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1 NATIONAL BANK OF BELGIUM WORKING PAPERS - RESEARCH SERIES FORECASTING WITH A BAYESIAN DSGE MODEL: AN APPLICATION TO THE EURO AREA Frank Smes (* Raf Wouers (** The views expressed in his paper are hose of he auhors and do no necessarily reflec he views of he Naional Bank of Belgium. This paper was prepared for he 23 Sveriges Riksbank Workshop on Small srucural models for moneary policy analysis: progress, puzzles and opporuniies and was presened a he 6h European Workshop on EMU: Curren sae and fuure prospecs in Rehymno on 24-3 Augus 23. We hank Chris Sims for simulaing commens. The views expressed in his paper are our own and do no necessarily reflec hose of he European Cenral Bank or he Naional Bank of Belgium. (* (** European Cenral Bank, CEPR and Universiy of Ghen, ( Frank.Smes@ecb.in. NBB, Research Deparmen, ( rafael.wouers@nbb.be. NBB WORKING PAPER No. 6 - SEPTEMBER 24

2 Ediorial Direcor Jan Smes, Member of he Board of Direcors of he Naional Bank of Belgium Saemen of purpose: The purpose of hese working papers is o promoe he circulaion of research resuls (Research Series and analyical sudies (Documens Series made wihin he Naional Bank of Belgium or presened by ouside economiss in seminars, conferences and colloquia organised by he Bank. The aim is hereby o provide a plaform for discussion. The opinions are sricly hose of he auhors and do no necessarily reflec he views of he Naional Bank of Belgium. The Working Papers are available on he websie of he Bank: hp:// Individual copies are also available on reques o: NATIONAL BANK OF BELGIUM Documenaion Service boulevard de Berlaimon 4 B - Brussels Imprin: Responsibiliy according o he Belgian law: Jean Hilgers, Member of he Board of Direcors, Naional Bank of Belgium. Copyrigh Naional Bank of Belgium Reproducion for educaional and non-commercial purposes is permied provided ha he source is acknowledged. ISSN: X 2 NBB WORKING PAPER No. 6 - SEPTEMBER 24

3 Absrac In moneary policy sraegies geared owards mainaining price sabiliy condiional and uncondiional forecass of inflaion and oupu play an imporan role. In his paper we illusrae how modern sicky-price dynamic sochasic general equilibrium (DSGE models, esimaed using Bayesian echniques, can become an addiional useful ool in he forecasing ki of cenral banks. Firs, we show ha he forecasing performance of such models compares well wih a-heoreical vecor auoregressions. Moreover, we illusrae how he poserior disribuion of he model can be used o calculae he complee disribuion of he forecas, as well as various inflaion risk measures ha have been proposed in he lieraure. Finally, he srucural naure of he model allows compuing forecass condiional on a policy pah. I also allows examining he srucural sources of he forecas errors and heir implicaions for moneary policy. Using hose ools, we analyse macroeconomic developmens in he euro area since he sar of EMU. JEL-classificaion: E4-E5 Key words: Forecasing; DSGE models; moneary policy, euro area NBB WORKING PAPER No. 6 - SEPTEMBER 24

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5 TABLE OF CONTENTS:. INTRODUCTION A BRIEF DESCRIPTION OF THE ESTIMATED EURO AREA MODEL The Smes-Wouers DSGE model Poserior parameer esimaes THE SMETS-WOUTERS MODEL AS A PROJECTION MODEL: SOME ILLUSTRATIONS Ou-of-sample forecas performance Forecas uncerainy and confidence bands Measures of risks o price sabiliy Projecions under alernaive moneary policy scenarios EURO AREA ECONOMIC AND MONETARY POLICY DEVELOPMENTS SINCE CONCLUSIONS...4 REFERENCES...5 APPENDIX: THE LINEARISED DSGE MODEL (Smes and Wouers, 23c...7 TABLES AND GRAPHICS...9 NBB WORKING PAPER No. 6 - SEPTEMBER 24 3

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7 . Inroducion Due o he lags wih which changes in moneary policy affec he economy, projecions of inflaion and economic aciviy play an imporan role in moneary policy sraegies geared owards mainaining price sabiliy, pracised in mos indusrial counries. A inflaion argeing cenral banks such as he Bank of England, he Reserve Bank of New Zealand and he Sveriges Riksbank, he inflaion forecas is a cenral ool for communicaing he oulook for price sabiliy and he associaed moneary policy decisions. While less prominen, projecions of inflaion and real GDP also play an imporan role a he European Cenral Bank and he Federal Reserve Board. 2 Tradiionally, hose forecass are derived using a combinaion of relaively large-scale macro-economeric models and a good deal of judgemen. 3 As discussed in Sims (22, he macro-economeric models ypically used a cenral banks for forecasing are esimaed using single-equaion mehods and ofen lack a heoreically consisen model srucure and reamen of expecaions. While smaller-scale models wih micro-foundaions are frequenly used for policy analysis, hey are no used as forecasing ools on he basis of he argumens ha hey are ofen oo simple and perform poorly in forecasing. In a recen se of papers (Smes and Wouers, 23a,b, we have shown ha modern micro-founded dynamic sochasic general equilibrium (DSGE models wih sicky prices and wages along he lines developed by Chrisiano, Eichenbaum and Evans (23 are sufficienly rich o capure mos of he saisical feaures of he main macro-economic ime series. Moreover, applying Bayesian esimaion echniques, we show in hose papers ha even relaively large models can be esimaed as a sysem. No only does he sysem-wide esimaion procedure deliver a more efficien esimae of he srucural model parameers, i also provides a consisen esimae of he srucural shock processes driving recen economic developmens. Undersanding he conribuion of he various srucural shocks o recen economic developmens is an imporan inpu in he moneary policy decision process. Finally, our recen papers have also demonsraed ha he esimaed DSGE models perform quie well in forecasing compared o sandard and Bayesian vecor auoregressions (VARs and BVARs. The combinaion of a sound micro-founded and heoreically consisen model srucure and good forecasing performance suggess ha hese models could be furher developed as an imporan ool for boh policy analysis and forecasing in cenral banking. The micro foundaions imply ha he srucural parameers are more likely o be invarian o various policy inervenions he policy makers may wan o consider. As such, one can more easily jusify considering projecions under differen hypoheical moneary policies using hose models. 4 The probabilisic naure of he esimaed model implies ha hose models can also easily be used o assess forecas uncerainy and o perform a See, for example, Bernanke e al (999. For he role of macro-economic projecions in he ECB s sraegy, see, for example, ECB (2. Sims (22 and Pagan (23 have recenly discussed and criicised he models radiionally used a cenral banks. See Leeper and Zha (22 for a discussion of modes policy inervenions in he conex of Bayesian VARs.

