bind, he presen value of he bank always exceeds he gain from divering funds. The ne worh evoluion can be rearranged in he following form: N R R R N K L L j j Regarding o equaion (20), he leverage raio is specified by a non-firm-specific componen. This allows us o obain he aggregae demand for asses and he aggregae ne worh of he financial sysem by summing over all individuals as follows: Q Z N (23) I I wih denoes he aggregae leverage raio in he banking secor, for an asse quaniy, and NI is he aggregae ne worh of he banking sysem. (22) ZI is he aggregae demand We can derive an equaion of moion for he ne worh of he banking sysem, by firs recognizing ha i is he sum of he ne worh of exising bankers N enering bankers N n. I can be expressed as he follows: e and he ne worh of N Ne Nn (24) Since he fracion of he bankers a period 1survive unil period, he ne worh of exising bankers is given by K L L 1 1 Ne R R R N (25) I can be observed ha he main source of variaion in pos reurn on he asse R. In addiion, he ne worh N K e N e will be flucuaions in he ex is increasing in he leverage raio. The enering bankers receive a ransfer from heir family as a sar up value, which is equal o fracion 1 of value of asses 1 Q 1Z1 ha exied bankers had ransferred ou in heir final operaing period. Thus, in he aggregae level, a fracion of new enering bankers can be wrien as

10 10 N 1 Q Z Q Z n Combining equaion (25) and equaion (26), once yields he following equaion of moion for ne worh: (26) K L L N R R R N Q Z Noe ha helps pinning down he seady sae of leverage raio QZ / N. (27) 2.3 Non-financial firms Nex, we urn o he producion and invesmen sides of he economy. There are compeiive non-financial firms engaged in he producion of a single radable reail good which serves as a numeraire. Producers combine capial and labor ino he Cobb-Douglas producion funcion o produce a final consumpion good, which is given by where 1 Y A K H, 0 1 (28) K is he capial sock and H denoes he labor inpu. The oal facor produciviy and he capial qualiy shocks are assume o follow an AR(1) process as follows: ln ln A ln A (29) A 1 A, ln (30) wih 1 1, 2 E A and A, i. i. d. N 0, A, 1 2 E and, i. i. d. N 0,. Following Gerler and Karadi (2011), he capial qualiy shock provides an exogenous source of variaion in he capial value. In he conex of he model, i corresponds o economic depreciaion of capial so ha K is an effecive capial quaniy a period. The capial qualiy shock causes he devaluaion of bank s capial and deerioraes he balance shee. Thus, banks face a financial disress condiion and evenually he crisis. When oupus are available o he firms a he end of he period, he wage bill WH be paid o he households. Firms have opions o sell depreciaed capial producers a he uniary price of 1 K will o he capial Q and he new capial sock K 1 is purchased for producion in subsequen period. The firms finance is capial acquisiion each period by borrowing funds from he financial inermediaries. To acquire he funds o purchase capial, firms issue claims which is equal o he number of unis of capial K 1, and price each claim a a uni price of capial Q. The relaionship beween he value of capial acquired and he value of claims agains capial is given by Z j

