Fire Sales and the Financial Accelerator

Transcription

1 WP//4 Fire Sales and he Financial Acceleraor Woon Gyu Choi and David Cook

2 2 Inernaional Moneary Fund WP//4 IMF Working Paper IMF Insiue Fire Sales and he Financial Acceleraor Prepared by Woon Gyu Choi and David Cook Auhorized for disribuion by Ling Hui Tan June 2 Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. During periods of financial urmoil, increases in risk lead o higher defaul, foreclosure, and fire sales. This paper inroduces a cosly liquidaion process for foreclosed collaeral and endogenous recovery raes in a dynamic sochasic general equilibrium model of he financial acceleraor. Consisen wih empirical evidence, we find ha recovery raes are pro-cyclical when collaeral is cosly o liquidae. Through links beween recovery raes, risk premia, and defaul risk, he model generaes an addiional liquidiy spiral, a feedback loop for he financial acceleraor. We illusrae how collaeral liquidaion and moneary policy aler he impacs of a financial shock. We also show ha a governmen subsidy on collaeral liquidiy and he endogenous accumulaion of liquidiy invenory help dampen he liquidiy spiral by shoring up recovery raes. JEL Classificaion Numbers: E27; E32; E58 Keywords: fire sales, financial acceleraor, endogenous recovery rae, financial shock, liquidiy spiral, collaeral Auhor s Address: wchoi@imf.org; davcook@us.hk Woon Gyu Choi is a Senior Economis a he IMF Insiue of he Inernaional Moneary Fund. David Cook is an Associae Professor of Economics a he Hong Kong Universiy of Science and Technology. We hank Enrica Deragiache, Burkhard Drees, and Ling Hui Tan for useful commens and suggesions.

3 2 Conens Page I. Inroducion...3 II. The Model...5 A. Compeiive Firms...5 B. Household...7 C. Capialiss...7 D. Reailers and Wholesalers... E. Cenral Bank and Shocks... F. Calibraion... G. Discussion: Financial Shocks and Liquidiy Spirals...2 III. Model Resuls...3 A. Impacs of Financial Shocks and he Role of Collaeral Liquidiy...3 B. Ineres Rae Policy Response: Concerns abou Recession Risk...7 C. Governmen Subsidy for Collaeral Liquidaion...2 D. Endogenous Accumulaion of Liquidiy Invenory...23 IV. Concluding Remarks...26 References...27 Figures. Recovery and Defaul Raes Financial Shocks and Liquidiy Spirals Responses o a Financial Uncerainy Shock: Liquid Model versus Illiquid Model Responses o a Financial Uncerainy Shock: Pure Inflaion Targeing versus Taylor Rule Responses o a Financial Uncerainy Shock: No Subsidy versus Subsidy for Collaeral Liquidaion Responses o a Financial Uncerainy Shock: No Invenory versus Liquidiy Invenory Collaeral Liquidaion

4 3 I. INTRODUCTION Jus as defaul is an imporan, if regreable, par of he lending process, so is he recovery of value from defauled loans. Evidence suggess ha recovery raes are volaile and vary wih he credi cycle (see Bruche and Gonzalez-Aguado, 26). In ime periods when bank loan defaul raes are high, he degree of recovery on loans falls, exacerbaing losses for banks. This paper examines he impac of endogenous flucuaions in recovery raes on he cyclical behavior of invesmen in a dynamic sochasic general equilibrium (DSGE) model wih sicky prices and credi marke imperfecions ha give rise o a financial acceleraor (see Bernanke, Gerler, and Gilchris, 999; Carlsrom and Fuers, 997, 998; Choi and Cook, 24; and Cook, 24). Specifically, his paper shows how he channel of endogenous recovery raes amplifies he impacs of a financial shock on he economy. In financial acceleraor models, deb wih defaul risk is used o finance risky capial invesmen. In he case of defaul, crediors can foreclose on he asses a some liquidaion cos. We presen a model in which bolenecks in he liquidaing process of collaeral reduce he abiliy of he economy o absorb foreclosed asses during imes of widespread defaul. Endogenous recovery raes exacerbae he balance shee effecs of negaive shocks, in conras wih exising models in which liquidaion coss are modeled as a consan proporion of asses. If he liquidaion coss of crediors rise in a downurn, lending erms for prospecive borrowers will worsen. A cenral aspec of he financial acceleraor model is he modeling of he risk premium on borrowing as a funcion of he probabiliy of defaul. In a model in which recovery raes are ime-varian, he risk of lending depends on no only he probabiliy of defaul bu also he fracion of collaeral ha will be received back in he case of defaul. We follow Chrisiano, Moo, and Rosagno (28) in modeling a financial crisis exogenously as a mean-preserving shock o he cross-secional variance of idiosyncraic firm-level produciviy. An increase in microeconomic randomness increases he probabiliy of defaul and naurally raises he cos of borrowing. The conracion in invesmen acs as a negaive demand shock. The rise in firm-level produciviy volailiy exogenously increases he probabiliy of defaul. As defauls become more common across firms, he illiquidiy of foreclosed asses reduces recovery raes, which, in urn, raise he risk premium. The greaer risk premium negaively affecs he aggregae economy and hus raises he probabiliy of defaul. Endogenous liquidiy of foreclosed properies hen acs as a feedback loop a liquidiy spiral which amplifies he financial acceleraor. Using a fairly sandard DSGE wih sicky prices, we examine he impac of a shock similar in size o ha experienced by he financial sysem of he Unied Saes in 28. We show ha he exisence of he endogenous liquidiy channel can sharply exacerbae he business cycle downurn beyond wha migh be expeced from he sandard financial acceleraor model. We calibrae he liquidiy of he foreclosure process o mach he volailiy of recovery raes. To give an empirical idea of he degree of volailiy of recovery raes, we collec defaul-relaed daa from Federal Deposi Insurance Corporaion s Hisorical Saisics on Banking. Figure shows recovery raes, which are calculaed as he accouning raio of

