Contributions. Monetary and Macroprudential Policy Rules in a Model with House Price Booms

Transcription

1 The B.E. Journal of Macroeconomics Conribuions Volume 12, Issue Aricle 16 Moneary and Macroprudenial Policy Rules in a Model wih House Price Booms Prakash Kannan Pau Rabanal Alasdair M. Sco Inernaional Moneary Fund, pkannan@imf.org Inernaional Moneary Fund, prabanal@imf.org Inernaional Moneary Fund, asco@imf.org Recommended Ciaion Prakash Kannan, Pau Rabanal, and Alasdair M. Sco (212) Moneary and Macroprudenial Policy Rules in a Model wih House Price Booms, The B.E. Journal of Macroeconomics: Vol. 12: Iss. 1 (Conribuions), Aricle 16. DOI: / Copyrigh c 212 De Gruyer. All righs reserved.

2 Moneary and Macroprudenial Policy Rules in a Model wih House Price Booms Prakash Kannan, Pau Rabanal, and Alasdair M. Sco Absrac Using a dynamic sochasic general equilibrium (DSGE) model wih housing, his paper shows ha srong moneary reacions o acceleraor mechanisms ha push up credi growh and house prices can help macroeconomic sabiliy. In addiion, using a macroprudenial insrumen specifically designed o dampen credi marke cycles would also provide sabilizaion benefis when an economy faces financial secor or housing demand shocks. However, he opimal macroprudenial rule under produciviy shocks is o no inervene. Therefore, i is crucial o undersand he source of house price booms for he design of moneary and macroprudenial policy. KEYWORDS: moneary policy, regulaory policy, housing prices The hree auhors are affiliaed wih he Inernaional Moneary Fund. We would like o hank Olivier Blanchard, Charles Collyns, Jörg Decressin, Anonio Faás, Jordi Galí, David Romer, wo anonymous referees and seminar paricipans a he Bank of Canada, Bank of England, Board of Governors of he Federal Reserve, IMF, and Her Majesy s Treasury for houghful discussions and commens. Any remaining errors are our own. This paper was previously circulaed as IMF Working Paper No. 9/251. The views expressed in his paper are hose of he auhors and should no be aribued o he IMF, is Execuive Board, or is Managemen.

3 Kannan e al.: Moneary and Macroprudenial Policy Rules 1. Inroducion The Grea Recession has caused policymakers o rehink he appropriae policy oolki o deal wih vulnerabiliies semming from nancial markes. Before he crisis, consensus was ha responding direcly o ucuaions in asse prices or oher nancial variables was poenially harmful due o he inheren di - culy in deecing asse price bubbles in real ime (Bernanke and Gerler, 21). However, a growing body of empirical work has found ha large movemens in a number of observable variables credi, residenial invesmen shares, and curren accoun de cis are reliable indicaors of fuure sock and house price buss, which in urn are ypically associaed wih subsanial falls in oupu. 1 These same variables do reasonably well in explaining he cross-counry variaion in house price declines during he Grea Recession. 2 Such evidence suggess ha if cenral bankers wish o miigae damaging asse price boom-bus cycles, hey should consider reacing o such variables raher han focusing mainly on radiional responses o in aion and he oupu gap. Noneheless, aggressive use of cenral bank policy raes o address he build-up of nancial imbalances, or o de ae an incipien bubble in some asse caegories, is viewed by some as oo blun a response, as oher secors of he economy will be adversely a eced as a consequence (Kohn, 21). Hence, macroprudenial policies are being proposed as a complemen o moneary policy and o address, or a leas miigae, he perverse e ecs of nancial secor imbalances and asse price bubbles. Several imporan quesions need o be addressed o deermine he appropriae policy response: Wha are he poenial gains from reacing o signs of emerging nancial vulnerabiliy? Is moneary policy he appropriae ool for reacing o such indicaors, or should oher policies be used? Wha are he rade-o s beween focusing policy on sabilizing he oupu gap and CPI in aion and aemping o reduce he risk of asse price crashes? This paper addresses hese quesions using a model economy wih housing spillover e ecs, in he spiri of Iacoviello (25) and Iacoviello and Neri (21). The model has some of he key feaures relevan for examining he poenial 1 See Kannan e al. (211). See also Borio and Lowe (24) and IMF (29). 2 See IMF (29). Published by De Gruyer, 212 1

4 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 role of moneary policy in miigaing he e ecs of house price booms. We focus on he e ecs of house price ucuaions because housing wealh is generally more imporan for households han nancial asses as a sore of wealh, and because he housing marke has been a he cener of he mos recen nancial crisis. The resuls from he simulaions sugges ha exending moneary policy o include credi aggregaes can help couner acceleraor mechanisms ha push up credi growh and house prices. We nd ha using a macroprudenial insrumen designed speci cally o dampen credi marke cycles is also useful, bu ha policy misakes are possible. In paricular, when nancial or housing demand shocks drive he credi and housing boom, using a macroprudenial insrumen ha reacs o credi growh will improve welfare. On he oher hand, resricing credi using macroprudenial policies when he source of he housing boom is produciviy would decrease welfare. Therefore, expecaions should be realisic abou wha can be achieved by using macroprudenial policies: invarian and rigid policy responses raise he risk of policy errors ha could lower, no raise, macroeconomic sabiliy. How do hese conclusions compare wih hose from oher sudies? There is a vas lieraure on moneary policy and asse prices. A long-sanding debae asks wheher cenral banks should reac direcly o asse prices; wo wellknown examples are Bernanke and Gerler (21), who conclude ha here is no role for asse prices in moneary policy rules, and Cecchei e al. (2), who argue ha cenral banks should reac o asse prices. More recen papers have suggesed ha here are gains from including addiional indicaors in moneary policy rules. Chrisiano e al. (27, 28), for example, sugges ha he cenral bank can improve welfare by argeing credi growh in a model wih asse price booms. Cúrdia and Woodford (21) include credi spreads in he moneary policy reacion funcion, and Gray e al. (211) nd a role for a nancial sabiliy indicaor in he moneary rule. This paper belongs o he recen growing lieraure on macroprudenial policies in dynamic sochasic general equilibrium (DSGE) models wih - nancial acceleraor e ecs. In general, his lieraure sresses ha in order o implemen opimal moneary and macroprudenial policies, i is criical o idenify he source of he shock driving he housing or asse price boom. Gruss and Sgherri (29) sudy he welfare implicaions of procyclical loano-value raios in a wo-counry inernaional real business cycle model wih borrowing consrains. However, because heir model does no have a nominal side, he reacion of moneary policy canno be addressed. Angelini, Neri and Panea (211) have also sudied he role of macroprudenial policies in a New Keynesian model wih a banking secor and nancial acceleraor e ecs 2