11 11 Q Z Q K (31) j 1 This condiion equaes he price of a uni of capial o he price of financial claim. The arising equiy conrac beween he financial inermediary and he non-financial firm yields he gross ineres rae K K R. This implies ha firms will pay j 1 R Q Z, a zero profi condiion in he non-financial secor, o he bank. Assuming ha here is fricionless beween his conracs which is an underlying assumpion, he inermediaries have perfec informaion abou he firms and have no problem enforcing payoffs. Thus, firms offer a perfecly sae-coningen deb o financial inermediaries, bes inerpreed as firms equiy. However, since banks suffer from he agency problem in financial markes, physical capial purchases are indirecly affeced hrough his consrain. Wihin he model, only financial inermediary faces capial consrains o obain funds and, hese consrains affec he supply of funds available o non-financial firms. The required rae of reurn on capial evenually rises. demand: A firm profi maximizaion problem yields he following opimal condiions for facors Y W (32) H 1 ER K 1 Y 1 E 1 1 Q 1 1K1 (33) Q The labor demand equaion (32) shows ha he marginal produciviy of labor equal o he wage rae. The capial demand depends on he marginal produciviy of capial and capial gains. 2.4 Capial producers The capial producers are se along wih Bernanke e al. (1999) o deermine he variaion in he endogenous price of capial. In addiion, he capial adjusmen coss are added ino he small open economy models o reduce he invesmen volailiy. There is a compeiive secor of idenical capial producers which is owned by he households. A he end of period, a compeiive capial producer buys depreciaed capial from firms a price Q and quaniies of capial sock K newly buil capial 1. The invesmen amoun I yields he gross I K K. Only ne invesmen is subjec o quadraic adjusmen coss, which is governed by a funcion I K wih, he seady sae. The capial

12 12 producers combine a quaniy of capial and new invesmen, I, wih a linear echnology o ge capial K 1. Then hey sell he newly produced capial sock K 1 o non-financial firms wih a compeiive price Q per uni of capial. The capial producers profi maximizaion problem is given by I, K1 i, 1 (1 ) ( ) (34) Max E Q K Q K I i i i i i i i i0 subjec o he law of moion of he capial sock I K K K 1 1 K (35) wih 2 I I K I K K 2 K The capial producers choose an opimal level of invesmen o maximize profi yields he Tobin Q equaion as follows: I Q 1 K K 1 The capial producers choose an opimal capial socks o maximize profi yields he invesmen demand equaion as follows: I I I K K K 1 K 1 1 where K 0 is he degree of capial adjusmen coss. The meaning of asse price equaion is ha capial producers sell capial a price equal o adjusmen cos. (36) (37) 2.5 Closing he model Finally, he exogenous processes for a foreign ineres rae and is shock need o be specified. Assuming ha a foreign ineres rae depends on a las-period foreign ineres rae and is shock, which is given by R R (38) * * * R 1 * R, The marke clearing condiions for a small open economy are given by Y C I D D H B 1 1 L D B B * j1 j1 j1

13 13 3. The model analysis 3.1 Calibraion Table 1 liss he choice of parameer values for he baseline model. Eleven parameers govern he seady sae and six parameers govern he dynamics. We sar a discussion abou he convenional parameers. We se a discoun facor as an annual gross real ineres rae , implying ha an annual realized ineres rae is 3%. This parameer can be 0.25 compued as The degree of risk aversion is assumed o be 0.2 which is, consisen wih he evidence of low sensiiviy of expeced consumpion growh o real ineres raes. is assumed o be , implying ha he elasiciy of labor supply is high. is se o be 1, implying ha here is no scaling disuiliy of labor supply. The probabiliy of banks surviving ino he nex period is se o be which is close o 1. This implies ha banks are difficul o be bankrupcy. The fracion of households ransferring o new enry bankers is se o be meaning ha only a small amoun of he asses will be ransferred ino he banking sysem a he beginning of he period. The capial income share is assumed o be 0.35 implying ha domesic firms are labor inensive in producion. The depreciaion rae of capial can be derived from he average annual depreciaion rae of capial sock of he year 1970 o 2012 based on 1988 prices, he Naional Economics and Social Developmen Board. The average annual depreciaion rae is 4.17 % which is (0.042 / 4) per quarer. The echnology shock persisence is se o be A I implies ha abou 80% of echnology improvemen from he las period affecs he producion in he curren period. According o Gerler and Karadi (2011), he iniial decline in capial qualiy shocks is fixed a five percen and he auoregressive facor is Absen any changes in invesmen, he shocks generae roughly a en percen decline in effecive capial socks. Tha is he source of financial crisis is a decline in asse values as opposed o he physical capial desrucion. The foreign ineres rae shock persisence is se o be I implies ha abou 80% of foreign ineres rae from he las period affecs he curren ineres rae. Table 1 Parameers Household Value Assigned Descripion Discoun facor 0.20 Degree of relaive risk aversion The elasiciy of labor supply 1 Disuiliy weigh