8 model and daa consisen risk analysis. Since he inroducion of he inflaion argeing regimes in he lae 98s and early 99s, he focus in he assessmen of he inflaion oulook has shifed from is cenral endency o an analysis of he full forecas disribuion and he associaed risks. 5 The Bayesian esimaion mehodology provides an easy-o-use se of ools ha can be used o perform such a risk analysis. Following our earlier work (Smes and Wouers, 23a,b, his paper furher illusraes how Bayesian DSGE models can become a useful ool for projecion and analysis in cenral banking. Following a brief descripion of he esimaed euro area model in Secion 2, Secion 3 sars wih a comparison of he forecasing performance of he DSGE model wih ha of VARs and BVARs. We hen illusrae how he empirical poserior disribuion of he model can be used o calculae he complee disribuion of he forecas, as well as various risk measures ha have been proposed in he lieraure. Moreover, we use he model o compue forecass condiional on a policy pah and show how he oulook for price sabiliy and he associaed risks may be affeced by alernaive moneary policy scenarios. An imporan assumpion underlying his exercise concerns he response of privae secor s expecaions o changes in he fuure pah of ineres raes. In Secion 4, we hen analyse economic and moneary policy developmens in he euro area since he sar of EMU hrough he lens of he esimaed DSGE model. The srucural naure of he esimaed model allows us o examine he srucural sources of he forecas errors and heir implicaions for moneary policy. Overall, he messages ha come from his exercise appear o compare well wih he policy assessmen made by he ECB over he pas years. 2. A brief descripion of he esimaed euro area model 2.. The Smes-Wouers DSGE model For his paper, we re-esimae he model developed and esimaed for he euro area in Smes and Wouers (23b,c over an exended sample period (98:-22:4. 6 The DSGE model conains a large number of nominal and real fricions and various srucural shocks. We refer o Smes and Wouers (23b for he deailed derivaion. The appendix conains a lis of he linearised model equaions. Households maximise a non-separable uiliy funcion in consumpion and labour effor over an infinie life horizon. Consumpion appears in he uiliy funcion relaive o a ime-varying exernal 5 6 The inroducion of fan chars is one example of his shif in focus. See also he discussion in Svensson (2 on inflaion forecas disribuion argeing. The imporance of risk assessmen by cenral bankers is also underlined in Greenspan (23. One difference wih Smes and Wouers (23a is ha we allow for a non-separable uiliy funcion in consumpion and labour. In Smes and Wouers (23b,c we inroduced his feaure o allow for a balanced growh pah. 2

9 habi variable ha depends on pas aggregae consumpion. Each household provides differeniaed labour inpus. Monopoly power in he labour marke resuls in an explici wage equaion and allows for he inroducion of sicky nominal wages as in he Calvo model (households are allowed o rese heir wage each period wih an exogenous probabiliy. Households ren capial services o firms and decide how much capial o accumulae given cerain coss of adjusing he capial sock. The inroducion of variable capial uilisaion implies ha as he renal price of capial changes, he capial sock can be used more or less inensively according o some cos schedule. Firms produce differeniaed goods, decide on labour and capial inpus, and se prices according o he Calvo model. The Calvo model in boh wage and price seing is augmened by he assumpion ha prices ha are no re-opimised in a given period are parially indexed o pas inflaion raes and he cenral bank s inflaion arge. Prices are herefore se in funcion of curren and expeced marginal coss, bu are also deermined by he pas inflaion rae. The marginal cos of producion depends on he wage and he renal rae of capial. Similarly, wages also depend on pas and expeced fuure wages and inflaion. 7 Finally, he model is closed wih a generalised Taylor rule, where he ineres rae is se in funcion of he deviaion of inflaion from a ime-varying inflaion objecive and he heoreically consisen oupu-gap (oupu in deviaion from he efficien flexible-price level of oupu. The model conains en idenified exogenous driving forces, which are assumed o be orhogonal o each oher. Six of hese processes are modelled as auoregressive processes of order one: oal facor produciviy, he invesmen-specific echnology process, he ineremporal preference process, he labour supply process, governmen spending and he inflaion objecive of he moneary auhoriies. The firs five of hese exogenous processes are assumed o affec he flexible-price level of oupu ha eners he cenral bank s reacion funcion as is arge level for oupu. The raionale for his assumpion is ha hose shocks derive from echnology and preferences and should herefore be accommodaed from a welfare perspecive. The remaining four shocks are assumed o be whie noise: a price and wage mark-up shock, an equiy premium shock and a radiional ineres rae (or moneary policy shock. Because hese shocks are assumed o creae inefficien emporary disurbances o he economy, hey do no ener he calculaion of he flexible-price oupu level used in he cenral bank s reacion funcion. As a resul hese shocks are more likely o creae a rade-off beween inflaion and oupu gap sabilisaion Poserior parameer esimaes As in Smes and Wouers (23a,b,c, he model is esimaed using Bayesian esimaion echniques on seven key macro-economic ime series for he euro area: real GDP, consumpion, invesmen, employmen, real wages, inflaion in he GDP-deflaor and he shor run ineres rae. These daa are aken from he Area Wide Model daabase (Fagan e al, 2 and updaed for he mos recen period 7 As in Smes and Wouers (23a, an ad-hoc calvo-ype employmen adjusmen equaion is used o ranslae he labour concep in he model (hours worked ino he observed employmen series. 3