5 Kannan e al.: Moneary and Macroprudenial Policy Rules on boh households and rms. Similar o our paper, hey nd ha macroprudenial policies are mos helpful o couner nancial shocks he lead o a credi and asse price boom. Lamberini e al. (211) sudy he role of exending moneary policy and inroducing macroprudenial ools in a model wih expecaions-driven business cycles. They nd ha having moneary policy respond o credi aggregaes or inroducing a loan-o-value rule for borrowers helps in reducing he volailiy of he oupu gap and credi aggregaes when he economy is hi by news shocks. The paper is srucured as follows. Secion 2 conains a descripion of he model and Secion 3 a descripion of he policy regimes evaluaed in he simulaions. Secion 4 summarizes he model s calibraion. The resuls of simulaion experimens are presened in Secion 5. In Secion 6, sensiiviy analysis is performed. The nal secion concludes. An appendix deails he linearized condiions for he model. 2. A Model for Analyzing House Price Booms The model used in his paper has a number of modi caions o he sandard New Keynesian model (Galí, 29) wih regard o he characerizaion of households and nancial markes, which creae a special role for asse prices. Because housing wealh is generally more imporan for households han equiies, and because house purchases ypically require deb nancing, we concenrae on he role of housing. In addiion, he housing marke has been a he cener of he mos recen nancial crisis. 3 Our model is closely relaed o hose in Iacoviello (25), Iacoviello and Neri (21), and Monacelli (29). Firs, households make choices abou how much o inves in housing, as well as how much o consume in nondurable goods. Housing is an asse ha provides uiliy for sheler services and is he main vehicle for accumulaing wealh in his economy. Second, we make a disincion beween borrowers and lenders, hereby creaing condiions for leverage. We assume ha savers canno lend o borrowers direcly. Insead, we inroduce nancial inermediaries ha ake deposis from savers and lend hem o borrowers, charging a spread ha depends on he ne worh of borrowers. Third, he lending rae is modeled as a spread over he policy rae ha depends on loan-o-value raios, he markup charged over funding (policy) raes, and, in some cases discussed below, a macroprudenial insrumen. Hence, lending raes can change for a number of reasons: for example, an 3 For a model ha considers he moneary policy implicaions of sock price ucuaions, see Chrisiano and ohers (27). Published by De Gruyer, 212 3

6 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 increase in house prices will raise marke valuaions of borrowers collaeral, lowering he average loan-o-value raio, and will herefore lead o a fall in lending raes even if moneary policy has no eased. Credi marke condiions can also change because of, say, changes in percepions of risk or compeiiveness in lending which could lead banks o adjus heir markups and herefore aler he lending spread. Boh of hese mechanisms help accelerae a rise in residenial invesmen, nondurable consumpion, and consumer prices. 4 In some simulaions, policymakers can a ec spreads direcly, using a macroprudenial ool, in addiion o in uencing lending raes via policy raes. In oher aspecs, he model has convenional New Keynesian foundaions. The heoreical framework consiss of a general equilibrium wo-secor model (durables and nondurables) in which each secor operaes under monopolisic compeiion and nominal rigidiies. Prices in boh secors are sicky in he shor run, as in Calvo (1983). Consumpion and residenial invesmen adjus slowly due, respecively, o habi formaion and adjusmen coss. I is cosly for workers o shif from working on he producion of consumpion goods o building houses, and vice versa. For simpliciy, here is no capial used in he producion of durable and nondurable goods and he economy is closed Households Households obain uiliy from consuming he sock of durables and he ow of nondurables. There are wo ypes of households in his economy, borrowers and savers. Borrowers are assumed o be more impaien han savers, by having a smaller discoun facor. In equilibrium, savers will provide nancing o borrowers. A fracion of households are considered o be savers, he remaining fracion 1 are borrowers Savers Each saver j 2 [; ] maximizes he following uiliy funcion: ( X 1 E " log(c j "C 1 ) + (1 ) D log(d j ) = L j 1+' 1 + ' #) ; (1) 4 These feaures draw on elemens of models by Aoki e al. (24), Cúrdia and Woodford (21), Iacoviello (25), and Monacelli (29). The nancial acceleraor mechanism goes back o Bernanke e al. (1998). In our model, he acceleraor works hrough housing nance raher han rms capial. 4

7 Kannan e al.: Moneary and Macroprudenial Policy Rules where C j denoes consumpion of nondurable goods, D j denoes consumpion of durable goods, and L j denoes oal hours worked by household j. is he discoun facor. Households form exernal habis in consumpion, as in Smes and Wouers (23) and Iacoviello and Neri (21), wih " denoing he imporance of he habi sock, which is las period s aggregae consumpion (C 1 ). The uiliy funcion is hi by a housing preference shock ( D ), ha follows a zero-mean AR(1) process in logs. Finally, following Iacoviello and Neri (21), we assume ha here is imperfec subsiuabiliy of labor supply across secors, such ha he labor disuiliy index can be wrien as L j = L L C;j 1+L + (1 ) L L D;j 1+L 1 1+ L ; (2) where L > ; is he economic size of each secor, and L x;j denoes hours worked by household j in each secor x = C; D. This imperfec subsiuabiliy implies ha reallocaing labor across secors following a shock is cosly. Noe ha when L = he aggregae is linear in hours worked in each secor, so here are no coss of swiching from working in one secor o he oher. This swiching cos helps he model explain posiive comovemen of real variables in boh secors in response o shocks, as in he daa. The budge consrain of he savers, in nominal erms, is given by P C C j + P D I j + B j R 1 B j 1 + W C L C;j + W D L D;j + j ; (3) where P C and P D are he price indices of durable and nondurable goods, respecively, W x is he nominal wage in each secor x = C; D, and B j denoes saving insrumens (such as deb insrumens or deposis) ha borrowers place in nancial inermediaries, a a gross ineres rae of R. j denoes nominal pro s from inermediae goods producing rms and nancial inermediaries, which are ulimaely owned by savers. I j denoes residenial invesmen. We assume ha he law of moion of he housing sock evolves as "!# D j = (1 )D j S I j I j 1 I j ; (4) where denoes he rae of depreciaion of he housing sock and, following Chrisiano, Eichenbaum, and Evans (25), we inroduce an adjusmen cos funcion, S (:), which is convex (i.e. S () > ). In he seady sae S = S= and S > : The aim of inroducing his cos is o allow for he possibiliy Published by De Gruyer, 212 5

