Handout for the Monetary Model and Its Use for Forecasting and Policy Analysis

Transcription

1 Handou for he Moneary Model and Is Use for Forecasing and Policy Analysis Emine Boz 1, Ales Bulir 2 and Jarek Hurnik 3 This noe inroduces a simple oupu gap model ha can be calibraed o fi sylized facs in mos counries and o prepare a simple inflaion forecas. I is a rimmed-down version of a generic Quarerly Projecion Model used in several cenral banks and oher insiuions such as he IMF. The objecive of his class of models is o help decide on an appropriae level of he policy ineres rae, given he inflaion arge and he curren sae of he economy. 1 Inernaional Moneary Fund, eboz@imf.org 2 Inernaional Moneary Fund, abulir@imf.org 3 Czech Naional Bank, jaromir.hurnik@cnb.cz

2 2 Table of Conens I. Inroducion...3 II. Before You Sar...3 III. The Model...4 A. Aggregae demand...4 B. Aggregae supply...4 C. Uncovered Ineres Rae Pariy...5 D. Policy Rule...7 IV. Model Calibraion...8 A. Calibraion of Long-erm Parameers...8 B. Calibraion: Business-Cycle Properies...10 C. Some Useful Calibraion Hins...12 D. How o Check he Model Properies...13 V. Forecasing...13 A. Daabase Preparaion...14 B. The Forecas...15 C. Inerpreing he Forecas...17 Sofware Insallaion...18 The Model Code...21

3 3 I. INTRODUCTION This noe inroduces a simple oupu gap model ha can be calibraed o fi sylized facs in mos counries and o prepare a simple inflaion forecas. I is a rimmed-down version of a generic Quarerly Projecion Model used in several cenral banks and oher insiuions such as he IMF (Berg, Karam and Laxon 2006a, 2006b). The objecive of his class of models is o help decide on an appropriae level of he policy ineres rae, given he inflaion arge and he curren sae of he economy. The model is solved numerically using he Malab sofware and IRIS Toolbox, however, no prior knowledge of eiher Malab or IRIS is required. The soluion algorihm and commands are explained in his noe. 4 We focus on hree pracical aspecs of he modeling process in he conex of inflaion argeing: (i) calibraion; (ii) esing he model properies and daa preparaion; and (iii) inflaion forecas, is analysis and inerpreaion. Sofware insallaion is described in Appendix I and compuer codes in Appendix II. II. BEFORE YOU START Before you can sar modeling in he IRIS environmen, you need o insall i and a few oher freeware programs (MiKTeX, Ghosscrip, Ghosgum, and X-12) on you compuer. Deailed insrucions are conained in Appendix I and we sugges ha you follow hem as closely as possible. Sar each session (afer you open Malab) by running he following line from he Malab command window: addpah c:/iris-oolbox; irissarup; replacing c:/iris-oolbox wih your own main IRIS folder chosen during insallaion. Navigae o your working folder o check ha i conains he following files (hey will be described in more deail in he following secion): 1. model.mod 2. readmodel.m 3. modelproperies.m 4. makedaa.m 5. forecas.m 6. daa.csv Wih he excepion of model.mod and daa.csv, all files are Malab programs (exension.m ) and work in he Malab environmen only. The programs ge sared in he following way. Type he name of a program, for insance readmodel, in he command window and push [ener]. Once he screen shows >> he program has been run successfully. You can check ha all programs are funcioning by execuing hem in he following sequence: readmodel, modelproperies, makedaa, forecas. From Windows explorer, in he 4 The IRIS Toolbox (hp:// is a Malab-based package for advanced macroeconomic modeling wrien by Jaromír Beneš (curren affiliaion: IMF Research Deparmen, jbenes@imf.org).

4 4 appropriae folder, double click on files ha are generaed o repor simulaion resuls: Repor_Shocks.ps, Sylized_facs.ps, Forecas.ps. Click [OK] and you should see chars and ables of various model oupus. III. THE MODEL The model we use for our exercises is a reduced-form, new-keynesian model, someimes also called he oupu gap model. More complicaed versions of i are being uilized in many cenral banks all around he world. The model consiss of four basic behavioral equaions and several ideniies. The behavioral equaions are: 1. Aggregae demand (IS curve) 2. Aggregae supply (Phillips curve) 3. Uncovered Ineres Rae Pariy 4. Moneary Policy Rule A. Aggregae demand The aggregae spending relaionship corresponds o he open economy version of he radiional IS curve and akes he form: ŷ yˆ a, (1) * 1yˆ 1 a2mci a3 yˆ where is he deviaion of he log of oupu from is noninflaionary level, i.e., he oupu gap; mci is he real moneary condiion index ha is defined as a weighed average of deviaions of he long-erm real ineres rae,, from is neural (noninflaionary) level, and * deviaion of he real exchange rae,, from is rend level; y is he foreign oupu gap and y z is an aggregae demand shock. The aggregae demand shocks are governed by a Normal disribuion and have no serial correlaion. The coefficiens a 1, a2, and a3 capure he persisence of oupu; he impac of moneary condiions on real economic aciviy; and he impac of foreign environmen, respecively. r y B. Aggregae supply The aggregae supply equaion (he Phillips curve) is defined as follows: b ˆ e ( 1 b b rmc, (2) 1 1 1) 1 2 where is he annualized quarerly change of he consumer price index, i.e., e inflaion; denoes model-consisen inflaion expecaions; rmc is he gap in firms real 1 marginal coss; and is an aggregae supply shock. Similar o demand shocks, he aggregae supply shocks are governed by a Normal disribuion and have no serial correlaion. The supply relaionship encompasses muli-period, overlapping nominal conracs of domesic producers as well as imporers. The laer is an imporan feaure of small open