10 using he ECB Monhly Bullein. Before esimaion, all daa are demeaned and he real variables are linearly derended. [Inser Table ] Table presens he 5, 5 and 95 perceniles of he poserior disribuion of he model parameers for wo esimaion periods (98:-22:4 and 98:-998:4. 8 The laer sample period will be used for he ou-of-sample forecasing exercises performed in Secion 3. In his case, he forecas sample sars wih he inroducion of he euro in January 999. Overall, he esimaes seem o be very similar in boh samples and broadly in line wih our previous esimaes. The oal facor produciviy and labour supply processes are esimaed o be he mos persisen wih a median firs-order auoregressive coefficien of abou.95. The hree demand shocks have lower persisence. 9 As a resul, he wo supply shocks, produciviy and labour supply, will end o explain mos of he forecas error variance for he real variables a he medium o longerm horizon. The non-saionary inflaion objecive shock has a relaively high sandard error of.%, which corresponds o a change in he inflaion objecive of.4% on a yearly basis. The esimaed inflaion arge follows a downward rend over he whole esimaion sample wih an inerrupion around 99. The ineres rae shock has a sandard error around.4% (or 56 basis poins on a yearly basis. Also he esimaes of he behavioural parameers are generally reasonable and close o hose esimaed in Smes and Wouers (23a,c. As in our previous paper, he Calvo parameer for price seing (.89 implies a very high degree of price sickiness wih prices on average remaining fixed for more han wo years. Neverheless, our esimae of he elasiciy of inflaion wih respec o he marginal cos is very similar o hose obained by Gali, Gerler and Lopez-Salido (2. The resuls for he hypoheical hisorical policy rule are relaively sandard. The long run reacion on inflaion is exacly equal o he one assumed in he original Taylor rule (.5. The long run reacion coefficien on he oupu-gap is smaller han in he prooype Taylor rule (.2. The policy reacion funcion exhibis a high degree of persisence wih a coefficien on he lagged ineres rae of.88. While policyconrolled ineres raes do no reac srongly o he level of he oupu gap, hey do o changes in he oupu gap. The reacion coefficien o curren changes in inflaion is somewha higher in he shorer sample, indicaing ha he recen mild reacion o he price mark-up shocks has lowered his parameer esimae. 8 9 The daa from 97:2 ill 979:4 were used o evaluae he unobserved sae variables, so ha he saring values a ime 98: are based on hese hisorical realisaions. The invesmen-specific echnology shock, he governmen spending shock and he ineremporal preference shock can be labelled demand shocks in he sense ha under he esimaed reacion funcion hey lead o a posiive correlaion beween oupu and he oupu gap. The oal facor produciviy and labour supply shock are supply shocks in he sense ha hey give rise o an opposie response of oupu and he oupu gap. 4

11 3. The Smes-Wouers model as a projecion model: some illusraions. 3.. Ou-of-sample forecas performance To illusrae he good predicion performance of he DSGE model, in his Secion we perform a radiional ou-of-sample predicion exercise over he pos-emu period 999: - 22:4. As he forecasing period is relaively shor, hese resuls are only indicaive. We compare he roo mean squared errors (RMSEs of he forecass from he DSGE model wih hose from sandard VARs and BVARS of order o 3 in Table 2. Saring from he pre-emu sample, he VAR and BVAR models are re-esimaed quarerly, while he DSGE model is re-esimaed only yearly. Given he relaively shor sample, Table 2 repors he RMSEs for horizons of o 4 quarers only. [Inser Table 2] Overall, his exercise confirms he good forecasing performance of he DSGE model, highlighed in Smes and Wouers (23a,b. The RMSEs are quie a bi lower han hose obained for he VAR models. This is rue for each of he macro-economic ime series (wih he parial excepion of he nominal ineres rae and a all horizons considered. Moreover, here is some evidence ha he forecas performance improves as he horizon lenghens Forecas uncerainy and confidence bands As discussed in he inroducion, he Bayesian esimaion mehodology provides a useful se of ools for calculaing he full probabiliy disribuion around he cenral forecas. Graph illusraes he uncerainy surrounding he projecions of each of he seven macro-economic variables a he beginning of 999. A comparison of he acual ime series wih he 5-95 percenile forecas inerval suggess ha here is no clear evidence of insabiliy in he esimaed model following he inroducion of he euro in 999. The bounds appear o be realisic measures of he forecas uncerainy in he sense ha here are only a few excepions in which acual developmens ouch he 5% ails of he forecas disribuion. [Inser Graph ] The calculaion of he forecas bounds in Graph akes ino accoun ha, for a given model, here are ypically wo sources of forecas uncerainy: he uncerainy coming from unexpeced fuure shocks and he uncerainy associaed wih he parameers of he model. Boh sources of uncerainy ypically conribue o large uncerainy bounds around sandard VAR-based forecass. Due o he relaively igh parameerisaion of our esimaed DSGE model, he main source of forecas uncerainy as illusraed in Graph comes from he shock uncerainy. Indeed, he forecas disribuion generaed by he esimaed parameer uncerainy is very limied. While he highly resriced DSGE model srongly reduces parameer uncerainy, one should ake ino accoun ha his probably leads o an 5