14 14 Financial inermediary Probabiliy of banker survival b Porfolio adjusmen cos 1 Desire level of deb raio Fracion of new enry ransfer Non-financial firm 0.35 Share of capial income Capial depreciaion rae Capial adjusmen cos K Dynamic parameers 0.80 Persisence of echnology shock A 0.66 Persisence of capial qualiy shock 0.80 Persisence of foreign ineres shock (-5,5) Degree of responsiveness 0.5 Preference over oupu y 0.1 Preference over policy change 3.2 Experimen The experimen is se o a downurn economy wih a negaive echnology shock by one percen of sandard deviaion and a negaive capial qualiy shock by five percen of sandard deviaion. The firs order Taylor approximaion is used in approximaion process. The model is simulaed by using Dynare. The impulse response funcion shown in a percenage change of decimal poin and iming is used wih quarerly daa. A negaive shock of echnology by one percen sandard deviaion wih auoregressive facor 0.80 dampens significanly he domesic economy, he oupu and inpu demands drop sharply. This leads weakens he bank s balance shee. Specifically, he leverage rises immediaely, while he ne worh and capial o asses raio significan decline as shown in he Figure 1. The iniial echnology shock induces a sharp conracion of oupus by 0.01 percen. A drop in producions induces a reducion of labor and invesmen demands, so he reurn o capial declines. The nominal wage decreases abou 0.01 percen. A reducion in he nominal wage leads furher a decline in household consumpion abou percen poin. As he reurn o capial declines, he household opimal savings decision by increasing a deposi ino he bank. In he financial secor, a reducion in spreads leads o a reducion of liabiliies demanded by he bank because he banks have a high borrowing cos and less expeced profis. Therefore, he ne worh drops dramaically, whereas he leverage and he asse rise immediaely. I induces a significan drops capial o asses raio. The high leverage of he bank incorporaing wih low capial of he bank leads o a high risk and he bank s balance shee weakening. Thus, he banking secor will

15 15 face a financial disress condiion and, if hey borrow exernal funds, hey will face high exernal financial coss. The second effec loop will sar when banks face a disress condiion and a high exernal finance premium. Finally, he impacs on boh financial aciviy and real aciviy become more severe because of a sharp conracion in he aggregae oupu and invesmen. A negaive capial qualiy shock by one percen of sandard deviaion wih auoregressive facor 0.66 induces a sharp conracion of he effecive capial quaniy. I leads furher o a significan drop in he aggregae oupu and invesmen immediaely. The shock conracs oupus by abou 0.01 percen, while he capial sock and invesmen demand drop by 0.03 percen. A reducion in oupus induces a decline in he labor demand and nominal wage. A significan drop in invesmen demand induces a decline in he reurn o capial and asse price. A reducion in he effecive capial quaniy leads o a furher conracion in he ne worh and capial o asses raio. A decline in capial induces a high leverage of he bank and a drop in spreads and asses. I leads o a furher decrease furher in profis and ne worh. So he banks face balance shee consrain and he financial problem arises. This is a rough way o inroduce a banking crisis ino he model. The second impacs become more severe when banks have a balance shee consrain and high leverage. This amplifies he effecs of financial problem o he economy. Figure 1 A Negaive Technology Shock