5 5 economies ha ypically have a powerful exchange rae channel of moneary ransmission. Tha is why we define in (3) he rmc as a weighed average of oupu gap (domesic producers) and he gap in real exchange rae (imporers) wih he coefficien 1 b ) approximaing he weigh of impored goods in he consumer baske. In he equaion ( 3 below, ẑ denoes deviaions of he real exchange rae from is neural (noninflaionary) level. 3 yˆ (1 b3 rmc b ) zˆ. (3) I is imporan o model expecaions properly, capuring he behavior of agens, some of which may be forward-looking, using model consisen (raional) expecaions, E 1, while ohers are backward-looking. Economic agens who are assumed o be fully forward-looking comprise ( 1 b1 ) of he populaion and b1 agens follow he rule of humb of pas inflaion. Anoher way of hinking abou his parameer is he persisence of inflaion he more persisen inflaion, he higher is b1. The coefficien b2 capures he influence of he gap in he real marginal coss on inflaion (he slope of he Phillips curve) and measures he sacrifice raio, i.e., how much oupu will be los in order o bring inflaion down by 1 percenage poin. C. Uncovered Ineres Rae Pariy We capure he relaionship wih he res of he world using alernaive versions of he uncovered ineres rae pariy condiion. In is pure forward-looking version, he UIP relaes he behavior of domesic and foreign ineres raes, and he nominal exchange rae: e ( i * s s 1 i prem ) / 4, (4) e where s is he nominal exchange rae; s 1 is he model consisen expecaion of he nominal * exchange rae in period +1; i is he domesic nominal ineres rae (annualized); i is he s foreign nominal ineres rae (annualized); prem is he risk premium; and is he exchange rae shock. Wih he canonical UIP, he model has difficuly in maching he observed behavior of he economy (looking, say, a impulse responses), because he exchange rae has lile persisence (Beneš, Hurník and Vávra, 2008). The pure forwardlooking elemen in Equaion (4) forces he curren exchange rae level o adjus immediaely o he sum of all fuure ineres rae differenials implied by he model behavior. This is clearly a odds wih he observed exchange raes. There are a few alernaive ways of increasing he persisence of he exchange rae. One way is o modify he pure UIP by conaining is forward-looking naure. This approach subsiues he model-consisen exchange rae expecaions in Equaion (4) by a combinaion of e backward-looking and model-consisen (forward-looking) expecaions ( s ). This can also be inerpreed as assuming backward-looking expecaions for a porion of he agens in he economy and forward-looking expecaions for he remaining. The approach below is more general han ha of Berg, Karam and Laxon (2006a, 2006b), allowing for a nonzero rae of E growh of he exchange rae in he long-run. Equaion for exchange rae expecaions ( s ) akes he form: s

6 6 where E e s 1 e1s 1 ( 1 e1 )( s 1 2 s ), (5) s z. (6) * In his seing, is domesic inflaion arge; rend (long-run) change in he real exchange rae. The coefficien * is foreign inflaion arge; and z is he deermines he degree of forward-looking behavior in he financial marke or he porion of he agens ha are assumed o be forward-looking. The second elemen in Equaion (5), ( s 1 2 s ), is he backward-looking exchange rae expecaion, which projecs he exchange rae in period + 1 as an exrapolaion of he pas ex-change rae using he rend rae of growh of he real exchange rae and he average inflaion differenial approximaed by he difference in inflaion arges. While such expecaions are no model-consisen in he shor-run, hey are consisen in he long-run, in line wih he finding ha he UIP holds a longer horizons only. The erm s is he change in he exchange rae consisen wih long-erm economic fundamenals represened by he inflaion arges and he real exchange rae rend. By consrucion, s s in he longrun, so he long-run properies of he model are inac. The above exension of he UIP is designed o make he nominal exchange rae more persisen, however, i does no reduce he overall volailiy of he exchange rae of he simulaed model (he flucuaions in he nominal exchange rae are more persisen, bu is sandard deviaion is no necessarily smaller). Alernaively, he UIP can be modified o accoun for he cenral banks ha use he FOREX inervenions acively (and he exchange rae channel) o mee he inflaion arge. 5 However, o model he exchange rae consisenly, he change in he ER arge mus be defined as a sum of he inflaion differenial and rend appreciaion as in Equaion (6). Moreover, o avoid unrealisic exchange rae behavior in he firs simulaed period, he las observed level of he exchange rae needs o be aken as he arge a ime -1. The argeed exchange rae is hen defined as: where T s s T T s s / 4, (7) 1 s s, (8) T 1 1 is he exchange rae arge a ime. Thus, firs, Equaion (6) deermines he longrun change in he nominal exchange rae as implied by PPP heory and makes he change in he exchange rae arge consisen wih he chosen inflaion arge. Second, he arge for he level of he nominal exchange rae is deermined by is connecion o he las observed level of he nominal exchange rae. The UIP hen becomes a weighed average of he ER arge and he canonical UIP e 1 5 A similar srucure of he UIP is used in he forecasing models in Boswana, Belarus, Ukraine, and Serbia. (Beneš, Hurník and Vávra, 2008).