12 underesimaion of he degree of uncerainy. I is likely ha he parameer uncerainy is parly replaced by model uncerainy, which could only be assessed by esimaing alernaive heoreical models and evaluaing heir influence on he forecas Measures of risks o price sabiliy While he inflaion forecas uncerainy can be summarised in fan chars, as, for example, produced by he Bank of England and he Sveriges Riksbank in heir Inflaion Repors, such forecas disribuions are ofen quie difficul o inerpre. In a recen paper, Kilian and Manganelli (23 propose simple risk measures ha quanify he relaive uncerainy in he forecass produced by a saisical model. In heir view, cenral bankers can be regarded as risk managers who aim a conaining inflaion wihin specified bounds. They develop simple formal ools ha are useful o quanify and forecas he risks ha cenral bankers will fail o obain he saed objecives. Kilian and Manganelli (23 propose he following measures o summarise he risks ha inflaion will move ouside pre-specified bounds. β ( EIR = Pr ob( > u * E[ ( u > u] β (2 = Pr ob( < l * E[ ( < l ] DR l The firs measure is a measure of excess inflaion risk. I is he expeced inflaion for nex period in excess of an upper bound where he power reflecs he relaive risk aversion in he cenral bankers preferences muliplied by he probabiliy (prob ha he inflaion realisaion is above he limi. The second measure is a measure of deflaion risk. In line wih he ECB s definiion of price sabiliy, we calculae hese measures for an upper bound ( of 2% and a lower bound ( of % for he u average inflaion rae over he nex four quarers 2. In line wih Kilian and Manganelli (23 and mos of he lieraure on opimal moneary policy, we assume a coefficien of risk aversion (β equal o wo. The sum of he projeced excess inflaion and deflaion risk measures can be seen as a measure of he projeced one-year ahead balance of risks o price sabiliy: (3 BR = EIR DR The poserior disribuion of he DSGE model can easily be used o calculae he risk measure proposed by Kilian and Manganelli (23. Graph 4, which will be discussed in deail in secion 4, illusraes he developmen of hose risk measures since he sar of EMU. For example, a he sar of 999 he balance of inflaion risks dropped quie considerably following he fall-ou from he Russian l See, for example, he discussion in Brock, Durlauf and Wes (23 and Sims (23. As he fan chars in he Inflaion Repors of he Bank of England and he Sveriges Riksbank are no based on saisically generaed disribuion funcions, bu raher reflec he subjecive uncerainy around he inflaion and oupu forecass of he policy makers, i is much more difficul o calculae such risk measures based on he fan chars. 2 This exercise reflecs he ECB's broad definiion of price sabiliy bu is no mean o reproduce in deail he acual sraegy of he ECB, which has been refined in he course of 23. 6

13 crisis. In secion 4 we will use hese measures o inerpre economic and moneary policy developmens in he euro area since Projecions under alernaive moneary policy scenarios The projecion exercises presened in he previous secions were performed under he assumpion ha he European Cenral Bank followed he ineres rae reacion funcion esimaed over he pre-emu period. Ofen such projecions are called uncondiional forecass. Typically, however, moneary policy makers prefer o use consan nominal-ineres-rae forecass. 3 Such condiional projecions provide a naural benchmark for assessing wheher ineres raes need o be changed given he cenral bank s goal of mainaining price sabiliy. They also avoid he need o specify he cenral bank s reacion funcion, which may no be very easy o do in paricular following a regime change such as he inroducion of he euro. However, producing such condiional projecions using raional expecaions models raises wo issues. Firs, i is well known ha raional expecaions models will ypically no solve under a consan nominal ineres rae pah because nominal ineres rae pegging ofen leads o an explosive pah for he ex-ane real ineres rae, oupu and inflaion. One soluion o his problem is o assume ha he nominal ineres rae is kep consan for a limied period of ime, say hree years, afer which a policy reacion funcion kicks in puing he economy again on an equilibrium pah. A second issue raised by a consan ineres rae projecion concerns how o implemen he consan ineres rae pah in a forward-looking model. A leas wo opions are available. One opion, applied in his secion, is o calculae he moneary policy shocks ha are necessary o keep he ineres rae on a consan pah relaive o he hisorically esimaed reacion funcion. The advanage of his opion is ha curren economic variables ha depend on expecaions of fuure ineres raes (such as various asse prices, bu also consumpion and invesmen will only gradually respond o he consan ineres rae scenario. This opion is also closes o he analysis of modes policy inervenions using Bayesian VARs in Leeper and Zha (23 4. Of course, as emphasised by Leeper and Zha (23, his assumpion only makes sense if he required unexpeced policy shocks are relaively small and comparable in size o he hisorically esimaed policy shocks. A second opion is o assume ha he privae secor has perfec foresigh of he consan ineres rae pah and adjuss is decisions in line wih his change in expeced policy. This approach is fully compaible wih he raional expecaions assumpion embedded in our esimaed DSGE model. However, i will ypically lead o relaively large jumps in all he forward-looking variables including consumpion and invesmen, which in some circumsances may be perceived as implausible. 3 4 Also a he European Cenral Bank he macro-economic projecion of he Eurosysem saff are based on he assumpion of consan nominal shor-erm ineres raes. Cogley, Morozov and Sargen (23 sugges an alernaive approach o generae a poserior disribuion around he forecas ha is condiional on a specific ineres rae pah: by resricing he ineres rae pah, he disribuion around he baseline scenario is shifed according o a minimum enropy mehod. This approach is applicable in BVAR models ha do no provide a srucural inerpreaion of he shocks. 7