5 4 Figure. Recovery and Defaul Raes Recovery Raes Defaul Raes Noes: This figure depics recovery and defaul raes for he period 9628 using he daa from FDIC s Hisorical Saisics on Banking. Recovery raes are he raio of recoveries o gross charge-offs; and defaul raes are he raio of gross charge-offs o gross loans. recoveries o gross charge-offs for commercial banks for Also shown are chargeoff raes or defaul raes, measured by he raio of gross charge-offs o gross loans. Defaul raes, on average less han one percen per year, are exremely volaile wih noable peaks during he recession of he early 99s and 2s. Recovery raes are equally volaile. Abou a quarer of loans are recovered on average, bu recovery raes vary over ime beween and 4 percens. Defaul raes edged up, and recovery raes edged down owing o he financial crisis saring from 27. We derend he naural logs of boh series using a Hodrick-Presco filer. In percenage erms, he sandard deviaion of recovery raes is 2.4 while ha of defaul raes is Noably, recovery raes are highly negaively correlaed wih defaul raes: he correlaion equals.89. The financial acceleraor in invesmen is currenly seen as an imporan par of invesmen dynamics a a business cycle frequency (see Bernanke, 27). In he models of he financial acceleraor based on monioring coss (Williamson, 987; and Bernanke and Gerler, 989, 99), borrowing is done hrough he opimal medium of risky deb (see Gale and Hellwig, 985). 2 The monioring coss ha drive hese models can be viewed hrough 2 Holmsrom and Tirole (997) consruc a model of bank liquidiy based on an asymmeric informaion channel. Following Kiyoaki and Moore (997), anoher srand of he lieraure on imperfec financial markes emphasizes he role of collaeral consrains: for example, Chen (2) examines he impac of asse price declines when he domesic banking sysem faces collaeral consrains.

6 5 he lens of liquidaion coss. Shleifer and Vishny (992) pioneer he modeling of liquidiyconsrained collaeral values. Subsanial evidence suggess ha recovery raes are reduced during periods of economic disress (see Alman and ohers, 23). Asquih, Gerner, and Scharfsein (994) find evidence ha indusry-level disress maers for recovery raes of individual firms. Acharya, Bharah, and Srinivasan (27) find evidence ha indusrial firms have lower recovery raes in periods of economic disress, especially for firms wih heavily indusry-specific asses ha enail higher liquidaion coss. Bris, Welch, and Zhu (23) find ha, when he economy recovers, liquidaed firms have worse recovery han oher firms do. An exreme form of financial disress is a financial crisis ha riggers fire sales in financial markes. Krugman (998) argues ha, following financial crises, foreign invesors are able o purchase roubled emerging marke asses a fire sale prices. Aguiar and Gopinah (25) provide evidence on pos-crisis FDI flows. Acharya, Shin, and Yorulmazer (27) sugges evidence ha foreign invesors ake over failing firms by providing exernal liquidiy hrough FDI inflows during financial crises. Our findings shed ligh on ineracions beween macro-prudenial surveillance and he characerisics of ransmission mechanism in he face of financial shocks. In ligh of he 2729 financial crisis, of crucial imporance is o beer undersand he ineracions beween he financial secor and macroeconomic policies hrough macro-prudenial surveillance (for example, Brunnermeier and ohers, 29; and Bank of England, 29) and o follow he resuling effecs on he ransmission mechanism of policies. Policymakers need o develop policy ools o dampen he amplificaion of boh financial cycles and business cycles. This paper argues ha he liquidaion of collaeral adds a liquidiy spiral o he financial acceleraor ha is responsible for he amplificaion of invesmen flucuaions upon a financial shock. We show how moneary policy can dampen he impacs of he financial shock. Furher, we show ha a governmen subsidy on collaeral liquidiy and he endogenous accumulaion of liquidiy invenory help dampen he liquidiy spiral by shoring up recovery raes. A. Compeiive Firms II. THE MODEL Compeiive firms comprise hree ypes of represenaive, price-aking producers: oupu producers, liquidaors, and capial producers.. Oupu Producers A firm produces oupu goods using he Cobb-Douglas echnology wih consan reurns o scale: Y AK H, ()