7 7 s e1 s (1 e1 )( s ( i i prem ) / 4), (9) T e 1 * wih he coefficien e 1 measuring he degree of he cenral bank inervenion on he FOREX marke. The exended UIP defined as in Equaion (9) sabilizes he exchange rae in a way ha resembles a managed exchange rae regime (Beneš, Hurník, and Vávra, 2008). The sabiliy of he exchange rae, however, comes a he cos of persisen deviaions of inflaion from he inflaion arge whenever a shock his he economy. Inuiively, he inroducion of an exchange rae arge is equivalen o swiching from an inflaion arge o a price level arge. Even if he cenral bank publicly defines is arge as a rae of growh of he price level, i simply means ha he arge is a price level growing a some consan rae. Any overshooing of such an inflaion arge mus sill be compensaed by subsequen undershooing and vice versa o joinly saisfy he inflaion and exchange rae arges. The model also saisfies he long-run version of he UIP expressed in real erms. This version of he UIP links he rend values for real exchange rae appreciaion (eiher due o he Balassa-Samuelson effec or some convergence inflaion as in Čihák and Holub, 2003) o he rend values of domesic and foreign real ineres raes: z * 1 r r prem. (10) * The seady-sae values of z, r and r are se as parameers in his model, requiring prior assessmen of hese rend values, 6 while he risk premium is calculaed endogenously, assuring he exisence of a consisen seady sae. Values of hose parameers frame he forecas over he medium o long run. D. Policy Rule The model is closed by a policy reacion funcion of he moneary auhoriy (Taylor, 1993). The rule is defined ypically for a cenral bank mainaining a floaing exchange rae regime, however, i can be modified o reflec he addiional objecive of conrolling he exchange rae. Floaers For simpliciy, we ake he hree-monh ineres rae o be he insrumen of moneary policy, and he auhoriy is assumed o respond o deviaions of nex-period inflaion from is arge and o he oupu gap. In oher words, we assume ha he credi markes flawlessly ransmi he changes in he policy rae ino money-marke raes. The las-period policy sance affecs he curren policy sance allowing he auhoriy o smooh ineres raes by adjusing hem gradually o he desired level implied by he deviaions of inflaion and oupu from equilibrium. Mahemaically, i f1 i ˆ, (11) n e T 1 ( 1 f1)( i f2( 1 ) f3 y ) s i 6 For example, we would assume ha a fas-converging ransiion economy would have an equilibrium real appreciaion o he une of 3-5 percen annually.

8 8 i where i is he domesic shor-erm nominal ineres rae and is a policy shock. The moneary auhoriy is fully forward-looking and uses model-consisen inflaion expecaions, e n 1. The policy-neural rae, i, is one ha keeps he oupu gap unchanged. We calculae i as he sum of he rend real ineres rae and model-consisen inflaion expecaions: n e ~ r. (12) Peggers i 1 Cenral banks aemping o conrol he exchange rae using foreign exchange inervenions find i difficul o conrol simulaneously also he money marke and hence he shor-erm nominal ineres rae. The domesic money marke ineres rae i becomes parly deermined by he UIP equaion and he policy rule needs o be modified as follows: i g * n e T i 1 ( s 1 i prem ) (1 g1)( f1i 1 (1 f1)( i f2( 1 ) f3 yˆ )), (13) The coefficien g 1 reflecs he degree of conrol he cenral bank reains over he domesic money marke (if g1 = 0, hen he bank has reained full conrol; if g1 =1 he bank has los conrol). Of course, he exended version of he policy rule needs o be doveailed wih he uncovered ineres pariy equaion (Equaion (9)) and he e 1 coefficien ( high values of g 1 require high values of e 1, and vice versa). Seing simulaneously a low value of e 1 and a high g 1 would lead o sysem indeerminacy. Inuiively, he cenral bank chooses wheher o sabilize inflaion hrough conrolling he exchange or ineres rae. For simpliciy we work wih he hree-monh ineres rae and do no use long-erm ineres raes. The model includes furher ideniies and ransformaions ha are repored in he model codes. IV. MODEL CALIBRATION The baseline version of he model is based on reasonable values for all he parameers, however, he model exhibis comparaively low persisence wih hese parameers. The calibraion process can be spli ino wo pars: 1) he calibraion of he rend variables, deermining he seady-sae levels of he model, 2) he calibraion of individual equaions parameers, pinning down he business-cycle properies of he model. A. Calibraion of Long-erm Parameers The model converges o he long-erm rend values of he real exchange rae, domesic and foreign real ineres raes, and risk premium and we impose hese values via parameers. 7 For simpliciy, also he arges for domesic and foreign inflaion are se as parameers. The choice of he inflaion arge predeermines he inflaion forecas he forecased inflaion converges o he arge. 7 Gap models do no ensure he sock-flow consisency of is variables and he seady-saes have o be imposed. For his reason we prefer o call hese variables long-run rends raher han seady saes.

9 9 The model srucure se in Equaions (1) o (7) deermines imporan long-run relaionships. The nominal ineres rae converges o he neural rae ha in urn equals o he sum of he rend real ineres rae and inflaion arge. (In he seady-sae, inflaion expecaions equal he inflaion arge). The seady-sae change in nominal exchange rae becomes he sum of seady-sae inflaion differenial vis-à-vis he world and seady-sae real exchange rae appreciaion. The risk premium is calculaed endogenously given he parameerizaion of domesic and foreign real ineres raes and he change in he real exchange rae. This approach no only keeps he model simple bu also ensures ha he rend values in Equaion (5) are on a consisen pah. The model requires seing six long-run parameers: 1. Inflaion arge 2. Foreign long-run inflaion (or foreign inflaion arge) 3. Domesic rend real ineres rae 4. Foreign rend real ineres rae 5. Equilibrium real exchange rae appreciaion/depreciaion 6. Poenial oupu growh We recommend ha afer changing o he model srucure you check he seady-sae consisency of he model. This is done by firs yping readmodel and pushing [ENTER] in he Malab command window, insrucing he program o solve he model seady-sae and reduced form, while replacing he old model parameers wih he new ones, and second by yping mss, o check he long-run properies. The screen message is self-explanaory and we sugges checking he following: 1. The domesic and foreign inflaion raes equal heir respecive inflaion arges. 2. The domesic and foreign real ineres raes equal heir rend parameers. 3. The change in he real exchange rae equals he assumed rend. 4. The risk premium equals he difference beween domesic and foreign real ineres raes minus he change in he real exchange rae (equaion 5). 5. The change in he nominal exchange rae mus equal he inflaion differenial adjused for he change in he real exchange rae. 6. All he gaps converge o zeros. Violaing any of hese condiions will resul in eiher inflaion missing is arge a he end of he forecas period or a non-convergence of he model. The mos likely misakes are: 1. A wrong parameer sign. 2. Violaed linear homogeneiy in one of he relevan equaions. For example, you may have inadverenly se f 1 >1 in he Taylor rule. See Table 1 for furher references on linear homogeneiy condiions.