14 [Inser Graph 2] Graph 2 plos he forecas disribuion of he seven macroeconomic variables a he end of 998 (similar o Graph under he assumpion ha he nominal ineres rae is kep consan for hree consecuive years (afer which he esimaed reacion funcion kicks in. The privae secor coninues o hink ha he cenral bank follows he esimaed reacion funcion and reas he deviaions of acual ineres raes from he expeced ineres raes as policy shocks. The graph shows ha because he moneary auhoriies keep nominal ineres raes persisenly below heir expeced pah (see Graph, he median forecas for oupu and inflaion is much higher han projeced in Graph. I is also clear from comparing Graphs and 2 ha he uncerainy surrounding he median forecas is much higher under he consan ineres rae pah. As moneary policy is passive he effecs of fuure shocks are projeced o be much larger. Table 3 summarises he effecs of he consan ineres rae assumpion on he inflaion and oupu growh forecas and he various risk measures a wo poins in ime: 998:4 and 2:4. These wo daes correspond o he sar of he wo sub-periods ha will be discussed below in Secion 4. In 998:4, he uncondiional median forecas for inflaion over he nex year and growh over he nex wo quarers was.5 percen and.63 percen respecively. According o his forecas, he balance of inflaion risks was slighly iled upwards and he probabiliy of a recession (defined as wo consecuive quarers of negaive growh was negligible a.. Under his scenario, shor-erm ineres raes were expeced o increase gradually o heir long-run neural level of abou 5.5%. The hird line in Table 3 shows he impac of a consan ineres rae pah for hree years. The inflaion and growh projecion increase by respecively.35 and.6% compared o he baseline scenario. The excess inflaion risk increases reflecing he increase in uncerainy, and he balance of risks also clearly increases suggesing ha upward inflaion risks would have dominaed under his scenario. The series of unexpeced shocks ha are necessary o keep he ineres rae pah consan for hree years saring in 998:4 are negaive and growing over he hree-year period. As such, hey can no be caalogued as a modes inervenion. 5 [Inser Table 3] The effecs of an alernaive and more realisic scenario, in which he ineres rae is decreased by 5 basis poins for wo consecuive quarers saring in 999: (compared o he baseline scenario is given in he second line of Table 3. In his case, he median inflaion forecas increases wih.7 percenage poins and he growh rae is revised upward by.42 percenage poins. Also in his case, he balance of inflaion risks would have shifed upward. As discussed below in Secion 4, he euro area faced significan negaive demand shocks in he firs wo quarers of 999 (parly following he fall-ou of he Russian crisis in 998 shifing he balance of inflaion risks downward. Scenarios such as he one repored in he second line of Table 3 may be quie informaive abou he policy choices 5 Leeper and Zha (22 show very similar resuls for he mean forecas under a consan ineres rae assumpion using heir VAR model for he US saring in Ocober 99. 8

15 ha policymakers where faced wih a he ime. The acual decline in he ineres rae ha occurred in April 999 can be parly seen as an aemp o resore he balance of risks. The lower par of Table 3 performs a similar exercise around he baseline uncondiional forecas of inflaion and growh in 2:4. A ha ime, he oulook for inflaion over he nex year and he associaed risks were very similar o he oulook a he beginning of 999. However, he oulook for oupu growh was less favourable wih a 7 percen probabiliy of a recession. The boom wo lines of Table 3 illusrae he effec of wo alernaive scenarios: a reducion and an increase in ineres raes of basis poins in oal. A reducion in ineres raes would have suppored growh considerably reducing he probabiliy of a recession, bu a a cos of increased inflaion by abou 7 percenage poins. In conras, he ineres rae increase would have increased he probabiliy of a recession quie considerably o 5%. The exercises performed in his secion illusrae he poenial usefulness of our Bayesian DSGE model in assessing he impac of alernaive moneary policy scenarios on he oulook for price sabiliy and he associaed risks. I is, however, imporan o re-emphasise ha he repored resuls crucially depend on he assumpions made abou how expecaions of privae agens adjus o he alernaive ineres rae pahs. In he exercises repored above, we implemened alernaive ineres rae pahs by shocking he esimaed ineres rae reacion funcion. As discussed in Leeper and Zha (23, his makes sense if he shocks are relaively modes. However, idenical ineres rae pahs could also be implemened under he assumpion of perfec foresigh or wih alernaive sysemaic moneary policy reacion funcions and heir associaed shocks. The impac of hese alernaive assumpions may very well be non-negligible. This is an imporan quesion for fuure research. 4. Euro area economic and moneary policy developmens since 999 One advanage of he srucural naure of he esimaed DSGE model is ha he model can be used o analyse he srucural sources of he shocks ha have affeced he euro area economy during he firs four years of EMU. As is clear from Graph, he firs four years of EMU (999:-22:4 can be roughly divided ino wo equal sub-periods. The firs sub-period (999:-2:4 was characerised by relaively srong oupu, employmen and real wage growh. In conras, he second sub-period (2:-22:4 is characerised by a slowdown in economic aciviy, a sabilisaion of real wages and a emporary surge in inflaion. In wha follows, we inerpre each of hose periods hrough he lens of he esimaed DSGE model. The firs wo years of EMU Graph shows ha, a he end of 998, he baseline projecion as capured by he median forecas of our model was for he economy o gradually reurn o is deerminisic growh pah following a slighly negaive oupu gap a he end of As a resul, he model predics as a median scenario 6 See Smes and Wouers (23a for a discussion and esimaion of he oupu gap concep in his model. 9