7 6 where K is insalled capial and H is labor. Oupu producers sell goods a a compeiive price, MC, o wholesale disribuors. The producers ren labor a wage rae, W, and capial a renal rae, RK. The profi maximizaion condiions are: 2. Liquidaors Y Y W ( ) MC, RK MC. (2) H K Foreclosing on asses requires a cerain amoun of liquidiy. Liquidaors conver reail goods ino markeable asses or liquidiy in he form of goods using a echnology wih diminishing reurns o scale. Thus, he cos of foreclosure will rise wih he aggregae level of foreclosures. The liquidiy provided is LQ Z N (3) where N is he quaniy of final goods used for liquidaion. The price level of he final good is P. The price of liquidiy services per liquidiy uni is F. Profis of liquidiy service providers are: PN F Z N. (4) The firs-order condiion for he liquidaors maximizaion problem is: F F LQ Z N. (5) P P N ( ) 3. Capial Consrucion Capial builders combine new invesmen and exising capial for he purpose of building capial for he fuure. New invesmen is combined wih old capial ne of depreciaion o insall he capial sock of he nex period: K ( ) K I. (6) Invesmen is purchased a price P, and exising capial is purchased aq. Insalled capial K is sold for price P in compeiive markes. Profi maximizaion of capial builders implies: K K P P, Q P ( ). (7)

8 7 B. Household Feliciy increases wih consumpion, C, and decreases wih marke labor, H, as in Greenwood, Hercowiz, and Huffman (988). A represenaive household maximizes he discouned sum of expeced feliciy: j Max ln C H { CHM,, } j. (8) The household earns money income by working a wage, W, and is paid lump-sum profis, П, and pays a lump-sum fiscal ax, TAX. The budge consrain allows purchases of a riskfree bond issued by capialiss: B WH ( i ) B C TAX. (9) The firs-order condiions are: C. Capialiss H W, () P () E ( i), P. C H. Individual Enrepreneurs Problem There is a uni range of enrepreneurs (capialiss), indexed by l. Capialiss are endowed wih a sochasic echnology ha allows hem o sore capial across ime. If k l is sored a ime, he capialis will have ω l k l a ime +. Sochasic echnology, ω l, is independenly disribued (across capialiss and ime) wih a log normal cumulaive disribuion funcion, Ф (ω l ) wih a mean of. Poenially, he disribuion may change from period o period according o a sochasic process. The capialiss begin wih ne worh, nw l, and borrow, from households o finance he purchase of capial: b p k nw. (2) l K l l l b, A solven enrepreneur can earn a pay-off by rening capial o oupu producers and by selling capial back o capial builders a price Q. Define he nominal pay-off as: PAY Q R. The financial conrac requires he capialis o pay off heir deb a an ineres rae, i rp, o he credior; if hey are unable o pay off, hey urn over all capial o he credior. The minimum level of idiosyncraic echnology ha will allow he enrepreneur o pay off heir deb is given by:

9 8 ( i ) b. (3) rp l l l PAY k l If he capialis has a echnology oucome less han, he credior forecloses. To foreclose, he credior mus purchase a quaniy of foreclosure services equal o a fracion of he capial l l sock, k, a price F. l l Assume ha he financial conrac chooses and k o maximize he expeced payoff o he capialiss subjec o bond holders receiving a payoff equal o he risk-free ineres rae. The capialiss earn zero if hey defaul, so he expeced payoff is he produc of he probabiliy of no defaul and he condiional expeced revenue if here is no defaul minus he ineres paid o crediors. Thus he expeced payoff o he capialiss is given by f PAY k l l l d wih f [ ]. The expeced payoff o he crediors is he recovery value adjused for he probabiliy of defaul plus he earned ineres adjused for he probabiliy of defaul. Thus he consrain associaed wih he expeced payoff o he crediors is given by (4), l l K l l g PAYk i P k nw l d wih g, ( ) [ ], (5) F where. The deb conrac maximizes he payoff o he enrepreneurs subjec PAY o he crediors receiving a payoff equal o he risk-free ineres rae: l l {, k} Max f PAY k l l l l K l l s.. g, PAY k i P k nw. The firs-order condiions of he enrepreneur maximizaion problem imply ha he expeced payoff per each uni of capial should cover he risk premium of he gross reurn on capial over he ineres rae. The degree of leverage, common across firms, generaes a common risk premium as a funcion of leverage and he ime-varying recovery rae: (6)