10 10 B. Calibraion: Business-Cycle Properies In his secion we discuss model calibraion o reflec counry-specific, business-cycle condiions by modifying parameers a1 o g1 in he file readmodel. Table 1 summarizes he 8 baseline parameerizaion of he model. Following Berg, Karam, and Laxon (2006), in seing he parameers values we follow (i) he economic heory; (ii) inernaional experience; and (iii) domesic-economy sylized facs, based, for example, on esimaed parameer values in a srucural VAR model. The esimaed values may be used only o he exen ha hey do no violae model assumpions. For example, a shor-sample regression for a fas-growing emerging marke economy may sugges ha inflaion declined when oupu has expanded above is poenial (he esimaed b3 coefficien in he Phillips curve is negaive). However, using a negaive value for b3 would violae he model convergence oward is seady-sae and users need o refrain from doing so. a 1 Table 1 Baseline Parameers and Oher Suggesions Oupu gap persisence varies beween 0.1 (exremely low persisence) o 0.95 (high persisence). The linear homogeneiy condiion: 0< a 1 < 1. Calibraion: Run an OLS regression of a log of oupu on is lagged value and a rend (linear, Hodrick-Presco, ec.) a Pass-hrough from moneary condiions o real economy. The value varies beween (low impac) o 0.5 (high impac); he higher he parameer he more responsive is he oupu gap o changes in moneary policy and, hence, policy reacions need o be less pronounced. The linear homogeneiy condiion: 0.9 < a 2 < 0.1. Calibraion: We sugges basing his parameer eiher on an impulse-response funcion in a srucural VAR (if available) or on exper assessmen. a 3 a 4 b 1 Impac of foreign demand on he oupu gap ypically varies from 0.1 o 0.5. Calibraion: Base he calibraion on he expor-o-gdp raio. The relaive weigh of he real ineres rae and real exchange rae in real moneary condiions in he IS curve (mci). The value varies beween 0.3 (open economy) and 0.8 (closed economy). Calibraion: Exper assessmen. Inflaion persisence deermines he share of forward-looking versus backward-looking agens on he goods markes. The value varies beween 0.4 (low persisence) and 0.9 (high persisence), he higher is he share of forward looking agens (he lower is he parameer). The less persisen he model becomes, he less pronounced policy reacions are required for a given disinflaion goal. The linear homogeneiy condiion: 0< b 2 < 1, oherwise moneary policy canno bring inflaion oward he arge wih zero gaps. Calibraion: Run an OLS 8 The model uses wo addiional parameers ha we sugges keeping unchanged. Firs, he parameer deermines he speed of convergence of domesic variable rend values wih respec o pas esimaed values and o heir seady-sae values and is se o 0.9. For example, rend real ineres rae reflecs pas rend raes and he seady-sae real ineres rae: r h1* r 1 (1 h1)* rss. Second, he parameer h2 deermines he * * y* persisence of exernal oupu gap: y h * y. See he file model.mod for he code. 2 1 h 1

11 11 b 2 b 3 d 1 e 1 f 1 f 2 f 3 g 1 regression of he rae of inflaion (quarer-on-quarer) on is lagged value and complemen wih exper assessmen. The impac of real marginal coss on inflaion (policy pass-hrough). The value ypically varies beween 0.1 (low impac and high sacrifice raio) o 0.5 (srong impac and low sacrifice raio). The higher he parameer he less cosly is disinflaion. Calibraion: Run an OLS regression of he rae of inflaion on oupu gap and complemen wih exper assessmen. Alernaively, daa permiing, you can compare he oupu gap and decline in inflaion during a clearly defined disinflaion period (Ball, 1993). The laer echnique is unlikely o produce meaningful resuls for emerging/ransiion economies. The relaive weigh of oupu gap and real exchange rae gap in firms real marginal coss. [(1-b3) is he share of impored goods in he consumpion good baske]. The value ypically varies beween 0.9 (relaively closed economy) and 0.6 (open economy). Calibraion: Base he calibraion on he share of impored goods in he CPI baske. Persisence of impor prices varies beween zero and 0.9. The linear homogeneiy condiion imposes 0< d 1 < 1, oherwise moneary policy canno bring inflaion oward he arge wih zero gaps. Calibraion: Run an OLS regression of he rae of impored price inflaion on is lagged value and complemen wih exper assessmen. Exchange rae persisence or cenral bank presence on he FOREX marke. The value varies beween zero (forward-looking FOREX marke or no cenral bank inervenions) o 0.9 (eiher heavily backward-looking FOREX agens or a cenral bank heavily inervening on he FOREX marke). Cavea: Inervenions sabilize he exchange rae bu can no violae he seady-sae consisency of he model e.g., he exchange rae will never appreciae as long as here is on average a posiive inflaion differenial ( * 0 ) and no rend real exchange rae appreciaion. The linear homogeneiy condiion: 0< assessmen. e 1 <1. Calibraion: Exper Policy rae persisence in he Taylor rule. The value varies beween zero (no persisence in policy seing) o 0.8 ( wai-and-see policy). Cavea: a value above 0.7 may be oo high when he model is calibraed as backward-looking. The linear homogeneiy condiion imposes 0< f 1 <1, oherwise he model does no converge. Calibraion: Run an OLS regression of he policy rae on is lagged value and complemen wih exper assessmen. Weigh pu by he policy maker on deviaions of inflaion from he arge in he policy rule. Ranges ypically vary from 0.3 o 1. The linear homogeneiy condiion: f 2 >0 (Taylor principle), oherwise moneary policy does no sabilize he economy. Calibraion: Exper assessmen. Weigh pu by he policy maker on oupu gap in he policy rule. The linear homogeneiy condiion: >0, oherwise he model does no converge. Typically varies from 0.3 o 1. f 3 Calibraion: Exper assessmen. Cenral bank s conrol of he domesic money marke and is shor-erm nominal ineres rae. The value varies beween 0 (full conrol of he shor-erm raes) and 1 (no conrol of he shor-erm raes). The laer case (g 1 =1) implies ha he cenral bank uses nominal exchange rae o sabilize inflaion by inervening in he FOREX marke. Cavea: high values of his coefficien in combinaion wih low values of he e 1 parameer invalidae he model soluion. Calibraion: Exper assessmen.