16 16 Figure 2 A Negaive Capial Qualiy Shock

17 3.3 Capial requiremen 17

18 18 Wihin his framework, here are wo moives of he capial requiremen ha aim o encourage banks o increase he qualiy and quaniy of capial and o discourage hem o exend more risky asses. As asse prices affec he borrowing consrains and balance shee, here exiss a pecuniary exernaliy ha banks do no properly inernalize when hey make decisions on heir balance shee srucure. The paricipans ake asse prices as given and since he asse price is deermined by an aggregae level. In he aggregae level, heir join behavior deermines asse prices and, by implicaion, he exen of balance shee effec and he degree of financial fragiliy in he economy. In paricular, hey induce banks o raise oo much deb, such as o purchase excessively shor mauriy asses and hus he banks ake excessive risk. In his sense, financial fragiliy is uninernalized by he produc of exernal finance made by individual insiuions. For policymakers, if we impose Pigouvian axes or regulaion o an individual insiuion o realize he exernaliy ha he conribues o he financial sysem. As a resul, he decenralized marke equilibrium is efficien and makes everybody in he economy beer off. A number of papers have emphasized his exernaliy o inroduce he impac of regulaion, axaion and subsidies o he banks balance shees which finally reward he ne worh. (Diamond and Rajan (2009) Korinek (2011) and Jean and Korinek (2013)). In his model, he capial requiremen is a regulaory policy imposed o he bank s balance shee o reduce he financial exernaliy and sysemic risk, bu rewards he ne worh. An increase in he oal ne worh (equiy) o he oal asse raio implies an increase in he capial s requiremen. In paricular, we suppose ha he governmen subsidizes banks per uni of ne worh. The subsidy is financed by a ax on an incremen of oal liabiliies. As regulaors impose he capial requiremen, he flow of funds consrain for he bank is now given by 1 N R Q Z R L (39) K s L The ne worh evoluion becomes: wih 1 1 N R R Q Z R N (40) K s L s L l E R R x l K s L, 1 1 1, 1, 1 1 s 1 1 n E R z n L, 1 1, 1, 1 1 The capial requiremen is se in responding o he capial requiremen in he seady sae and he deviaion from he aggregae credi level as follows: s QZ ss ln QZss (41)

19 19 where he parameer ss denoes he seady sae of capial requiremen. QZ denoes aggregae of credi and QZ is he seady sae level of aggregae credi. The parameer 5,5 ss degree of responsiveness of capial requiremen. is he The performance of capial requiremen can be deermined by he economic loss. The loss funcion depends on uncondiional variance of oupu and he erm of policy change as follows: 2 2 Lcap y y. (42) where 2 y is he asympoic uncondiional variances of oupu and 2 is he variances of he capial requiremen changes, respecively. y is a weigh of policymakers preference on variances of oupu and denoes a weigh of policymakers on variances of capial requiremen changes. The leas value of loss funcion is he bes policy performance. A negaive echnology shock induces a conracion in he ne worh and weakens he balance shee. I leads furher o a financial disress condiion and a significan drop in invesmen. Inroducing capial requiremen in responding o he asse growh deviaing from is seady sae affecs direcly he bank s balance shee. An increase in capial requiremen by one percen of is seady sae level wih he lower degree of responsiveness 1.5 o he asse growh induces an increase in he leverage raio and asse growh. The capial requiremen increases he coss o he financial inermediaries for addiional exernal funds, herefore he spreads decline. This reduces furher he demand for liabiliies. The capial requiremen acceleraes he ne worh growh which induces laer an improvemen of ne worh and balance shee. In addiion, he capial requiremen reduces he banker s incenive o diver more asses for heir personal purposes. However, he capial requiremen does no affec real aciviies. The impacs of he echnology shock on oupu, invesmen, and consumpion as well as inpus demand remain unchanged from he baseline model. Figure 3 Capial Requiremen and Technology Shock

20 20 The negaive capial qualiy shock affecs he economy hrough a reducion of effecive capial quaniy and herefore oupu and invesmen conrac sharply. A reducion in values of capial and asses leads o a deerioraion of he bank s balance shees. Banks face a higher exernal finance premium and hus increase lending raes. This induces firms o cu back all invesmen projecs. The balance shee consrain and high leverage amplify he impacs of financial problem on he economy. Inroducing he capial requiremen wih more aggressiveness 3.5 in response o he asse growh ha deviaes from is seady sae level is he mos effecive policy. The capial requiremen changes he bank behavior. Tha is, i reduces bank leverage by 0.1 percen and leads o a drop in asse growh. I increases he spreads by over 0.05 percen. I increases he bank ne worh by abou 0.05 percen and improves he bank s capial o asses raio. Finally, i srenghens he bank s balance shee and reduces he financial disress condiion. Figure 4 Capial Requiremen and Capial Qualiy Shock