10 9 E PAY P K, i, (7) where he risk premium, (), is of he form:, g, g, f f ' A ime +, he capialis receive a payoff from each uni of capial hey own.. (8) A fracion λ of enrepreneurs will die in every period and consume heir ne worh. The nex period s ne worh will be: 2. Aggregaion l l nw ( ) f PAY k. (9) Aggregaing he budge consrain for he enrepreneurs is: B P K NW. (2) K The aggregae payoff o crediors is: The level of liquidaors oupu is:, K ( ) g PAY K i B. (2) K d LQ. (22) The ne worh of enrepreneurs follows as: Consumpion by enrepreneurs is: NW ( ) f PAY K. (23) PCK f PAY K. (24)

11 D. Reailers and Wholesalers Reail firms combine a uni measure of differeniaed wholesale goods. The producion funcion of he reail good is: Y y l, dl. (25) The demand for each reail good l is a funcion of is price, p l,, as implied by y Y p l, l, P, (26) where he price index is given by P pl, dl. (27) A wholesaler produces differeniaed good l wih a one-for-one ransformaion of he producion good. Therefore, he marginal cos of producing he wholesale good, MC, is he price of he producion good. In each period, a fracion of wholesalers, (κ), receives he opporuniy o change heir nominal price. Wholesalers are owned by he workers and maximize he discouned sum of profis. A firm wih he opporuniy o change is price will maximize he discouned sum of profis: j Max E jpl, yl, j MC jyl, j. (28) { p} j Given he demand for each good, (26), we can wrie (28) as The opimal price is: Max E Y P p MC p { p} j,,. (29) j j j l j l j p j E jyjpj MCj j. (3) j E jyjpj j

12 The price level evolves according o P P p. (3) Using he Galí and Gerler (999) and Sbordone (22) echnique, we can wrie ha P inflaion,, follows a process in a linearized form: P ( )( ) mc E. (32) In equilibrium, oupu goods will be used for consumpion by households, C, and consumpion by enrepreneurs, CK, new invesmen by capial builders, I. Final oupu will also be used as an inpu, N, by liquidaors: E. Cenral Bank and Shocks Y C CK I N. (33) The cenral bank ses he ineres rae, following a Taylor (993) rule: Y YSS i iss SSY. (34) Y Following Chrisiano, Moo, and Rosagno (28), we assume ha he disribuion of an 2 idiosyncraic financial echnology shock in a given period is log-normal: log N(, ). The shock is subjec o persisen flucuaions, following he process: SS. (35) Noe ha an i.i.d. shock,, is realized a ime and impacs he variance a ime +. F. Calibraion Many parameers of he model are sandard in he dynamic general equilibrium lieraure. We se β =.99, δ =.25, and θ =.36, as in Hansen (985). We se so ha H 3 in he seady sae. Following Greenwood, Hercowiz, and Huffman (988), he Frisch elasiciy of labor supply is se a /ψ =.7. The fracion of firms seing prices in each is se a a sandard

13 2 level: κ =.75 (Galí and Gerler, 999). We assume an acivis moneary policy wih.5. The persisence of he financial echnology shock is esimaed o be.95. A more involved process will be he consrucion of he financial problem. Normalizing FSS he liquidaion echnology gives he seady-sae price of liquidaion services as: P. In a given year, he fracion of loans ha are charged off is ( ) d. For U.S. commercial banks, annual gross charge-offs relaive o oal loans for 9628 is on average.73 percen. The recovery rae of financial inermediaries in collecing on bad loans is: SS rr d PAY K ( ) B. (36) The raio of recoveries o gross charge-offs on U.S. commercial bank loans averages 23.4 percen for The annualized reurn spread beween BAA and -year governmen securiies for he same period is on average 27 basis poins. To mach hese oucomes wih he seady sae of our model, we se a σ =.368, λ =.6 and μ =.59. This generaes seady-sae values: ( SS ) =.8 which annualizes o.72 percen; R SS =.232; and,.675, indicaing 27 basis poins of risk premium per annum. SS SS G. Discussion: Financial Shocks and Liquidiy Spirals Figure 2 illusraes inuiively he response of he economy o financial shocks. A large negaive financial shock immediaely raises defaul risk which calls for endogenous subsequen effecs on recovery raes and risk premium. Illiquidiy in he collaeral repossession process plays a crucial role in he downward cycle. Firs, he rise in defaul risk can lead o repossession and sales of collaeral. Since collaeral markes are illiquid, increases in he aggregae defaul level raise he liquidaion cos of collaeral, which reduces recovery raes and increases he riskiness of lending a a given defaul rae. The resuling increase in risk premium on lending exacerbaes he downurn in invesmen demand which will have disinflaion effecs. Second, he real price of capial goods will also decline wih reduced invesmen demand, weakening corporae balance shees. Third, enrepreneurs debs are denominaed in nominal erms; herefore, disinflaion increases deb burdens and hurs heir balance shees he deb deflaion logic rooed in Irving Fisher (933). 3 3 The deflaionary impac on balance shees has been incorporaed in recen sudies including Mendoza and Smih (26), and Durdu, Mendoza, and Terrones (29).