12 12 1 Speed of exchange rae adjusmen from acual daa o he exchange rae arge ( 1 ). This coefficien is used only if an exchange-rae-arge adjused UIP is used. Plausible values are: 0 < 1 < 0.5 In addiion o bivariae regressions, srucural VAR models and heir impulse responses may be used for parameer calibraion of exchange rae or oupu shocks. Many such VARs have been published on naional cenral bank websies. We would cauion, however, agains using he impulse responses o he policy shock as he model we presen is designed o capure sysemaic policy behavior. In oher words, he moneary auhoriy is assumed o figh agains he shocks as opposed o creaing hem and he policy pass-hrough esimaed in VAR model is likely o be underesimaed. To summarize, he calibraion exercise includes he following seps. Firs, sar wih he parameer values esablished in he heory. Second, look for a reasonable esimae of he IS curve, Phillips curve, or policy rule. If here is no such esimae available, run a simple bivariae regression yourself o ge a sense of he persisence in he economy. Third, look for a srucural VAR model already esimaed for he economy you are calibraing, focusing especially on he exchange rae pass-hrough. C. Some Useful Calibraion Hins 1. To change he speed of he exchange rae pass-hrough, change impor price persisence ( d 1 ). 2. To make he policy response more (less) sluggish, increase (decrease) he persisence in he policy rule ( f 1 ). Be aware, however, ha by increasing (decreasing) persisence in he policy rule you ceeris paribus increase (decrease) he impac of moneary policy on he real economy (via boh he real ineres and exchange raes). 3. To make he whole economy more persisen, increase (decrease) he persisence parameer in he Phillips curve ( b 1 ). As a resul, a more (less) pronounced policy reacion will be needed for a given disinflaion goal. 4. To force a faser (slower) convergence oward he rend ( seady-sae ) values, increase (decrease) he policy pass-hrough eiher hrough he real moneary condiion parameer in he IS curve ( a 2 ) or he real marginal cos parameer in he Phillips curve ( b 2 ). As a resul, moneary policy becomes more (less) powerful. 5. To make he exchange rae pah more (less) persisen or sable, increase (decrease) he persisence (inervenions) parameer in he UIP equaion ( e 1 ). 6. To make he ransmission mechanism really sluggish, you may inroduce a lag for moneary condiions in he IS curve ( a 2 ) or a lag for he real marginal cos in he Phillips curve ( b 2 ) insead of he curren values presen in he canonical version. Similarly, o make he exchange rae pass-hrough really slow, inroduce a lag for impor prices in he Phillips curve. You should exercise cauion in increasing persisence in he economy. There exiss a poin, no easily defined in advance, when he economic agens may become oo persisen for he

13 13 cenral bank o be able o sabilize he economy. For example, if you make boh he Phillips curve and he UIP fully backward looking, you should leave a leas he policy rule o be forward looking, oherwise he model may become unsable. D. How o Check he Model Properies Afer he model has been calibraed, you may wan o check visually he behavior of he model economy. You will do i by running he program modelproperies in he Malab command window 9 and hen inspecing six pages of prinous in a file Repor_shocks.ps or.pdf (PosScrip of Acroba, respecively): Aggregae demand shock; 2. Inflaionary shock; 3. Exchange rae shock; 4. Moneary policy shock; 5. Foreign demand shock; 6. Foreign inflaion shock. Noe ha if your opion is se for PosScrip (.ps), you can (i) change he model calibraion by edi readmodel ; (ii) save i; (iii) run he readmodel program; (iv) run modelproperies wihou having o close and open he Repor_shocks.ps file every ime you run he modelproperies program. The Repor_shocks.ps file changes wih he change in model calibraion while being open a useful propery when fine uning he model. If you decide o change he model srucure, for insance by including he lagged oupu gap in he Phillips curve, change he code in he model.mod file as follows: %% Phillips Curve (Aggregae supply) dl_cpi = b1*dl_cpi{-1} + (1-b1)*dl_cpi{+1} + b2*rmc{-1} + shk_dl_cpi; Save he file; run he readmodel file; check he model s seady sae ( mss ); and run he file modelproperies. V. FORECASTING This secion discusses he use of he model for a basic forecasing exercise, he goal of which is o decide on an appropriae level of he policy rae. Raher han providing an unconsrained forecas of inflaion, his class of models brings inflaion close o he arge by consrucion and he focus is on he pah of he policy rae ha would be consisen wih such an inflaion rae. The policy rae pah depends on (i) he model srucure, (ii) model parameerizaion, and 9 You can open he file by yping he edi modelproperies [ener] in he command window. 10 You can change he prinou forma in he very las line of he file modelproperies by replacing.pdf (Acroba) wih.ps (PosScrip): compile(x,'repor_shocks.pdf').