8 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 ha he model can generae hump-shaped responses of residenial invesmen o shocks. The rs order condiions o he household maximizaion problem are given by he following expressions, where is he Lagrange muliplier associaed wih he budge consrain, and is he Lagrange muliplier associaed wih equaion (4): 5 U C = P C ; (5) U D = (1 )E +1 ; (6) and " # 2 P D I = 1 S S I I +E I 1 I 1 I +1 S I+1 I+1 : 1 I I (7) Absen adjusmen coss o residenial invesmen (i.e. when S = ), hese hree equaions can be reduced o he following condiion: P D P C = 1 D (C "C 1 ) D + (1 )E C "C 1 P D C +1 "C +1 P C +1 Noe ha if he durable good is in fac compleely nondurable (i.e. = 1), his condiion simply equaes he marginal uiliies of he wo consumpion goods o heir relaive prices. Since he durable good has a residual value he following period, an exra erm for he value of holding an addiional uni of he durable good appears. The Euler equaion for he consumpion of nondurable goods wih habis is sandard: P C 1 = R E P+1 C C "C 1 C +1 "C and he labor supply condiions o boh secors are given by L ' L L L C L W C = ; C "C 1 P C and L ' L (1 ) L L D : ; (8) L W D = : (9) C "C 1 P C 5 Since all savers behave he same way, we drop he j subscrips in wha follows. 6

9 Kannan e al.: Moneary and Macroprudenial Policy Rules Borrowers Each borrower j 2 [; 1] maximizes he following uiliy funcion: E 8 >< >: 1X = B; log(c B;j "C B 1) + (1 ) D log(d B;j ) L B;j 1 + ' 1+' 39 >= 7 5 >; ; (1) in which all variables wih a B superscrip are he borrowers analog o he savers variables above. B < is he discoun facor of he borrowers; i is assumed ha borrowers are more impaien han savers. Their budge consrain in nominal erms is given by P C C B;j + P D I B;j + R L 1B B;j 1 B B;j + W C L C;B;j + W D L D;B;j : (11) Borrowers can obain loans from nancial inermediaries a a lending rae of R L : In he following subsecion we discuss how he spread of he lending rae over he deposi rae is deermined. We assume ha he funcional forms for aggregae labor supply (L B;j ) and for he law of moion of housing sock (D B;j ) are he same as in he case of savers. Hence, he rs order condiions for he borrower households are given by similar equaions o (5) o (9), bu wih he relevan ineres rae R L in he Euler equaion Financial Inermediaries The single mos imporan elemen in his model is he presence of nancial inermediaries and he deerminaion of he spread beween he lending rae and he deposi rae. We assume ha savers canno lend o borrowers direcly. Insead, we inroduce nancial inermediaries ha ake deposis from savers and lend hem o borrowers, charging a spread ha depends on he ne worh of borrowers. The pro s of nancial inermediaries are ransferred o savers, who own hem. To be clear, our funcional form for he deerminaion of he spread is assumed raher han derived from a pro maximizaion problem. However, he funcional form follows he nancial acceleraor idea of Bernanke e al. (1998) for he spread of he bank lending rae (R L ) over he deposi/risk free rae (R ). I also embeds he idea ha he supply of credi is an upward-sloping curve wih respec o lending ineres raes. 6 6 Cúrdia and Woodford (21) assume ha he spread beween borrowing and deposi raes depend on he amoun of new credi in a given period. Published by De Gruyer, 212 7

10 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 Hence, he spread beween he lending and he deposi raes is given by he following funcional form: R L B B = F : (12) R P D More precisely, he ingrediens of he spread are as follows: is a nancial shock ha follows an AR(1) process in logs. In he seady sae, is mean value denoes he markup in he banking secor. Changes in can be hough of as a reducion in he margin banks charge over funding coss, caused by an increase in compeiion and a ques for marke share, or by a reducion in perceived lending risk. F is an increasing funcion of he leverage of borrowers, denoed by he raio of deb o he value of he housing sock, B B =P D D B. We assume ha F () > and ha F (1 ) = 1, wih being he seady-sae downpaymen required from borrowers. The parameer 1 denoes he loan-o-value raio. In he model, he seady-sae loan-o-value raio is viewed as a suggesed value by regulaory auhoriies raher han a legally binding one. 7 If borrowers do no mee his requiremen, and demand a higher leveraged loan, hey are charged a higher lending rae. While he model does no have risk of defaul, his variable could be seen as a proxy for credi risk. 8 is a macroprudenial insrumen ha allows he cenral bank o affec marke raes by imposing addiional capial requiremens or loan provisions whenever credi growh is above is seady-sae value. BIS (21) explains how hese requiremens can a ec ineres raes in he money marke, which in urn a ec macroeconomic oucomes. Below, we discuss speci c funcional forms for his policy ool. The mechanism embedded in equaion (12) inroduces a more exible borrowing consrain han wha is usually assumed in he lieraure. In Iacoviello (25), he equilibrium real ineres rae is smaller han he inverse of he discoun facor of borrowers. Hence, borrowers would like o borrow an in nie amoun and he borrowing consrain is always binding: ha is, 7 This is he case in mos advanced economies, see IMF (211). 8 Models wih explici defaul risk such as Aoki e al. (24) and Forlai and Lamberini (211) derive an expression relaing credi spreads wih he ne worh of agens ha borrow using housing as collaeral. D B 8