16 relaively sable growh of he economy, wih a slighly above average growh for invesmen and employmen in he firs years of he forecas exercise. Inflaion is expeced o increase slighly owards he implici inflaion arge of moneary policy ha is esimaed o be somewha below 2 % a he end of 998. As par of his move o equilibrium, he nominal ineres rae is forecas o reurn relaively quickly o is equilibrium level. Graph also shows ha by he end of 2, mos of he acual ime series were close o heir projeced values. One excepion is employmen, which grew much sronger han expeced. Moreover, his end-of-2 snapsho masks some volailiy in economic developmens during he firs wo years of EMU. Graph 3 presens he esimaed srucural shocks during his period ogeher wih a onesandard-error band. Graphs 4 and 5 show he resuling evoluion of he balance of inflaion risks and is componens over he period. [Inser Graph 3] Saring from a slighly posiive balance of risks in he fourh quarer of 998, our esimaed model suggess ha deflaion risks rose while excess inflaion risks fell during he firs half of 999 (Graph 4. As a resul, he risks were quie balanced in he second quarer of 999. This is mainly a resul of he negaive spending shock in he firs quarer of 999 (mosly reflecing a fall in he demand for ne expors following he fall-ou from he Russian financial crisis a he end of 998 and he subsequen negaive preference shock in he second quarer of 999. As a resul, in conras o wha was forecas by he model, nominal ineres raes fell during he firs half of 999. However, he ineres rae appears o have fallen by more han prediced by he esimaed policy reacion funcion, hereby supporing oupu and invesmen in he following year. Subsequenly, deflaion risks fell, while excess inflaion risks rose owards he end of 999 and in 2. This led o a reversal and gradual rise in policy-conrolled ineres raes, which approach he forecas level owards he end of 2. The mos sriking developmen in he firs sub-period is he sronger han expeced developmen of employmen, which conribued o a sabilisaion of real wages in he second half of 2. The posiive effecs on oupu are, however, parly offse by a series of negaive produciviy shocks over he same period 7. [Inser Graph 4] A reading of he Ediorials of he ECB s Monhly Bullein suggess ha he changing balance of risks as capured by our model in he firs wo-years of EMU more or less corresponds o he ECB s inerpreaion of evens. In he beginning of 999, HICP inflaion was lower han previously expeced and was explained by subdued growh of uni labour coss in 998 and by he downward risk following he Asian crisis. The March 999 Monhly Bullein read: "In he ligh of recen developmens in real economy indicaors, and aking ino accoun he curren level of HICP inflaion 7 Overall he idenificaion of he srucural shocks by our DSGE model produces resuls ha are in line wih resuls of SVAR models. Typically, SVAR exercises idenify supply, demand, policy and inflaion (or oil shocks. See Peersman (24 for a recen applicaion on similar daa.

17 raes, i appears ha here is no risk of HICP inflaion exceeding he 2% ceiling in he near fuure. A he same ime, he paern of upward and downward risks o price sabiliy has remained broadly unchanged on balance." The reducion of official ineres raes from 3% o 2.5% in April 999, was moivaed in he April 999 Monhly Bullein by increased downward inflaion risks: "This picure is also refleced in recen downward revisions o real GDP forecass for he euro area in 999 and 2 by major inernaional organisaions.... he downward revisions in he growh forecass and uncerainy concerning hese forecass have reinforced expecaions of somewha lower inflaionary pressure arising from economic aciviy his year." Also he favourable developmens in he labour marke were clearly idenified as unexpeced surprises in he following quoe from he Sepember 2 Monhly Bullein. "Euro area employmen growh has recenly been revised upwards, in paricular for he pas wo years, and is now esimaed o have reached a remarkable annual rae of growh of close o 2% in he firs half of 2. This dynamism reflecs robus economic growh and wage moderaion, and may also poin o some progress in labour marke flexibiliy. Coninued moderae wage increases would conribue o mainaining he favourable rends in labour marke developmens in he conex of sill high unemploymen." However, he fall in oal facor produciviy idenified by our model was no commened upon. Finally, he series of ineres rae increases ha sared in December 999 and coninued during he course of 2 were largely based on a rise in he upward risks o price sabiliy due o srong oupu and employmen growh in a favourable inernaional environmen and he delayed pass-hrough of he depreciaion of he euro and he rise in energy prices. Due o he use of he GDP deflaor raher han he HICP, hese cos-push shocks only show up wih a delay in our model s forecass. 8 For insance, in he April 2 Monhly Bullein, he official ineres increase from 3.25% o 3.5% daed 7 March was commened upon as follows: "This picure of coninuing srong domesic demand suppors he favourable oulook for economic growh in he euro area as shown in recen forecass. The posiive prospecs for euro area aciviy are also benefiing from he cyclical upswing in he world economy, which has become broadly based across indusrial and emerging economies and which is expeced o coninue in coming years.... Agains his background, moneary policy mus remain vigilan in assessing upside risks o price sabiliy and ake appropriae acion if and when 8 From he comparison wih he policy discussions in he Monhly Bullein, i is clear ha he DSGE model misses some informaion because he HICP is no included in he daa se. The pass-hrough of energy prices, he exchange rae and volaile food prices ino he GDP deflaor is much slower han ino he HICP series. However, he inerpreaion of hese shocks was largely in line wih he role of he mark-up shocks in he model as unexpeced shor run disurbances o inflaion. Moneary policy is raher ineffecive in reducing he shor run inflaion impulse coming from hose shocks and is confroned wih a clear rade-off problem if i reacs oo srongly o such shocks. The price increases ha were affecing he HICP already in he second half of 2, where clearly inerpreed as emporal price shocks as is clear from his quoe from he November 2 Monhly Bullein: "Owing o developmens in energy prices and he pas decline in he euro, consumer proce inflaion may remain above 2% for longer han was expeced jus a few monhs ago. In his respec, in order o suppor he mainenance of price sabiliy over he medium erm, i is imporan ha economic agens accuraely perceive he naure of curren price developmens. In paricular, i needs o be recognised ha curren upward pressures can be overcome mos smoohly if economic agens see hem for wha hey are, namely one-off or emporal price increases resuling from exernal facors. If, as he markes expec, oil prices do no rise furher, he effecs of pas oil price increases will gradually drop ou of he annual inflaion rae"

