Real and Nominal Effects of Monetary Policy Shocks

Transcription

1 Real and Nominal Effecs of Moneary Policy Shocks A Thesis Submied in he College of Graduae Sudies and Research In Parial Fulfillmen of he Requiremens For he Degree of Masers of Ars In he Deparmen of Economics Universiy of Saskachewan Saskaoon By Rokon Bhuiyan Augus 2004 Copyrigh Rokon Bhuiyan, All righs reserved. i

2 PERMISSION TO USE In presening his hesis in parial fulfillmen of he requiremens for a posgraduae degree from he Universiy of Saskachewan, I agree ha he Libraries of his Universiy may make i freely available for inspecion. I furher agree ha permission for copying of his hesis in any manner, in whole or in par, for scholarly purposes may be graned by he professor or professors who supervised my hesis work or, in heir absence, by he Head of he Deparmen or he Dean of he College in which my hesis work was done. I is undersood ha any copying or publicaion or use of his hesis or pars hereof for financial gain shall no be allowed wihou my wrien permission. I is also undersood ha due recogniion shall be given o me and o he Universiy of Saskachewan in any scholarly use which may be made of any maerial in my hesis. Requess for permission o copy or o make oher use of maerial in his hesis in whole or par should be addressed o: Head of he Deparmen of Economics Universiy of Saskachewan Saskaoon, Saskachewan S7N 5A5 ii

3 DEDICATION To he Insrucor of my Quanum Mediaion Course Gurugi Mahajaakh iii

4 ABSTRACT Using Canadian daa we esimae he effecs of moneary policy shocks on various real and nominal variables using a fully recursive VAR model. We decompose he nominal ineres rae ino an ex-ane real ineres rae and inflaionary expecaions using he Blanchard-Quah srucural VAR model wih he idenifying resricion ha ex-ane real ineres rae shocks have bu a emporary impac on he nominal ineres rae. The inflaionary expecaions are hen employed o esimae a policy reacion funcion ha idenifies moneary policy shocks. We find ha a posiive shock inroduced by raising he moneary aggregaes raises inflaionary expecaions and emporarily lowers he exane real ineres rae. As well, i depreciaes he Canadian dollar and generaes oher macro effecs consisen wih convenional moneary heory alhough hese effecs are no saisically significan. Using he overnigh arge rae as he moneary policy insrumen we find ha a conracionary moneary policy shock lowers inflaionary expecaions and raises he ex-ane real ineres. Such a conracionary moneary policy shock also appreciaes he Canadian currency, decreases indusrial oupu and increases he unemploymen rae. We obain qualiaively beer resuls using he overnigh arge rae raher han a moneary aggregae as he moneary policy insrumen. Our esimaed resuls are robus o various modificaions of he basic VAR model and do no encouner empirical anomalies such as he liquidiy and exchange rae puzzles found in some previous VAR sudies of he effecs of moneary policy shocks in an open economy. iv

5 ACKNOWLEDGEMENT My profound graiude and hanks goes o my supervisor Professor Rober F. Lucas firs for being an excellen coach in guiding me hrough his hesis. I sincerely acknowledge his rigorous commimen and endless effor o ensure he qualiy of his hesis as well as he imely compleion of i. His in deph knowledge, inellecual abiliy and generosiy has helped me o have a good undersanding of he Moneary Policy issues. In addiion, he principles and he values I learned from him would be an inspiraion in my life. I was a maer of good luck for me o be his hesis suden. I graefully acknowledge he generous help from Professor David O. Cushman hroughou he whole process. A lo of very imporan commens and suggesions from him significanly improved he qualiy of his hesis. My sincere appreciaion also goes o Professor Kien C. Tran and o he exernal examiner Professor Marie Racine for heir useful commens. I am indebed o Mr. Jan Goschalk a he IMF for providing me wih he RATS program codes o esimae he Blanchard-Quah SVAR model. I am also hankful o Mr. Tom Maycock a he ESIMA for his coninuous assisance wih he RATS programming. I am graeful o all my professors for heir conribuions o my knowledge in Economics. I acknowledge he financial assisance and suppor from he Deparmen of Economics, Universiy of Saskachewan. I am graeful o he counless help and generous cooperaion ha I received from our Graduae Chair Professor Mobinul Huq. I am hankful o Professor Joel Bruneau for he friendly assisance I received from him. I am hankful o Madeleine George, Mary Jane Hanson, Nadine Penner and Margaria Sanos for heir help during hese wo years a U of S. I acknowledge he encouragemens and help of my friends and classmaes in pursuing my sudies. I acknowledge he greaes sacrifice of my parens-he bes parens in he world, my broher and oher family members. Finally I acknowledge my insrucor of he Quanum Mediaion course-gurugi Mahajahak who augh me a very differen way of hinking abou life. His eaching abou he incredible capabiliy of human being is my moivaion in life. v

6 CONTENTS ABSTRACT iv CHAPTER : INTRODUCTION CHAPTER The Theory o Decompose Nominal Ineres Rae The Blanchard-Quah VAR Model Impulse Response Funcions Variance Decomposiion 8 CHAPTER Saionariy Properies of Daa Variance Decomposiion and Impulse Responses Ex-ane Real Ineres Rae and Inflaion Expecaions 27 CHAPTER A Framework for Analyzing he Effecs of Moneary Policy Shocks The Recursive VAR Model o Esimae Moneary Policy Shocks The Feedback Rule, Exogenous Moneary Policy Shock and Impulse Response Funcions 37 CHAPTER 5: ESTIMATED RESULTS 4 5. The Impulse Responses of he Basic Model The Augmened Model Impulse Responses Using he overnigh Targe Rae 50 CHAPTER 6: CONCLUSIONS 57 REFERECNES 60 APPENDIX 63 APPENDIX 2 65 APPENDIX 3 67 vi