11 Kannan e al.: Moneary and Macroprudenial Policy Rules B B = (1 ) P D D B. In our model, borrowers can increase heir leverage if hey wish o do so, bu a a higher rae. Also, when house prices increase, borrowers can eiher ake more deb, re nance a a lower rae, or a combinaion of boh. In addiion, he following assumpions ensure he reurn o he seady sae: (i) boh ineres raes equal he inverse of he relevan discoun facors: R L = ( B ) 1 and R = 1 ; (ii) a he loan-o-value raio, F (1 ) = 1; (iii) he macroprudenial insrumen is = 1; and (iv) he mean of he nancial shock is exacly he credi spread: = = B. Hence, in he seady-sae, he amoun of credi is B B = (1 ) P D D B, bu he loan-o-value will ucuae when shocks hi he economy. Our model can accommodae Iacoviello s mechanism by assuming ha F () = 1 whenever B B di ers from (1 ) P D D B, in addiion o F (1 ) = 1. In his case, borrowers are always a heir seady-sae loan-o-value raio because i is oo cosly o deviae from i. There is ample evidence ha morgage credi spreads increase wih loano-value raios, which provides empirical suppor o equaion (12). Ambrose e al. (24) esimae he elasiciy of morgage credi spreads wih respec o loan-o-value raios using a sample of more han 26, individual loans originaed beween 1995 and 1997 in he U.S. Afer conrolling for individual characerisics of borrowers such as FICO scores, ages, income, and conforming loan saus, hey repor elasiciies beween :2 and :68. Evidence for he euro area also suggess ha morgage spreads are an increasing funcion of he loan-o-value raio, as discussed in Sorensen and Lichenberger (27) and ECB (29). In paricular, he ECB (29) sudy repors ha, on average, an increase of loan-o-value raios from 75 o 95 percen is associaed wih an increase of morgage spreads of abou 2 o 4 basis poins. An increase of loan-o-value raios from 5 o 75 percen is associaed wih an increase of morgage spreads of beween and 2 basis poins Producers There is a coninuum of producers ha supply imperfecly subsiuable inermediae goods and a coninuum of nal goods producers in each of he wo secors ha operae under perfec compeiion and exible prices. Published by De Gruyer, 212 9

12 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar Final goods producers In he durable secor, nal goods producers purchase inermediae goods producers and aggregae hem according o he following producion funcion: Y D Z 1 D (i) D 1 D 1 D di : (13) Y D Pro maximizaion delivers he following demand for individual inermediae nondurable goods: Y D (i) = P D P D (i) D Y D ; (14) where he price level is given by imposing he usual zero-pro condiion P D Z 1 P D (i) D D di : In he nondurable goods secor, expressions are similar Inermediae goods producers Inermediae goods producers face a Calvo-ype resricion when seing heir prices. In each period, a fracion 1 k in each secor (k = C; D) receive a signal o rese heir price opimally. In addiion, a fracion ' k index heir price o las period s secorial in aion rae whenever hey are no allowed o rese heir price. Inermediae goods in boh secors are produced wih labor only, according o he producion funcions: Y C (i) = A C L C (i); for all i 2 [; 1]; and (15) Y D (i) = L D (i); for all i 2 [; 1]: (16) In he nondurable secor, he producion funcion is hi by a oal facor produciviy (TFP) shock, which follows an AR(1) in logs. In each secor, cos minimizaion implies ha he real marginal cos of producion is MC C = W C =P C A C ; and MC D = W D =P D. Even hough labor is he only producion inpu, labor coss may di er across secors because of imperfec labor subsiuabiliy, which can lead o di eren 1

13 Kannan e al.: Moneary and Macroprudenial Policy Rules real (produc) wages. Also, real uni labor coss can di er because of he secor-speci c echnology shocks in he nondurable secor. In he remaining par of his subsecion, we work ou he condiions for he durable secor pricing decisions. Firms in he durable secor face he following maximizaion problem: max E P D(i) 82 1X >< k 6 D ;+k 4 >: k= P D (i) P D 'D +k 1 P D 1 P D +k MC D +k Y D +k (i) 9 >= >; ; subjec o fuure demand where ;+k = k +k ( ^P D ) is given by 8 ^P D P D = D ( D 1) E Y D +k (i) = >< >: P D (i) P D P+k D +k 1 P D 1 'D D Y D +k; is he sochasic discoun facor. The opimal choice 1X k k D +k k= 1X k k D +k k= ky s=1 ( D +s 1) ' D ky s=1 D +s ( D +s 1) ' D D +s! D MC D +k Y D! 1 D Y D +k +k 9 >= : (17) Given he assumpions abou Calvo pricing, he evoluion of he price level is P D = D P D 1 D 'D 1 D 1 1 D 1 D 1 + (1 D ) ^P D : (18) Firms in he nondurable secor face a similar maximizaion problem, and hence he opimal price and he evoluion of he price level have similar expressions, wih he appropriae change of noaion Marke Clearing Condiions For each inermediae good, supply equals demand. We wrie he marke clearing condiions in erms of aggregae quaniies. Toal producion in he nondurable secor is equal o oal consumpion: Y C = C + (1 ) C B : (19) >; Published by De Gruyer,