18 required. Moneary policy has o be forward-looking, since responding o risks o price sabiliy before hey maerialise will avoid he need for cosly process of disinflaion a a laer sage." Less favourable developmens han projeced during he 2-22 period Graph 5 depics he forecas disribuion based on informaion up o he fourh quarer of 2 for he seven euro area macro variables in 2 and 22. The esimaed DSGE model prediced a more modes growh of consumpion, invesmen and oupu han realised growh in 2. Employmen was projeced o remain consan and wages were projeced o increase relaively srongly as he model expeced he favourable labour supply shocks over he firs wo years of EMU o gradually die ou over ime. Inflaion and he nominal ineres rae were prediced o gradually reurn o heir long run levels corresponding o a.5% inflaion objecive (esimae a 2:4 and a 5.5% equilibrium nominal ineres rae respecively. Wih he excepion of he labour marke developmens, he acual oucome in 2 and 22 was much less rosy han projeced. Real GDP and paricularly real invesmen urned ou much lower han expeced due o a series of negaive invesmen echnology, equiy premium and produciviy shocks (Graph 3. The impac of he drop in invesmen on oupu is somewha offse by he mosly posiive labour supply shocks over his period. In he las quarer of 2, he negaive shocks o invesmen are reinforced by a large negaive preference shock reflecing he confidence effecs of he Sepember aacks in he US on consumpion. Also on he inflaion side he news was predominanly negaive as a series of posiive price mark-up shocks pushed inflaion above he projeced level in spie of he favourable developmens in real wages. [Inser Graph 5] The implicaions of he various shocks in 2 and 22 for he evoluion of he one-year ahead projeced inflaion and he balance of inflaion risks is again shown in Graphs 4 and 5. Despie he large posiive mark-up shocks which reflec he effecs of he depreciaion of he euro and rising food and energy prices on inflaion, he balance of risks rapidly dropped from is maximum in he firs quarer of 2 o a negaive value in he hird quarer of 2, indicaing he dominance of downward risks o price sabiliy. The model sees hrough he emporary effecs of he mark-up shocks and pus a dominan weigh on he negaive demand shocks when assessing he risks o price sabiliy. Following a brief surge in he excess inflaion risks due o a new series of price mark-up shocks, he downward risks clearly dominae during mos of 22. This occurred in spie of he fac ha he easing of moneary policy appeared o be sronger han could be expeced on he basis of he hypoheical hisorical reacion funcion as indicaed by he negaive moneary policy shocks hroughou mos of 2 and 22 (Graph 3. 9 In he second half of 22 he probabiliy of one-year ahead deflaion is esimaed o be relaively high a around 25%. 9 The large negaive policy shock in he firs quarer of 2 is he counerpar of he weak response of moneary policy o he srong mark-up shocks. As discussed in Secion 3, he esimaed shor-run coefficien in he policy rule over he period 98: 22:4 is indeed lower han he one over he shorer period ha excludes hese observaions. 2

19 The picure drawn by he one-year ahead balance of risks indicaor produced by our model again corresponds quie closely wih he discussion in he ECB s Monhly Bulleins. The firs sign of increased concern abou he inernaional environmen appeared in he December 2 Monhly Bullein coinciding wih he sligh drop in our excess inflaion risk indicaor during he las quarer of 2. While in January 2 he risks o price sabiliy were sill predominanly seen on he upside, in February and even more clearly in March, he risks appeared o be evaluaed as more balanced han in lae 2, alhough i was also saed ha here were no ye signs ha he slowdown in he US economy had significan or lasing spill-over effecs on he euro area. In he April 2 Monhly Bullein he balance clearly iled o he downside. This foreshadowed he policy easing ha was in he pipeline and evenually happened on May, mainly based on he risk analysis raher han on observed daa. During his period he ECB expressed a clear saisfacion wih he mainained wage moderaion ha has suppored employmen growh, while repeaedly warning for possible spill-over effecs from he price shocks. In he July 2 Monhly Bullein, here was a firs clear recogniion ha growh was lower han expeced: "The firs Eurosa esimae of real GDP growh in he firs quarer of 2 was.5%, as compared wih he.6% in he las quarer of 2. The slowdown appears o be relaed o he exernal environmen and o he weak growh of domesic demand. The significan decline in he growh rae of domesic demand was sronger han expeced, wih invesmen being affeced boh by he adverse influences from he world economy and by specific domesic developmens relaed o consrucion invesmen. A he same ime, growh in consumpion was weak, which may in par be explained by adverse income effecs relaing o he increases in energy and food prices." A he same ime HICP inflaion rose o 3.4% in May following he increase in food and energy prices. However, he ECB sressed ha due o he special naure of hese shocks, hey were likely o only have a emporary effec on inflaion. Also in he Augus 2 Bullein he lower han expeced growh rae was emphasised, evenually leading o furher ineres rae easing. In he November issue he November 8 decline in he policyconrolled ineres from 3.75 o 3.25% was moivaed as follows: "Several economic indicaors which have become available for he euro area and beyond poin o weakening demand of boh domesic and exernal origin. In line wih his and aking ino accoun expecaions of furher weak daa in he period ahead, forecass and projecions will in all likelihood show downward revisions. The curren environmen of high uncerainy is likely o lead o delays in invesmen and, o some exen, also o negaively affec privae consumpion in he euro area. This has led o expecaions of weak daa for he euro area real GDP growh in he second half of 2. Real GDP growh is now expeced o remain below poenial for par of nex year." In sum, our sylised esimaed DSGE model seems o perform relaively well in capuring he evoluion of he perceived risks o price sabiliy. A he same ime, i allows for a srucural inerpreaion of he sources behind he developmens in he risks o price sabiliy. 3