14 3 Figure 2. Financial Shocks and Liquidiy Spirals The deerioraion in balance shees will also make defaul more likely in he fuure, exacerbaing he impac on he risk premium. Furher rises in he risk premium inensify disinflaion or he risk of he Fisherian deb deflaion hrough balance shee effecs. Worsening balance shees, in urn, increases he likelihood of defaul, which exacerbaes illiquidiy in collaeral markes and drives recovery raes furher down a liquidiy spiral. III. MODEL RESULTS A. Impacs of Financial Shocks and he Role of Collaeral Liquidiy We examine he response of he U.S. commercial banking secor o he financial crisis of 28. We specify he size of he financial shock and he collaeral liquidiy parameer in equaion (3), α, o mach wo facs observed in he daa upon his crisis: ) a rise in defaul raes; and 2) a decline in recovery raes. The FDIC repors ha defaul raes (calculaed as he raio of gross charge-offs o oal loans) increased from.67 o.38 percen beween 27 and 28. This change can be wrien as a 7.3 percen increase in defaul raes (in logarihmic erms). We consider a 5.5 percen shock o he idiosyncraic riskiness of lending,.55, which generaes a rise in defaul raes similar o hose observed in he daa. A he same ime, recovery raes on loans (calculaed as recoveries o gross charge-offs) fell from 7.62 o 8.62 percen. This can be wrien as a 7.5 percen logarihmic decrease. An aggregae increase in defaul raes makes he collaeral of defauling firms less liquid when α <. We calibrae he collaeral liquidiy parameer a α =.6 in our benchmark Illiquid model o generae a decline in recovery raes similar o ha seen in he daa. For

15 4 comparison, we consider he Liquid case when α = which leads o roughly consan recovery raes. We focus on he pure inflaion argeing case, seing Y =. Figure 3. shows responses of financial variables o a financial crisis shock in he Liquid and Illiquid cases. Idiosyncraic volailiy does no respond in he period of he shock, bu expeced volailiy rises from period 2 and beyond. This has equilibrium effecs which cause some firms o defaul immediaely. However, he bigges impac on defaul raes is in he period afer he shock, when idiosyncraic risk rises direcly (see Panel B). During period 2, he defaul rae rises o a peak of abou 7 percen (in log erms) in boh cases. The rise in he defaul rae leads o a rise in he risk premium on lending,,, far more severely in he Illiquid case han he Liquid case due o he downward liquidiy spiral (Panel A). In he Illiquid case, disposing collaeral becomes more expensive when defaul raes sar o rise and recovery raes sharply decline (Panels B and C). Recovery raes fall by abou 7 percen (by consrucion) in he Illiquid case, and remain virually unchanged in he Liquid case. Falling recovery raes render lending more risky and, in he downward liquidiy spiral, lead o more damage o firm balance shees. Leverage, defined as P K / K NW, rises in he Illiquid case by almos percen while rising by less han.5 percen in he Liquid scenario (Panel D). The increase in leverage and he drop in recovery raes raise he risk premium by.7 percen (or abou 28 annualized basis poins) in he Illiquid case, compared o abou.4 percen poin in he Liquid case. Figure 3. also shows he response of enrepreneurial consumpion, CK, which is proporional o enrepreneurs real ne worh, NW / P (Panel E). This falls approximaely wice as much in he Illiquid case. The quaniy of final goods used for liquidaion, N, increases subsanially afer he shock: in period 2 when i reaches is peak, 6 percen above is seady sae (Panel F). Noe, however, ha he size of N in he seady sae is less han. percen of overall oupu. Hence he cyclical rise in liquidiy needs has lile impac on he overall demand for oupu. Figure 3.2 demonsraes how collaeral liquidiy affecs he business cycle properies upon he financial shock. Household consumpion s response depends on wo opposing effecs. Firs, reduced real ineres raes have a posiive effec on consumpion hrough ineremporal subsiuion. Second, under Greenwood, Hercowiz, and Huffman s (988) preferences, a decline in employmen direcly reduces he marginal uiliy of consumpion. Inuiively, households subsiue addiional leisure for consumpion. Moreover, given he persisen decline in capial, workers wages and income should negaively affec permanen income. Consequenly, in he Illiquid case, he negaive effecs of leisure subsiuion and lower permanen income dominae he posiive effecs of reduced real ineres raes, leading o a persisen decrease in household consumpion. In he Liquid case, he same happens only afer a brief lag as he employmen-income effecs are ouweighed iniially by he ineres rae effecs (Panel A). Invesmen declines, more sharply wih higher increases in he risk premium in he Illiquid case: he decline in invesmen is approximaely 3 percen in he Liquid case and 5 percen in he Illiquid case (Panel B).