14 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 Toal durable producion equals aggregae residenial invesmen: Aggregae real GDP is Y D = I + (1 ) I B : (2) Y = Y C + (1 )Y D : (21) Toal hours worked equal labor supply in each secor: Z 1 Z 1 L C (i)di = L D (i)di = Z Z L C;j dj + L D;j dj + Z 1 Z 1 L C;B;j dj; and (22) L D;B;j dj: (23) Marke clearing in he deposi/lending marke is given by: B + (1 )B B = : (24) In he following secion we discuss he role of moneary and nancial policies. A his poin, i is convenien o de ne he equilibrium of his economy, ha we presen in he appendix. 3. Policy Regimes and Welfare In his model, wo ypes of policy inervenions are possible. Firs, due o he presence of sicky prices, moneary policy has real e ecs. Second, because of he presence of nancial fricions, we assume ha policymakers can a ec he marke lending rae by imposing addiional capial requiremens or addiional provisioning when credi growh is above is seady-sae value he erm in equaion (12). We focus on credi growh because in relaed empirical work (Kannan e al., 211) we nd ha signi can deviaions of his variable from average levels are associaed wih subsequen house price buss. We focus on boh Taylor rules and macroprudenial insrumens ha reac o lagged indicaors. This choice is due o wo reasons. Firs of all, when we searched for opimal coe ciens on boh insrumens when hey reac o curren variables, we found implausibly large values for he coe ciens in he rules. Tha is, by promising a large reacion when variables change due o a shock, he policymaker achieves sable oucomes wihou having o deliver large ucuaions in he insrumens. This problem is reduced when backward looking insrumen rules are implemened, alhough opimal coe ciens 12

15 Kannan e al.: Moneary and Macroprudenial Policy Rules are sill large. We also experimened wih a version of he model where he macroprudenial rule reacs o conemporaneous credi growh. In his case, we found ha he opimal value of he reacion coe cien () was arbirarily large: he second insrumen is capable of perfecly o seing he disorion associaed wih nancial fricions, which is he opimal policy, bu unrealisic. 9 Second, from a pracical poin of view, policymakers receive informaion wih lags (or, hey produce nowcass and shor-erm forecass based on recen pas daa), and hence, i makes sense o specify heir reacion funcions in erms of las period s observables. Given hese wo insrumens, we model four policy regimes used in he experimens ha follow. The baseline policy regime is a Taylor rule, speci ed wih a weigh of 1:3 on CPI in aion and :5 on he oupu gap (which means a value for y = :125 in quarerly erms). 1 We allow for ineres rae ineria, and as we jus discussed, he variables on he righ hand side of all rules are lagged. The coe cien on ineres rae smoohing is se o R = :7. Le Y be he level of poenial oupu, which is de ned as real GDP when he economy does no include nominal or nancial rigidiies, and all agens are homogeneous (hough cosly labor reallocaion is in place). The Taylor rule regime is herefore described by he policy rule P C R = R 1 P C 2 Y 1 Y 1 y 1 r (R 1) r : (25) where we have normalized seady-sae in aion o zero. Wih ha benchmark, we invesigae gains o be achieved by incorporaing informaion from indicaors of poenial nancial vulnerabiliy. Hence, he second regime is implemened as a Taylor-ype rule in which moneary policy, in addiion o CPI in aion B B reacs o he growh rae of nominal credi, 1 B B 2 and he oupu gap. Hence, he augmened Taylor rule regime has he form: P C R = R 1 P C 2 Y 1 Y 1 y B B b 1 r 1 (R 1) r : (26) B B 2 The macroprudenial rule speci es he reacion of a macroprudenial insrumen o lagged nominal credi changes (he same variable as in he augmened 9 This resul is similar o he one obained by Gerler and Karadi (21) in a slighly di eren conex. In heir model, he cenral bank could o se ine cien ucuaions in he spread beween lending and deposi raes by providing as much funds as needed by he privae secor in a siuaion of nancial sress. 1 We found ha a slighly lower value han he one calibraed by Taylor (1993) of 1:5 works beer in order o he sandard deviaion of CPI in aion, deposi raes, and credi growh. See Secion 4. Published by De Gruyer,

16 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 Taylor rule 26): B B = 1 : (27) B B 2 As he macroprudenial insrumen a ecs lending raes, we are assuming ha policymakers can direcly o se, o some degree, ucuaions in spreads caused by he changes in collaeral values and nancial shocks described above (see equaion 12). This can be hough of as a simple shor cu ha mimics he e ecs of, say, regulaions ha require banks o se aside more capial as asse prices rise, hence raising he margin ha banks have o charge over funding coss (he policy rae). 11 Combining he macroprudenial rule wih he augmened Taylor rule produces he augmened Taylor plus macroprudenial regime. We sudy hese hree regimes in Secion 5.1 below. The nal policy regime is a variaion on he hird, in which he weigh on each variable is deermined by an opimizaion procedure ha seeks he bes response by opimizing over ; y ; r ; b ; and. This will be ermed he opimized augmened Taylor plus macroprudenial regime, which we sudy in Secion 5.2. The welfare crierion ha we use o rank all policy opions (and ha he opimizaion under he las regime is based on) is he following: P C W = V ar =P C C 1 + &V ar (Y =Y ) : (28) Hence, we employ a sandard welfare crierion whereby he policymaker cares abou minimizing he variance of CPI in aion (i.e. nondurables in aion) and he oupu gap. 12 Microfounded versions of equaion (28) ha come from aking a second order approximaion o he uiliy funcion of a represenaive household (in a one-secor, one-agen economy) end o give a low value for &, because he presence of nominal rigidiies is he mos imporan fricion in he economy, and giving a high relaive weigh o CPI in aion sabilizaion is opimal. 13 However, in pracice, cenral banks also care abou sabilizing he 11 See also BIS (21). 12 Hence, we absrac from he complicaed ask of deriving he appropiae welfare crierion based on household s uiliy funcion. Noe ha deriving such a crierion is complicaed by he fac ha he economy is subjec o many nominal, real and nancial fricions. In addiion, here are wo ypes of agens in he model wih di eren discoun facors. A welfare crierion ha maximizes he discouned sum of each ype of household s lifeime uiliy funcion will aach more weigh o he curren uiliy of he impaien household. I is no clear ha his propery of welfare is desirable. 13 See Schmi-Grohé and Uribe (27) and Woodford (23). In he example provided by Woodford (23), & = :48. 14