20 5. Conclusions Modern sicky-price DSGE models of he ype used in his paper and esimaed using Bayesian echniques combine a sound, micro-founded srucure necessary for policy analysis wih a good probabilisic descripion of he observed daa and forecasing performance. In his paper we illusraed how such Bayesian DSGE models can become an addiional useful ool in he forecasing ki of cenral banks. Firs, we show ha he forecasing performance of such models compares well wih a- heoreical vecor auoregressions. Moreover, we illusrae how he poserior disribuion of he model can be used o calculae he complee disribuion of he forecas, as well as various inflaion risk measures ha have been proposed in he lieraure. Finally, he srucural naure of he model allows compuing forecass condiional on a policy pah. I also allows examining he srucural sources of he forecas errors and heir implicaions for moneary policy. Using hose ools, we briefly analysed and inerpreed macroeconomic developmens in he euro area since he sar of EMU. Of course, many challenges sill lie ahead. Here i suffices o highligh hree of hose challenges. Firs, he srucure of he model remains relaively simple and in many cases he micro-foundaions are no very deep. Much more work is needed o boh deepen and broaden he scope of he exising DSGE models. For example, he inroducion of more realisic financial and labour markes is one vibran area of curren research. For pracical forecasing exercises, he inroducion of an open economy dimension and he HICP-inflaion in addiion o he inflaion in he GDP-deflaor migh allow for a beer idenificaion of exernal demand and price shocks. Second, he assumpion of model consisen expecaions is heoreically appealing and relaively easy o implemen. However, in realiy consrains on informaion processing, pervasive model uncerainy and he associaed need for perpeual learning highligh he limis of he raional expecaions assumpion. When forecasing in a policy conex, realisic assumpions abou how privae secor expecaions will adjus o alernaive policy scenarios are of crucial imporance. Finally, he lineariy of he model used in his paper is an aracive feaure from a compuaional and esimaion poin of view. Linear models are ypically also more robus in forecasing. However, non-lineariies due o shifing economic relaionships, imevariaion in he sources of shocks, various insiuional and echnical consrains and he nonmonoone adjusmen of expecaions are imporan facors in he risk analysis of moneary policy makers. While i would be impossible o ake ino accoun all hose sources of non-lineariies in one model, an analysis of he implicaions of each of hem is an imporan area of curren and fuure research. 4

21 References Bernanke, B., T. Laubach, F. Mishkin and A. Posen (999. Inflaion argeing: Lessons from he inernaional experience. Princeon Universiy Press, Princeon NJ. Brock, W., S. Durlauf, K. Wes (23, Policy evaluaion in uncerain economic environmens, Brookings Papers on Economic Aciviy, 23:2. Chrisiano, L., M. Eichenbaum and C. Evans (23, Nominal rigidiies and he dynamic effecs of a shock o moneary policy, Journal of Poliical Economy, forhcoming. Cogley, T., S. Morozov and T.J. Sargen (23, "Bayesian fan chars for U.K. inflaion: Forecasing and sources of uncerainy in an evolving moneary sysem", mimeo. European Cenral Bank (2, A guide o Eurosysem saff macroeconomic projecion exercises, European Cenral Bank, Frankfur. Fagan, G., J. Henry and R. Mesre (2, An Area-Wide Model (AWM for he euro area, European Cenral Bank Working Paper 42. Gali, J., M. Gerler and D. Lopez-Salido (2, European inflaion dynamics, European Economic Review, 45(7, 2-5. Greenspan, A. (23, Moneary policy under uncerainy, Remarks a a symposium sponsored by he Federal Reserve Bank of Kansas Ciy, Jackson Hole, Wyoming, 29 Augus 23. Kilian, L. and S. Manganelli (23, The cenral bank as a risk manager: Quanifying and measuring inflaion risks, European Cenral Bank Working Paper, April 23. Leeper, E. and T. Zha (23, Modes policy inervenions, Journal of Moneary Economics, Vol. 5, pp Pagan, A. (23. Repor on modelling and forecasing a he Bank of England, Bank of England, London. Peersman, G. (24, "Wha caused he early millennium slowdown? Evidence based on vecor auoregressions", Journal of Applied Economerics (forhcoming Sims, C. (22, The role of models and probabiliies in he moneary policy process, Brooking Papers on Economic Aciviy, 22:2, -62. Sims, C. (23, Probabiliy models for moneary policy decisions, work in progress, Princeon Universiy. Smes, F. and R. Wouers (23a, An esimaed dynamic sochasic general equilibrium model of he euro area, Journal of he European Economic Associaion (5, Sepember 23,

22 Smes, F. and R. Wouers (23b, Shocks and fricions in US business cycles: a Bayesian DSGE approach, mimeo, European Cenral Bank. Smes, F. and R. Wouers (23c, Comparing shocks and fricions in US and euro business cycles: a Bayesian DSGE approach, forhcoming in Journal of Applied Economerics Svensson, L. (2, Price sabiliy as a arge for moneary policy: defining and mainaining price sabiliy, in Deusche Bundesbank (ed., The moneary ransmission process: Recen developmens and lessons for Europe, Palgrave, New York,

23 Appendix: The linearised DSGE model (Smes and Wouers, 23c. The consumpion equaion: ( C h ( σ c = C EC ( h h σ ( ( h l l h ( h σ Consumpion c ( R E c h ( h σ c λ ( ε b w Ĉ depends on a weighed average of pas and expeced fuure consumpion, he ex-ane real ineres rae ( R E, expeced employmen growh ( l l and a preference shock b ε. h represens he habi formaion coefficien and σ c is he analogue of he ineremporal elasiciy of subsiuion. The invesmen equaion: β / ϕ I (2 Î Î E Î ( Q = ε β β β Invesmen Î depends on pas and expeced fuure invesmen, he value of he exising capial sock I Q and an invesmen-specific echnology process, ε. β is he rae of ime preference and ϕ is he parameer ha summarises he invesmen adjusmen coss. The Q equaion : (3 Q τ k = ( R k r E k Q E k r η τ r τ r The value of he capial sock depends negaively on he ex-ane real ineres rae, and posiively on is k Q expeced fuure value, he expeced renal rae r and an equiy premium shock η. The capial accumulaion equaion: (4 K = ( τ K τî τ ε I The capial sock K depreciaes wih a rae τ. The inflaion equaion: (5 p = ( βγ ( p βγ p βγ p β E ( βξ ( ξ p ξ p p k a p [ αr ( α w ε ( α γ] η The deviaion of inflaion from he arge inflaion rae γ Q depends on pas and expeced fuure inflaion deviaions and on he curren marginal cos, which iself is a funcion of he renal rae on capial, he real wage ŵ and he produciviy process. α deermines he share of capial and labour 7