14 14 (iii) iniial condiions. We have discussed he model srucure and parameerizaion in he preceding secion and discuss below he imporance of iniial condiions. A. Daabase Preparaion A hisorical daabase, which provides iniial condiions, is necessary o run he model forward. As a minimum, he daabase mus conain a value for any variable ha appears wih a lag in he model srucure. Thus, for a forecas saring in 2007Q1, we need iniial condiions for 2006Q4 for all he variables wih he lag of order one. In pracice, however, he daabase is prepared and mainained using a longer ime series daa for all he relevan variables. For example, some of he variables needed for he iniial condiions may be unobserved (oupu gap) and have o be esimaed using he hisorical series. The longer he daa se, he more precise is he esimaion of unobserved variables. The program makedaa is se o prepare he daabase for paricipan inspecion wihou manual calculaions of seasonal adjusmen, de-rending or char preparaion. Neverheless, before running makedaa in Malab a basic daa se needs o be compiled: Domesic economy Series Table. Daa Requiremens Forma GDP a consan prices Billions of naional currency or an index CPI Index (no a rae of growh) Nominal ineres rae Annualized rae, i.e., 5% Nominal exchange rae Unis of domesic currency per one uni of foreign currency Foreign economy GDP a consan prices Billions of naional currency or an index CPI Index (no a rae of growh) Nominal ineres rae Annualized rae, i.e., 5% These series compiled in any program, including Microsof Excel need o be saved ino he file daa.csv in he ex forma ( csv ). 11 For more deails see he emplae file daa.csv. Four your counry series you have o use exacly he same names as in daa.csv, oherwise he code would no recognize your series. If any of your series is no seasonally adjused, exend he series ile wih a suffix _u (for insance from cpi o cpi_u ). The program makedaa will recognize seasonally unadjused series and will run he seasonal adjusmen (Census X12) auomaically, saving he newly 11 In Excel, selec Save As; in he Save As window click on Save as ype ; scroll down o CSV (MS-DOS); and selec his opion.

15 15 seasonally adjused series wihou he suffix _u. The program makedaa calculaes he naural logarihm of all series (excep ineres raes), growh raes for relevan variables, and he real ineres rae. I also esimaes he rend and gap for real oupu, real exchange rae and domesic and foreign real ineres rae. For he sake of simpliciy he sandard Hodrick- Presco filer is used. Visual inspecion of he daa is a useful check of your prior inuiion abou he economy in quesion. Program makedaa creaes panels of domesic and foreign inflaion, nominal ineres raes, exchange raes and esimaed rends and gaps. I should be possible o recognize mos misakes or omissions in he daa.csv file jus by inspecing he figures. We recommend checking especially he esimaes of rends and gaps, as hese will influence he forecas he mos. The esimaes of rends and gaps should correspond o your priors abou he economy. If he esimaed rends or gaps seem biased, you may overwrie hem manually (see below). 12 In fac, i suffices o change he las observaion (iniial condiion) only, as only his informaion maers for he forecas. Noe ha wih he excepion of he year-on-year inflaion rae he model conains no lags of order higher han one. For example, he Hodrick-Presco filer may generae an unreasonable rend for domesic real ineres raes, while your priors sugges ha his rend rae is in fac equal o, say, 1 percen annually. To manually change he daabase: 1. Open he program makedaa yping edi makedaa in Malab command window [ener] 2. Go o he secion Exper change in he daabase (row 55) and ype: d.rr_eq(qq(2006,4)) = 1; 3. Save he program makedaa and run i again yping makedaa in Malab command window. Your domesic rend real ineres rae is now se o equal one in he fourh quarer of I is sufficien o change he las observaion only as previous observaions do no influence he forecas he forecas depends only on he iniial condiions. B. The Forecas Mechanically, he making of he forecas is he shores par of he whole process, however, is qualiy depends on previous work (calibraion and daa preparaion) and ex pos analysis. The forecas is produced by running he program forecas. This program reads he model ( readmodel ) and hisorical daa (iniial condiions) from he daabase ( makedaa ) and simulaes he model forward. Furhermore, he program produces indicaor figures and ables ha can be viewed by doubleclicking on he file Forecas.ps (or Forecas.pdf ). 12 For example, he Hodrick-Presco filer may be an inappropriae echnique given he presence of a srucural break in he series or because of end-period measuremen error.

16 16 Reminder: You need o run readmodel any ime you change eiher he parameers or model srucure and makedaa any ime you change your daa before you run he program forecas. The Programming Code of forecas The following secion briefly summarizes he code of he program forecas and can be skipped by mos readers who are no ineresed in Malab and IRIS programming. The program sars wih reading he model and daa ino he objecs m and h respecively (command loadsruc) and ses he forecas range. You can change he range depending on your curren daa sample. The key command for running he forecas is simulae wih he following synax: S = simulae(m,h,fcasrange) The simulaion resuls are saved ino he daabase objec s and he command dboverlay adds h o s, overlaying he hisorical daa wih he curren projecions. The whole daabase is saved ino he file fcasdaa.ma (by he command savesruc) and he figure and ables are saved ino he Forecas.ps file (or Forecas.pdf ). How o Pre-Se Fuure Values You may wan o se one or more fuure variables o an exac number, eiher because you do no believe ha he model s AR(1) process forecass a paricular variable well (for example, some of he foreign variables) or because some near-erm variables are beer forecas by ime-series models (for example, inflaion one period ahead). You save he daase daa.csv wih hese fuure values and ell he program forecas o use hese values using he command plan wih he following synax: simplan = plan(m,fcasrange) The command plan creaes an objec simplan ha iniially conains an empy plan for model m over he forecasing range. In he nex sep you specify which variable are o be aken from daa.csv using commands exogenize and endogenize. Assuming we wan o pre-se he exernal rae of inflaion and ineres raes, he synax is as follows: simplan = exogenize(simplan,{'dl_x_cpi','x_rn'},fcasrange) The command exogenize specifies which variables are going o be aken as exogenous variables and decides over which horizon his will hold (in his case over he whole forecas horizon; if you wan o pre-se hese variables only for he nex wo quarers, replace fcasrange wih qq(2007,1):qq(2007,2), and so on). Pre-seing a variable causes, however, a discrepancy beween he lef-hand side of he respecive equaions (he pre-se values) and heir righ-hand sides (he daa generaing processes). Boh sides of he equaion are equalized hrough he residual erm, which now becomes an endogenous variable, see endogenize: Simplan = endogenize(simplan,{'shk_dl_x_cpi','shk_x_rn'},fcasrange) Inuiively, you can pre-se only hose variables ha have a residual erm in heir equaions specified in model.mod.