17 Kannan e al.: Moneary and Macroprudenial Policy Rules oupu gap. For insance, he Federal Reserve has a dual mandae for price sabiliy and maximum susainable employmen, which can be inerpreed as keeping oupu a is poenial. Therefore, for he U.S. case, seing & = 1 seems appropriae. To incorporae a wide range of policymakers preferences, we rank he di eren policy regimes by assuming a range of preferences for he cenral bank, from a very hawkish one (& = :1) o a very dovish one (& = 1). In addiion, we assume ha he role of he macroprudenial insrumen is o suppor he cenral bank in achieving is objecives Calibraion The calibraion of he model is summarized in Table 1. We aim o mach he sandard deviaion of main macroeconomic ime series for he U.S.: consumpion growh, residenial invesmen growh, consumer price index (CPI) in aion, nominal house price in aion, shor-erm deposi raes, spreads beween deposi and lending raes, and nominal credi growh (Table 2). All growh raes of nominal and real quaniies are quarerly, and all ineres raes are also measured on a quarerly basis. We obain daa on personal consumpion and residenial invesmen from he Bureau of Economic Analysis, CPI in aion from he Bureau of Labor Saisics, and nominal house prices from he OECD. The shor-erm (deposi) ineres rae is he 3-monh T-bill rae, while credi spreads are compued as he di erence beween he e ecive rae on all morgage loans closed and he 3-monh T-bill rae (boh obained from he Haver daabase). Finally, nominal credi growh is measured as he quarerly growh rae of all household credi marke deb coming from he Flow of Funds daa of he Federal Reserve Board. We base he calibraion of parameers governing real and nominal rigidiies on empirical esimaes by Iacoviello and Neri (21), bu we adjus he calibraion o make sure we can mach he relevan second momens in he daa. For insance, in order o mach he low volailiy of personal consumpion growh we need a degree of habi formaion of :8, which is somewha higher han mos esimaed DSGE models. 14 The objecive of he macroprudenial rule should be nancial sabiliy, loosely speaking. There is no consensus in he lieraure as of how his objecive should be inroduced in a macroeconomic model. However, episodes of nancial insabiliy are associaed wih large ucuaions in oupu and in aion such ha he goals of moneary and macroprudenial policy can safely be assumed o be perfecly aligned. Published by De Gruyer,

18 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 Table 1: Calibraed Parameers Parameer Descripion Value Discoun facor savers.99 B Discoun facor borrowers.98 Depreciaion rae.25 Share of savers.5 Down paymen rae (1 minus LTV).2 =( 1) Average markup 1.1 L Labor disuiliy of swiching secors 1 ' Inverse Frisch elasiciy of labor supply 1 " Habi formaion.8 Adjusmen cos residenial invesmen.5 Elasiciy of spread wih respec o ne worh.5 Share of nondurables in GDP.9 c Calvo loery nondurable.75 d Calvo loery durable.75 c Backward looking behavior nondurable 1 d Backward looking behavior durable 1 Taylor rule coe cien on in aion 1.3 y Taylor rule coe cien on oupu gap.125 r Taylor rule coe cien on lagged ineres raes.7 b Augmened Taylor rule coe cien on credi growh.3 Augmened Taylor rule plus macroprudenial coe cien on credi growh.3 a AR(1) coe cien on TFP shocks.98 v AR(1) coe cien on nancial shock.95 d AR(1) coe cien on housing demand shock.95 a Sandard deviaion TFP shock (in %) 1.5 v Sandard deviaion nancial shock (in %).125 d Sandard deviaion housing demand shock (in %) 2.5 An imporan aspec of our calibraion is ha we inroduce sicky prices in he durable secor (housing). In he lieraure, here is a long sanding debae on he degree of nominal rigidiies beween housing and he oher secors of he economy, and how his migh a ec he ransmission mechanism of moneary policy. In Iacoviello and Neri (21), housing prices are assumed o be exible. However, as shown by Monacelli (29), his assumpion is problemaic because, in he model, a moneary conracion leads o an expansion of residenial invesmen ha is a odds wih he daa (a fac know as 16

19 Kannan e al.: Moneary and Macroprudenial Policy Rules he comovemen problem ). This resul arises because he di ering degree of nominal rigidiy across secors causes a srong movemen of relaive prices. Therefore, in our calibraion, we assume ha house (durable) prices are as sicky han nondurable prices, and his helps us overcome he comovemen problem. Table 2: Second Momens in he Daa and in he Model Sd. Dev. Variance Decomposiion Daa Model TFP HD Financial Consumpion Growh Residenial Invesmen Growh CPI In aion Nominal House Price In aion Deposi Rae Spread Credi Growh Oupu Gap The parameer is key in he model since i measures he size of he nancial acceleraor e ec. We calibrae he elasiciy of credi spreads wih respec o he loan-o-value raio o = F (1 ) = :2, which is on he lower side of he esimaes repored by Ambrose e al. (24). If is calibraed o a higher value, hen he model falls shor of explaining he volailiy of credi aggregaes while i implies a volailiy of credi spreads ha is oo large. Overall, he calibraed value for srikes he righ balance beween hese rade-o s and he available empirical evidence. We assume ha half of he populaion are borrowers and half are savers. Two oher aspecs of he model s seady sae are paricularly imporan for he resuls. Firs, we assume ha deb is an imporan componen for nancing he purchase of houses he seady-sae loan-o-value raio is 8 percen. Second, he share of residenial invesmen in GDP is calibraed o 1 percen, which is higher han for mos counries, bu accuraely re ecs he ypical share of residenial invesmen in he sum of consumpion and residenial invesmen (which is he de niion of GDP in his model). Togeher, hese shares creae a signi can role for housing in economic ucuaions. We se he persisence of all shocks o high values. The AR(1) coe ciens of he housing demand and nancial shocks are se o :95. We also increase he persisence of he TFP shock in he nondurable secor o a higher value of :98. We found ha higher persisence of TFP shocks in he model helps Published by De Gruyer,