16 5. Financial Variables Figure 3. Responses o a Financial Uncerainy Shock: Liquid Model versus Illiquid Model.8 (A) Risk Premium 8 (B) Defaul Rae % Deviaion (C) Recovery Rae (D) Leverage % Deviaion (E) Enrepreneurial Consumpion 8 (F) Liquidiy Demand % Deviaion Liquid Illiquid Noes: This figure shows he benchmark model responses of financial variables associaed wih he financial problem of capialiss o a financial shock in period under ) he Liquid model in which defaul has non-increasing liquidaion coss; and 2) he Illiquid model in which defaul has increasing liquidaion coss.

17 6 2. Macroeconomic Aggregaes.5 (A) Household Consumpion (B) Invesmen % Deviaion (C) Oupu (D) Nominal Ineres Rae % Deviaion (E) Real Ineres Rae (F) Inflaion Rae % Deviaion Liquid Illiquid Noes: This figure shows he Benchmark model responses of macroeconomic aggregaes o a financial uncerainy shock in period under ) he Liquid model in which defaul has non-increasing liquidaion coss; and 2) he Illiquid model in which defaul has increasing liquidaion coss.

18 7 Given sicky prices, he declines in invesmen and household consumpion, along wih he decline in enrepreneurial consumpion, have more severe negaive impacs on oupu in he Illiquid case where oupu falls by.3 percen, compared o a.6 percen decline in he Liquid case (Panel C). Oupu declines iniially owing o he reduced demand, and persisenly as he financial acceleraor prolongs he negaive impac on capial invesmen. The larger decline in demand in he Illiquid case generaes a sharper disinflaion. Inflaion declines by.6 percen under he Liquid case bu by nearly.3 percen under he Illiquid case (Panel F). The sharper disinflaion in he Illiquid model generaes sharper declines in nominal and real ineres raes (Panels D and E). B. Ineres Rae Policy Response: Concerns abou Recession Risk In his secion, we examine how moneary policy can be used o offse some of he impacs of he financial shock, considering a Taylor rule hrough which he cenral bank adjuss ineres raes in response o boh inflaion and oupu. The ineres rae rule is defined as.5 and Y.5. We show he responses of he economy o a financial crisis shock of size.55 in he Illiquid collaeral scenario wih α =.6. For comparison, we also show he response of he economy under pure inflaion argeing wih.5 and Y, also wih illiquid collaeral. Figure 4.2 suggess ha moneary policy responding o oupu amelioraes he impac of he financial shock on he risk premium and, hus, he economy. As seen previously, he financial shock leads o a persisen oupu decline. In response, he Taylor rule induces a sharper and more persisen cu in boh nominal and real ineres raes, compared o pure inflaion argeing (Panels D and E). Sharper decreases in real ineres raes dampen he negaive impac of he shock on invesmen and household consumpion (Panels A and B). This less sharp drop in demand leads o a milder decline in oupu and milder disinflaion (Panels C and F). The moneary policy reacion o negaive pressure on oupu indirecly couners deerioraion in he financial secor, as shown in Figure 4.. The milder disinflaion under he Taylor rule dampens he persisen rise in he risk premium and reduces he adverse impac of he shock on enrepreneurs balance shees. The relaively limied damage o enrepreneurs balance shees somewha amelioraes persisen rises in he risk premium and defaul raes, and persisen falls in recovery raes (Panels A C). Under pure inflaion argeing, enrepreneurs consumpion, proporional o ne worh, falls sharply and persisenly; and under he Taylor Rule, enrepreneurs ne worh and consumpion fall by a smaller amoun and recover rapidly, surpassing is seady-sae level from 3 periods afer he shock (Panel E). This implies mild and brief increases in he leverage of enrepreneurs above he seady sae (Panel D) and less need for collaeral liquidiy (Panel F). However, he financial shock does increase he risk premium and reduce recovery raes under eiher moneary policy, and he effec of moneary policy on hese facors is relaively weak. We also noe ha moneary policy reacions can be consrained by he zero bound on ineres raes if he prevailing policy rae is very low.