17 17 To summarize, if you decide o pre-se he wo variables above, in he program forecas pu a percenage sign % in fron of S = simulae(m,h,fcasrange) and remove he percenage signs from he following four lines: simplan = plan(m,fcasrange); simplan = exogenize(simplan,{'dl_x_cpi','x_rn'},fcasrange); simplan = endogenize(simplan,{'shk_dl_x_cpi','shk_x_rn'},fcasrange); s = simulae(m,h,fcasrange,'plan',simplan); C. Inerpreing he Forecas The simulaions of your model need o be carefully inerpreed and his secion suggess some seps oward his objecive. All relevan resuls are conained in file Forecas.ps (or Forecas.pdf ) in he form of a figure and wo ables. Noe ha he inflaion forecas converges o he argeed inflaion, possibly wih some iniial flucuaion. This is a normal propery of he so-called uncondiional forecas where he moneary auhoriy does all i can o keep he inflaion rae close o he argeed one wihin he ransmission period (usually 6-8 quarers). The mos ineresing variable is hus he rajecory of nominal ineres rae se by he cenral bank raher han he forecased inflaion rae. The simulaed pah of he policy ineres rae provides a policy reacion given he pas daa and he model srucure. In addiion o inflaion and he nominal ineres rae, he figure shows he forecas of he nominal exchange rae, oupu gap, and moneary condiions. The las char he real ineres and exchange rae gaps plos boh he direc and indirec exchange rae channels and he ineres channel. Based on his char, one can observe how igh he moneary sance mus be (he real ineres and exchange rae gaps) in order o mee he inflaion arge and wha would be he cos of his sance in erms of real economic aciviy (he oupu gap). The forecas prinou also conains wo ables: Main Indicaors and Decomposiion. The former able is self-explanaory and all variables correspond direcly o he variables discussed earlier. The laer able provides a breakdown of he conribuing facors o your forecass based on he relevan equaions. For example, he aggregae demand (he IS curve) is a funcion of he pas oupu gap, real moneary condiions, and exernal demand and he second block of he forecas decomposiion able provides his informaion (Oupu Gap Decomposiion). Similarly, he Phillips curve breakdown is provided in he hird block (Inflaion Facor Decomposiion). You should be able o exrac an economic sory from his able o back up your inflaion scenario.

18 18 Sofware Insallaion Appendix I The Malab sofware does no provide a specific oolbox for economic modeling and serves only as he environmen for he necessary marix algebra. For he economic modeling i is necessary o insall he IRIS oolbox, which is a Malab-based package for advanced macroeconomic modeling. Alhough he curren IRIS oolbox can be downloaded from we provide you wih a package ha conains he version of he IRIS ha is used for all presened simulaions. The package can be downloaded from The insallaion of IRIS oolbox requires copying wo files from he package in a specific direcory (recommended: c:/modeling/iris_insall): 1. he zip file iris-oolbox.zip ; 2. he Malab file insalliris.m Noe ha boh files mus be copied exacly in his form. Before you sar IRIS insallaion i is useful o insall on your compuer X12 Census package for seasonal adjusmen and he MiKTeX, Ghoscrip and Ghosgum (GSView) packages for reporing. No previous knowledge of X12, MiKTeX or Ghosscrip - Ghosgum is required. The IRIS Toolbox uses all of hem auomaically. We recommend creaing a folder c:/modeling ha conains he following folders: 1. FOLDER iris-insall, i.e., c:/modeling/iris-insall, wih iris-oolbox.zip and insalliris.m files. 2. FOLDER FS (free sofware),i.e., c:/modeling/fs, where he insallaion folder for MiKTeX, and files for Ghosscrip and GSView are saved. Copy all he insallaion files from he downloaded package. If ineresed, you can download he curren versions of he MiKTeX Insaller a and and hp:// for Ghosscrip and Ghosgum. 3. FOLDER x12, i.e., c:/modeling/x12, where he insallaion file for X12 is copied. Afer execuing he omegaxp.exe file, he X12 program is insalled auomaically in he same folder. The curren version can be downloaded from hp:// ( omegaxp.exe ). 4. FOLDER iris-oolbox, i.e., c:/modeling/iris-oolbox, where he IRIS Toolbox is insalled. 5. FOLDER exmf, i.e., c:/modeling/exmf, where he MiKTeX is insalled. X12 Insallaion We sar wih he X12 Census insallaion: 1. Go o he c:/modeling/x12; 2. Execue he downloaded omegaxp.exe file. X12 Census is auomaically insalled in he same folder. MiKTeX Insallaion