20 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 in explaining he high volailiy of residenial invesmen and house prices beer, since i leads o larger and more persisen wealh e ecs. Finally, we calibrae he sandard deviaion of he shocks o help mach he volailiy of he second momens of he daa. As in Iacoviello and Neri (21), he housing demand shock is more volaile han he TFP shock, and i is needed in order o explain he higher volailiy of house prices and residenial invesmen wih respec o CPI in aion and real consumpion. The volailiy of he nancial shock is much lower (5 basis poins on an annualized basis). This is in he range of esimaed moneary shocks in similar DSGE models (see Chrisiano, Eichenbaum and Evans, 25). The sensiiviy of he resuls o some of he parameers relaing o non-sandard aspecs of he model such as he endogeneiy of lending raes is evaluaed laer. In Table 2 we presen he second momens from he daa and from he model. The second momens from he daa are obained wihou any lering mehod (i.e. he rs row of Table 2 is he sandard deviaion of he quarerly growh rae of personal consumpion in he U.S.), and we apply he same ransformaion o he daa and o he model (i.e. growh raes and ineres raes are quarerly). The growh rae of residenial invesmen is abou 6 imes more volaile han he growh rae of personal consumpion, while he sandard deviaion of nominal house price in aion is abou 2 imes ha of CPI in aion. The model wih hree shocks can easily mach all hese sandard deviaions. The model can also easily mach he volailiy of deposi raes, credi spreads, and credi growh. If we had chosen he original Taylor parameer values, and in paricular a coe cien of of 1:5, he o he daa would have been worse. This is why we pick a slighly lower value of of 1:3. In Table 1, we also include he values for he reacion o credi growh in he augmened Taylor rule ( b ), and he value for he reacion o credi growh in he macroprudenial insrumen (). The las hree columns of Table 2 show he variance decomposiion of he main macroeconomic variables. A large share of he ucuaion on prices and real quaniies is due o TFP shocks, as in mos of he real business cycle lieraure. However, housing demand shocks are also needed o explain he higher volailiy of residenial invesmen and house prices: if we calibraed TFP shocks o mach he volailiy of housing variables, hen he model would imply a oo large volailiy of personal consumpion and CPI in aion. We noe ha he TFP and housing demand shocks have a small e ec on credi growh and in paricular credi spreads, which are mosly driven by he nancial shock. Financial shocks explain abou a sixh of CPI in aion and oupu gap ucuaions (where poenial oupu is de ned as he dynamics of real GDP in he model wihou nominal and nancial fricions, so here is no counerpar in 18

21 Kannan e al.: Moneary and Macroprudenial Policy Rules he daa in Table 2). Hence, he e ec of nancial shocks on he macroeconomy is no negligible and policymakers migh wan o respond o hem o sabilize he cycle. In he following secion we sudy he appropriae policy response o each of he hree shocks, and o a combinaion of hem. 5. Simulaion Resuls The behavior of he model economy is examined under di eren policy regimes, following shocks ha produce susained rises in residenial invesmen and house prices. The objecive is o deermine which policy regime is beer a sabilizing he economy in he face of pressures in he housing marke. In oher words, we look for policies ha can help preven nancial vulnerabiliies, raher han policies ha help pick up he pieces afer a bus. The conclusions ha can be drawn from his analysis depend crucially on which shocks drive he housing boom. To illusrae he imporance of correcly idenifying he drivers of he housing boom, we es he policy regimes using all hree shocks of he model. Alhough asse booms can arise from changes in expecaions of capial gains wihou any change in fundamenals, we do no model bubbles or irraional exuberance. Similarly, we do no aemp o model evens ha rigger house price crashes. In Secion 5.1 we sudy he performance of simple policy rules wih arbirary coe ciens, o sudy he role of exending he Taylor rule wih an addiional indicaor (credi growh) or of inroducing a macroprudenial insrumen. This allows us o beer undersand he change in policy in response o each of he shocks of he model, and he e ecs on he broader macroeconomy. Aferwards, in Secion 5.2, we opimize over all he coe ciens of he Taylor rule and he macroprudenial insrumen The Performance of Simple Policy Rules In his subsecion, we sudy how he model economy reacs o each of he hree shocks when moneary and macroprudenial policies change according o he di eren rules described in Secion 3. We compare he behavior of hese hree simple policy regimes in Table 3. Firs, we sudy he e ecs of a nancial shock, and show ha he volailiy of main variables is reduced when moneary and macroprudenial policies reac o credi aggregaes. Nex, we nd ha under a housing demand shock, here are welfare improvemens o reacing o credi growh via moneary policy. The bene s of having he addiional macroprudenial insrumen depend on he preferences of he policymakers. Finally, we show ha when TFP shocks hi he economy, he augmened Taylor Published by De Gruyer,

22 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 rule performs bes, bu inroducing he addiional macroprudenial insrumen decreases welfare. Table 3: Performance of Simple Policy Rules (Sandard Deviaions) Financial Housing TFP All Shocks CPI Gap CPI Gap CPI Gap CPI Gap Taylor Augmened Taylor Augmened Taylor macroprudenial Noe: CPI is CPI in aion, Gap is he oupu gap Reacion o Financial Shocks Figure 1 shows he responses o a nancial shock ( ), modeled as a relaxaion in lending sandards ha immediaely reduces lending raes by 25 basis poins in he baseline Taylor regime. Three pahs are shown, corresponding o he hree di eren policy regimes discussed in Secion 3. In he baseline case, moneary policy is guided by he simple Taylor rule, and, wih no macroprudenial reacion, he nancial shock causes an immediae increase in residenial invesmen and house prices. Because banks are assumed o lower lending raes when collaeral rises, he shock feeds on iself: housing demand raises house prices, collaeral values increase, lending raes are lowered, and households ake ou more loans. This is he credi acceleraor mechanism a work. In addiion, lower raes also lead o higher demand for nondurable consumpion goods by borrowers, pushing up CPI in aion. Some of he characerisics of a house price bus are eviden in he afermah of his shock: as nancial condiions normalize, residenial invesmen mus undershoo for a period o bring he housing sock back o equilibrium. This process spills over o he res of he economy, causing a emporary recession and raising volailiy in all markes. The reacion of a cenral bank following a simple Taylor rule is sraighforward: o he exen ha he oupu gap and CPI in aion are posiive following he increase in housing demand, policy raes are raised. Evenually, oupu and in aion sabilize. Nex we consider he augmened Taylor rule, which promps he cenral bank o reac direcly o credi growh, in addiion o he oupu gap and in aion. For illusraion, we assume ha he cenral bank pus an arbirary weigh of b = :3 on changes in nominal credi growh. This rule produces greaer sabiliy across he board, as can be seen from Figure 1: he volailiy 2