21 21 The negaive foreign ineres rae shock by five percen induces a conracion in he liabiliies demand because a drop in he reurn o liabiliies. I leads furher a reducion in he asse growh and leverage. A reducion in he asse growh and leverage induce a decline in he ne worh growh and deeriorae he bank s balance shee. Banks furher face a high exernal finance premium and hus increase he lending raes. This leads firms o cu back an invesmen. Inroducing a capial requiremen wih more aggressiveness 5in response o he asse growh is beneficial o he banks. The capial requiremen sabilizes he bank s leverage. Tha is, i increases he bank s ne worh by 0.01 percen and he spreads rises over 0.02 percen. Finally, an aggressive capial requiremen rewards he capial o asse raio. Thus, he banks capial rises and reduces financial disress condiion. In addiion, we find ha he capial requiremen regulaion affecs o he bankers behavior and heir balance shees. Figure 5 Capial Requiremen and Foreign Ineres Shock

22 22 The performance of he policy can be deermined by he abiliy of he policy in sabilizing he bank balance shee. To achieve his objecive, we vary he policy choice agains asse growh and find he degree of responsiveness ha can sabilize he value of loss funcion and balance shee variables. The financial problem induces a high variaion of ne worh and leverage raio. Shock Technology shock 0,5 Capial qualiy shock 0.5, 2.5 Foreign ineres shock Table 2 The Impac of Capial Requiremen Loss 2 y Capial requiremen 0.5, 0.1 y 2 2 Lcap y y 2 2 NW Source: Auhor s Calculaion

23 23 The variances of oupu, policy changes, ne worh and leverage raio, respecively, are shown in Table 2. Specifically, he capial requiremen is less effecive in response o he echnology shock because varying he policy parameer does no reduce he loss funcion and variance of ne worh. However, he response of capial requiremen o he financial shock is more efficien. Tha is, less degree of responsiveness of capial requiremen 0.5 o he asse growh generaes he minimum values of loss funcion. Also, i helps sabilizing he bank balance shee and generaes he minimum variance of ne worh and leverage raio. 4. Conclusion and remarks The objecive of his paper is o invesigae he impac of capial requiremen in response o he shocks, which dampens down he economy. Also, we aim o find how i improves he bank s balance shee. A negaive shock of echnology has a significan negaive effec on he domesic economy, paricularly, a drop in he oupu and inpu demand sharply. This leads o he bank balance shee weakening. The leverage rises immediaely, while he ne worh and capial o asses raio significanly decline. Hence, banks face a financial disress condiion. A negaive capial qualiy shock induces a sharp conracion of he effecive capial quaniy. I decreases an aggregae oupu and invesmen immediaely. The significan drop in invesmen demand induces a decline in he reurn o capial and asse price. A reducion in an effecive capial quaniy leads o a furher conracion in he ne worh and capial o asse raio. A decline in capial induces a high leverage of he bank incorporaing wih a drop in spreads and asses. I leads o a decrease furher in profis and ne worh. So banks face balance shee consrain and he financial problem arises. The capial requiremen is efficien in response o he financial problem. I increases he bank ne worh and reduces he leverage raio. Finally, a less aggressive policy generaes he minimum loss and sabilizes variaion of ne worh and bank leverage. A high degree of responsiveness is required if auhoriies aim o accelerae a ne worh accumulaion and overcomes he banking crisis. However, he capial requiremen is less effecive in response o he echnology shock, so he capial requiremen canno sabilize ne worh and balance shee in his case. References

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