19 8. Financial Variables Figure 4. Responses o a Financial Uncerainy Shock: Pure Inflaion Targeing versus Taylor Rule.8 (A) Risk Premium 8 (B) Defaul Rae % Deviaion (C) Recovery Rae (D) Leverage % Deviaion (E) Enrepreneurial Consumpion 8 (F) Liquidiy Demand % Deviaion Inflaion Targe Taylor Rule Noes: This figure shows he benchmark illiquidiy model responses of financial variables o a financial uncerainy shock in period under ) pure inflaion argeing; and 2) a Taylor rule.

20 9 2. Macroeconomic Aggregaes.5 (A) Household Consumpion (B) Invesmen % Deviaion (C) Oupu (D) Nominal Ineres Rae % Deviaion (E) Real Ineres Rae.5 (F) Inflaion Rae % Deviaion Inflaion Targe Taylor Rule Noes: This figure shows he benchmark illiquidiy model responses of macroeconomic aggregaes o a financial uncerainy shock in period under ) pure inflaion argeing; and 2) a Taylor rule.

21 2 C. Governmen Subsidy for Collaeral Liquidaion Consider if he governmen subsidizes liquidiy for he financial sysem, financed by a lump-sum fiscal ax, during he financial crisis. Suppose ha a subsidy, s, reduces he price F of acquiring liquidiy for he firm. We hen wrie as: ( s ). We assume PAY ha he governmen ses his subsidy as: s sss rp rpss, (37) s rp ss ss so ha he governmen conribuion o he liquidiy of he financial marke increases wih he risk premium. For a Subsidy case, we se sss.5 wihou adjusing SS (or he seady sae in any way) and se =2. The subsidy is financed by a lump-sum ax on households (who are Ricardian-equivalen). Since he governmen budge consrain requires he lumpsum ax o be equal o he subsidy ha is small a seady sae, changes in he subsidy or ax over business cycles are of second order in size in he household budge. This suggess ha he subsidy o reduce liquidaion coss has small income effecs relaive o is impacs hrough he financial acceleraor on business cycle dynamics. Liquidaion coss affec he economy by raising he cos of capial: especially near he seady sae, invesmen demand is very sensiive o small changes in he cos of capial. Hence, he subsidy ha offses hese small changes in he cos of capial can counervail srongly he adverse impac of a financial shock on aggregae demand. Figure 5 shows he responses of he economy o he financial shock in he Subsidy case, along wih he No Subsidy case ( sss and = ). The financial impacs of he argeed subsidy are depiced by Figure 5.. The financial shock increases he risk premium and defaul rae (Panels A and B). In he model wihou governmen suppor for he liquidaion of collaeral, he rise in defaul leads o a sharp decline in recovery raes. In he case where he governmen suppors he liquidaion of collaeral, recovery raes remain fairly sable around he seady sae (Panel C), while he demand for collaeral liquidiy is largely unaffeced (Panel F). As a resul, he increase in he risk premium is relaively limied, and he level of leverage and he reducion of enrepreneurial consumpion hrough balance shee effecs are dampened (Panels D and E). As shown in Figure 5.2, he impacs of he financial shock on he macroeconomy are subsanially reduced under he governmen s suppor for collaeral liquidaion. The dampened increase in he risk premium resuls in more moderae decreases in invesmen, oupu, and household consumpion (Panels AC), accompanied by more moderae disinflaion and smaller cus in nominal and real ineres raes (Panels DF).

22 2. Financial Variables Figure 5. Responses o a Financial Uncerainy Shock: No Subsidy versus Subsidy for Collaeral Liquidaion.8 (A) Risk Premium 8 (B) Defaul Rae % Deviaion (C) Recovery Rae (D) Leverage % Deviaion (E) Enrepreneurial Consumpion 8 (F) Liquidiy Demand % Deviaion No Subsidy Subsidy Noes: This figure shows he benchmark illiquidiy model responses of financial variables o a financial uncerainy shock in period under ) no subsidy o collaeral prices; and 2) a subsidy o collaeral prices.

23 22 2. Macroeconomic Aggregaes.5 (A) Household Consumpion (B) Invesmen % Deviaion (C) Oupu (D) Nominal Ineres Rae % Deviaion (E) Real Ineres Rae (F) Inflaion Rae % Deviaion No Subsidy Subsidy Noes: This figure shows he benchmark illiquidiy model responses of macroeconomic aggregaes o a financial uncerainy shock in period under ) no subsidy o collaeral prices; and 2) a subsidy o collaeral prices.