23 Kannan e al.: Moneary and Macroprudenial Policy Rules.3.2 Consumpion 1.5 Res. Inv..3.2 Real GDP Taylor Aug.Taylor Aug.Taylor+Reg CPI Inflaion.3 Nom. House Price Infl..3 Oupu Gap Policy Rae.1 Lending Rae.8 Nominal Deb Growh Figure 1: Effec of a Financial Shock. Noe: Horizonal axis measures quarers afer he shock, verical axis are percen deviaions from seady- sae values. Published by De Gruyer,

24 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 of consumpion and residenial invesmen is lower, and here is a considerable reducion in he volailiy of he oupu gap. House price and CPI in aion are also less volaile. Noe ha he volailiy of ineres raes is lower as well, even hough he policy rule is more aggressive. This is because a model wih fully forward-looking privae agens, such as his one, has very srong expecaions e ecs households anicipae a sronger reacion from he cenral bank and facor i ino heir decision-making. The resul is ha moneary policy works hrough he hrea of a sronger reacion, raher han by acually delivering ha sronger reacion. Macroeconomic sabilizaion is even beer served under he hird regime, under which he cenral bank complemens he augmened rule wih he use of he macroprudenial insrumen. For illusraion, he growh rae of nominal credi in he macroprudenial rule has also an arbirary weigh of = :3, wih he oher weighs mainained as for he augmened Taylor rule. The macroprudenial rule allows policymakers o direcly couner he easing of lending condiions ha induces borrowers o ake on more deb as house prices rise. Therefore, here is an improvemen in furher reducing he volailiy of CPI in aion and he oupu gap. More ineresingly, because here is a second policy insrumen, moneary policy does no have o reac so srongly o nancial shocks. As can be see from he rs wo columns of Table 3, he volailiy of boh CPI in aion and he oupu gap is decreased when boh moneary and macroprudenial policies reac o credi growh. To summarize, adding anoher indicaor o he moneary policy reacion funcion and anoher policy insrumen can improve macroeconomic sabiliy when he economy is hi by a nancial shock. The responses hin ha policy reacions guided by he sandard Taylor rule are oo weak in he face of loosened lending sandards and credi acceleraor e ecs, wih he consequence ha housing invesmen is insu cienly dampened Reacion o Housing Demand Shocks Nex, we sudy he behavior of he economy under a housing demand shock ( D ) in Figure 2. In his case, under he original Taylor rule, an increase in he demand of housing (for boh savers and borrowers) leads o an increase of residenial invesmen and house prices. In he original Taylor rule case, acceleraor e ecs lead o a decline of lending raes, and hence, as in Iacoviello and Neri (21), privae consumpion also increases when housing demand increases. Hence, he calibraed model wih a convenional Taylor rule exhibis posiive comovemen beween privae consumpion and residenial invesmen. This feaure ypically holds in he daa, due o wealh e ecs from higher house 22

25 Kannan e al.: Moneary and Macroprudenial Policy Rules.1.5 Consumpion Res. Inv Real GDP Taylor Aug.Taylor Aug.Taylor+Reg CPI Inflaion.6 Nom. House Price Infl..15 Oupu Gap Policy Rae.5 Lending Rae.15 Nominal Deb Growh Figure 2: Effec of a Housing Demand Shock. Noe: Horizonal axis measures quarers afer he shock, verical axis are percen deviaions from seady- sae values. Published by De Gruyer,

26 The B.E. Journal of Macroeconomics, Vol. 12 [212], Iss. 1 (Conribuions), Ar. 16 prices and beer access o credi for hose agens who wan o borrow. These spillover e ecs lead o higher CPI in aion, and herefore, in he baseline, he cenral bank ighens moneary policy. Exending moneary policy o include addiional indicaors works mosly hrough aenuaing he impac of he spillover e ecs of housing o nondurable consumpion, raher han cooling o he housing marke direcly. In he augmened Taylor rule regime, he cenral bank reacs o credi growh. As a resul, he volailiy of credi is reduced, and he acceleraor e ec is dampened: nondurable consumpion acually decreases slighly insead of increasing. This decline in he demand for nondurables makes CPI in aion decline on impac. The e ecs on he oupu gap are modes, because he augmened Taylor regime canno do much o reduce he volailiy of residenial invesmen, which is he main driver of he response of he oupu gap. Similar o he case of nancial shocks, he mos imporan channel of moneary policy is o a ec expecaions, and ulimaely, he cenral bank raises ineres raes by less han in he baseline case. A any rae, volailiy is reduced and welfare improved when moneary policy reacs o credi (see Table 3, columns 3 and 4). In he augmened Taylor plus macroprudenial regime, he volailiy of all variables is very similar o ha obained wihou macroprudenial measures. The welfare e ecs are ambiguous since he volailiy of CPI in aion declines bu he volailiy of he oupu gap increases. Hence, he nal evaluaion depends on he welfare crierion of he policymaker and he relaive weigh ha is given o he variance of he wo variables. We commen on his issue below, afer describing he e ecs of a TFP shock Reacion o Produciviy Shocks Broader and more aggressive policy regimes can improve sabiliy in he face of nancial shocks, and can also help in he face of housing demand shocks, bu hey raise he possibiliy of policy misakes in he face of oher ypes of shocks. This can be seen from he las se of simulaions, which shows reacions o an increase in produciviy in he nondurable goods secor (A C ) ha, in he case of he original Taylor rule, delivers an immediae 1/2 percen increase in oupu (Figure 3). 15 The iniial sages of his shock resemble a housing boom: residenial invesmen, house prices and he demand for credi all rise, jus as in he case of a nancial shock. Personal consumpion increases. However, he prices of consumpion goods fall. Indeed, he fac ha CPI in aion was 15 Alhough he shock is cenered on he producion of nondurable consumpion goods, households spend more on residenial invesmen as well as nondurables consumpion because of expecaions of higher income. 24