19 19 1. Go o he c:/modeling/fs/miktex; 2. Execue he downloaded file seup exe file. 3. When asked for he insallaion folder, do no insall he MiKTeX ino he auomaically offered Program Files, bu change he folder via browse opion o c:/modeling/exmf; 4. Insall. Ghosscrip and Ghosgum Insallaion 1. Go o he c:/modeling/fs; 2. Execue he respecive.exe files (heir names may vary wih he version you downloaded). 3. Boh programs can be insalled ino he Program Files. IRIS Insallaion 1. For his we sar Malab firs. 2. Se he curren direcory (on he op and in he middle of he screen) for he direcory where he IRIS insallaion files are saved, i.e., c:/modeling/iris_insall; 3. Wrie he command insalliris in he Malab s command window, [ener]. 4. You will be asked for he desired IRIS Toolbox folder. Type c:/modeling/iris-oolbox, [ener]. IRIS Toolbox is insalled in his folder. Malab is case sensiive and you mus wrie your folder names exacly. 5. You will be asked for he pah o he LaTex (MiKTeX) program (insalled in he previous sep). Type c:/modeling/exmf/mikex/bin, [ener]. 6. You will be asked for he pah o he X12. Type c:/modeling/x12, [ener]. 7. Now he IRIS Toolbox has been insalled and he pahs o MikTEX and X12 have been se. Saring he IRIS Toolbox Anyime you open Malab for a modeling exercise you mus pah he IRIS Toolbox o he Malab. This mus be done via Malab s command window yping: addpah c:/modeling/iris-oolbox; irissarup, [ener]. 13 You receive he message The IRIS Toolbox Version ready. Noe ha you should no pah he IRIS Toolbox via Se Pah opion in he Malab s File menu. Model Files Nex sep is o creae subfolder Model in your Modeling folder, i.e., c:/modeling/model. Unzip he file model.zip ha is a par of he downloaded package. Once unzipped he folder Model should conain he following files: 13 Malab will remember he command and nex ime you can ype a and push arrow up, Malab will bring up his command.

20 20 1. model.mod 2. readmodel.m 3. modelproperies.m 4. makedaa.m 5. forecas.m 6. daa.csv We describe hese files in he secion Modeling. Wih he excepion of model.mod and daa.csv, all files are Malab programs (exension.m ) and work in he Malab environmen only. Before running hem he Malab s curren direcory mus be swiched o he folder Model where he programs are saved. Thus swich he curren direcory from c:/modeling/iris_insall o c:/modeling/model ( cd c:/modeling/model, [ener]). You may check ha you are in he righ direcory yping he command ls, [ener]. Malab will give you a lis of files saved in is curren direcory. Now you can execue he programs readmodel, modelproperies, makedaa and forecas. The programs ge sared in he following way. Type he name of he program, for insance readmodel in he command window and push [ener]. Once he screen shows >> he program has been run successfully. Noe ha if you run he programs for he firs ime you should follow sequence: readmodel, modelproperies, makedaa, forecas. Be aware ha while running he program modelproperies for he firs ime, he MiKTeX applicaion may ask you wice for addiional insallaion. Choose yes as he insallaion uses he package insalled previously and calls for some sub-packages ha were insalled auomaically. Please check ha all is running: 1. Execue readmodel, modelproperies, makedaa and forecas, 2. Sar Windows explorer, 3. From c:/modeling/model double click on files Repor_Shocks.ps, Sylized_facs.ps, Forecas.ps. 4. [OK] and you should see chars and ables of various model oupus.

21 21 The Model Code Appendix II For he model code see he file model.mod and you may open i in he Malab s edior yping he command edi model.mod in he command window. 14 The model code has four basic pars: endogenous variables, equaion residuals, parameers, and equaions: The lis of all endogenous (ransiion) variables. The lis of all residuals defined in individual equaions. The lis of parameers. Noe ha his lis mus be idenical o he parameers defined wihin he readmodel program any parameer change in model.mod mus be refleced in readmodel, and vice versa. The lis of equaions defining he endogenous (ransiion) variables. The number of ransiion variables mus equal he number of ransiion equaions. The program readmodel (as a Malab file i has an exension.m ) akes he code wrien in he model.mod, assigns he parameers values, and solves he model for is reduced form. To modify model parameers and seady-sae values you need o open he readmodel in he Malab edior yping he command edi readmodel in he Malab command window or using he File menu. The IRIS commands used for handling he model are as follows: The firs command is model: m = model('model.mod','linear',rue,'assign',p); Tha reads he ex file model.mod conaining he model code and assigns he model parameers and rend values prese in he daabase p o he model. In addiion i ransforms he model for he marix algebra. Transformed model is wrien in he objec m. The opion linear is logical funcion. If your model is linear you assign he value rue. This makes he ransformaions and calculaions easier and saves ime. Second, he model is solved for is seady-sae using he command ssae: m = ssae(m); The command ssae akes he ransformed model wrien in objec m and calculaes is seady-sae. This is done via ieraions using he Malab s opimizaion oolbox. The seadysae values are wrien in objec mss ha may be viewed by yping he mss [ener] in he Malab command window. I is useful o check he seady-sae values any ime you change he model srucure (see secion Calibraion for furher deails). Finally, he model is ransformed in is reduced form using he command solve. Exac quoaion looks as follows: 14 Anyhing ha is wrien afer % signs is a commen (or an inacive porion of he code) and does no consiue a par of he model.

22 22 m = solve(m); For he ransformaion he Blanchard-Kahn algorihm is used. The objec m conains he reduced form of he model ogeher wih he seady-sae values. Using he command savesruc he objec m is saved in he daabase file model.ma. This is used laer for shock analysis and forecasing. You may run he readmodel simply by yping: readmodel [ener] in he Malab command window. The evidence ha he readmodel works properly is eiher he appearance of file model.ma in you curren direcory (if i was no here before) or he lis of seady-sae values if you ype mss [ener] in he Malab command window once he readmodel has been run.