24 23 D. Endogenous Accumulaion of Liquidiy Invenory We now examine a model in which liquidaors can build up liquidiy invenory as buffers agains srains on liquidiy in collaeral markes, as opposed o he previous case where he liquidiy availabiliy o foreclosing crediors is saic regardless of condiions in he economy. Liquidiy invenory, in he form of oupu goods, promoes he provision of liquidiy services in collaeral markes: LQ Z N V, (3 ) where V is he liquidiy invenory ha is accumulaed hrough he liquidaor s invesmen, LI, by purchasing oupu goods: Opimal demand for he liquidiy invenory is: The equilibrium level of oupu becomes: V V LI. (38) F LQ E P P. (5 ) LI Y C CK I N LI. (33 ) Figure 6 shows model responses o he financial shock when he financial sysem can build up a liquidiy invenory o handle he collaeral repossession process. We compare he responses o he No Invenory case where no invenory is buil up. Figure 6. suggess ha he impacs on he financial secor appear similar o he case of he governmen subsidy case. The excepion is ha he endogenous liquidiy buildup is refleced in reduced demand for collaeral liquidiy while ensuring recovery raes around he seady sae. The rise in idiosyncraic risk leads o an increase in he defaul likelihood (Panel B). The expeced rise in collaeral liquidiy needs (Panel F) calls for an increase in liquidiy invenory, V, in he Liquidiy Invenory case. The increase in liquidiy invenory resuls in a minimal and emporary drop in recovery raes in he Liquidiy Invenory case, compared o he large drop in he No Invenory case (Panel C). Naurally, he risk premium rises by subsanially less in he Liquidiy Invenory case han he benchmark case (Panel A). The overall effec of he financial shock on he macroeconomy is less conracionary when he financial sysem is able o build a liquidiy invenory, as shown in Figure 6.2. The buildup of liquidiy invenory helps dampen he rise in he risk premium, resuling in reduced conracions in invesmen, consumpion, and oupu (Panels A C). As a resul, he Liquidiy Invenory case generaes more moderae disinflaion along wih smaller cus in nominal and real raes (Panels D F).

25 24. Financial Variables Figure 6. Responses o a Financial Uncerainy Shock: No Invenory versus Liquidiy Invenory.8 (A) Risk Premium 8 (B) Defaul Rae % Deviaion (C) Recovery Rae (D) Leverage % Deviaion (E) Enrepreneurial Consumpion 5 (F) Liquidiy Demand % Deviaion Invenory No Invenory Noes: This figure shows he benchmark illiquidiy model responses of financial variables o a financial uncerainy shock in period in ) he No Invenory case wih no abiliy o accumulae liquidiy invenory over ime; and 2) he Liquidiy Invenory model when liquidiy invenory can be accumulaed.

26 25 2. Macroeconomic Aggregaes (A) Household Consumpion (B) Invesmen % Deviaion (C) Oupu (D) Nominal Ineres Rae % Deviaion (E) Real Ineres Rae (F) Inflaion Rae % Deviaion Invenory No Invenory Noes: This figure shows he benchmark illiquidiy model responses of macroeconomic aggregaes o a financial uncerainy shock in period in ) he No Invenory case wih no abiliy o accumulae liquidiy invenory over ime; and 2) he Liquidiy Invenory model when liquidiy invenory can be accumulaed.

27 26 IV. CONCLUDING REMARKS This paper focuses on he business cycle impac of endogenous flucuaions in recovery raes upon defaul. The resoluion of defauled loans relies upon he liquidiy of he collaeral marke. A financial crisis, accompanied by a rise in defaul risk, inherenly axes he abiliy of he financial sysem o liquidae collaeral. The increase in defaul risk causes an increase in risk premium and a fall in recovery raes, reducing liquidiy in he collaeral marke, which, in urn, exacerbaes he increase in risk premium. Our model characerizes a cerain ype of liquidiy spiral responsible for he amplificaion of a financial crisis. We sugges ha endogenous responses of collaeral liquidiy, manifesed by dynamic responses of recovery raes, provide an addiional source of amplifying he financial acceleraor. This mechanism generaes a sharper disinflaion process and reinforces he poenial risk of deb deflaion relaive o sandard financial acceleraor models. This paper demonsraes some poenial policy responses o dampen he liquidiy spiral. Firs, moneary policy clearly can play he role of moderaing downurns in economic aciviies by lowering he policy rae unless he zero bound consrain on ineres raes is binding. Second, direc subsidies which alleviae he loss of value of collaeral can also ameliorae he negaive business cycle impacs of he financial crisis. Third, endogenous liquidiy invenory buildups help increase he resilience of he economy o a financial shock and promoe inheren financial sabiliy. As is well-known, ineres rae policy has he obvious lower bound on he reducion of he nominal rae in he face of persisen financial shocks when he prevailing rae is already very low. We also noe ha governmen liquidiy subsidies (for example, by shoring up funding liquidiy) will require public resources and evenually be financed by governmen axes. In conras, he liquidiy buildup by enrepreneurs can be suppored by privae resources on he basis of marke signals.

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