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8 . INTRODUCTION Alhough here has been much research in he pas decade on he effecs of moneary policy shocks in various macro-economic variables, mos of hem encounered puzzling dynamic responses. For example, he liquidiy puzzle is he finding ha an increase in a moneary aggregae (such as M0, M and M2) is associaed wih an increase raher han a decrease in nominal ineres raes (Leeper and Gordon, 99). The price puzzle is he finding ha, when moneary policy shocks are idenified as innovaions in an ineres rae, he moneary ighening is associaed wih an increase raher han a decrease in he price level (Sims, 992). The exchange rae puzzle is he finding ha while a posiive innovaion in he ineres raes in he Unied Saes is accompanied by an appreciaion of U. S dollar relaive o oher G-7 counries (Eichenbaum and Evans, 995), such moneary conracion in he oher G-7 counries is ofen associaed wih depreciaion in heir currencies (Grilli and Roubini, 995; Sims, 992). Empirical research involving boh open and closed economies addressed hese puzzles, and provided suggesions on how o explain hose puzzles. According o Sims (992), in he presence of money demand shocks, innovaions in he moneary aggregaes do no correcly represen exogenous changes in moneary policy. He, herefore, proposed innovaions in he shor-erm ineres raes as he indicaor of a moneary policy change. Sims soluion, however, was no widely acceped as i leads o he price puzzle: a moneary conracion is accompanied by a persisen increase in he price level. Some oher auhors (Srongin, 995; Eichenbaum and Evans, 995) hen suggesed idenifying moneary policy shocks wih innovaions in he narrow moneary aggregaes, such as non-borrowed reserves. One possible explanaion of he price puzzle according o Sims is ha ineres rae innovaions parly reflec inflaionary pressures which in urn cause price increases. Grilli and Roubini (995) provided evidence ha his explanaion of price puzzle also explains For an exensive review of hese puzzles and early aemps o resolve hem, see Kim and Roubini (2000).

9 he exchange rae puzzle. Laer on, o es his explanaion of price puzzle, Sims and Zha (995) proposed a Srucural VAR approach wih conemporaneous resricions ha includes variables proxying for expeced inflaion. The resuls obained in his way were consisen wih he heory of moneary policy conracion: a moneary policy conracion was accompanied by an increase in ineres raes, a reducion in he money supply, a ransiory fall in oupu and a persisen reducion in he price level. In a small open economy conex, Cushman and Zha (997) and Kim and Roubini (2000) argued o use he srucural VAR mehod wih conemporaneous resricions on some variables o properly idenify he policy reacion funcion. They believe ha as he exernal shocks are also very imporan for domesic moneary policy in a small open economy, i is imporan o ake hose influences under consideraion. By incorporaing some foreign variables ino he policy reacion funcion, hey were able o solve he puzzles encounered by he previous sudies. In a differen approach o he same problem, Kahn e al. (2002) argued ha if inflaionary expecaions are no observable, one can no infer from an observed increase in nominal ineres raes ha a commensurae increase in he real ineres rae occurred. I is, herefore, difficul in sudies ha examine nominal ineres raes o disinguish beween he ineracion of cenral bank policy wih real ineres raes and is ineracion wih inflaionary expecaions. Also hese sudies canno examine he exen o which moneary policy leads or reacs o changes in inflaion and inflaionary expecaions as hey consider realized inflaion raes raher han inflaionary expecaions. To address hese problems, Kahn e al. (2002) used he Israeli daa of real ineres raes and inflaionary expecaions, calculaed from he marke prices of indexed- and nominalbonds, o measure he effecs of moneary policy using he fully recursive VAR model. They found ha moneary policy shocks, inroduced by raising he overnigh rae of he Bank of Israel, raises -year real ineres raes, lowers inflaionary expecaions and appreciaes he Israeli currency, effecs which are consisen wih economic heory. They also found ha he moneary policy impacs are mainly concenraed on shor-erm real raes. 2

10 I can be, herefore, summarized ha he puzzling responses of various macro-economic variables o moneary policy shocks originae eiher due o he lack of he consideraion of inflaionary expecaions or due o he incorrec idenificaion of moneary policy. In his hesis, o ake ino accoun of hese facs, we proceed in wo seps. Firs, we calculae inflaionary expecaions and ex-ane real ineres raes using he Srucural VAR mehod proposed by Blanchard and Quah (989) wih he idenifying resricions ha real ineres rae innovaions have emporary effecs while inflaionary expecaions innovaions have permanen effecs on nominal ineres raes 2. In he second sep, using he daa on real ineres raes and inflaionary expecaions, we explicily examine he separae reacions of boh ex-ane real ineres raes and inflaionary expecaions o moneary policy shocks. To do his, we use he fully recursive VAR model as used by Chrisiano e al. (996), Edelberg and Marshall (996), and Khan e al. (2002). We also examine he reacion of he cenral bank s moneary policy o changes in invesor inflaionary expecaions and how he shor-erm end and he long-erm end of he erm srucures of real ineres raes reac o moneary policy shocks. In addiion, o have a diagnosic check of our model, we augmen our basic model o include some non-financial variables ha may also impac real ineres raes and inflaionary expecaions. The exclusion of hese variables may give us some misleading resuls if hey are relaed o cenral bank moneary policy. The addiional variables in he augmened model are indusrial oupu, he unemploymen rae and he US dollar exchange rae of Canadian currency. Therefore, in sum, in our sudy, using a beer se of daa (inflaionary expecaions and ex-ane real ineres raes) han was available in he previous sudies, we are able answer he following quesions: How do moneary policy shocks affec real ineres raes and inflaionary expecaions? How differenially does he moneary policy impac on real raes of differen mauriies 3? If he cenral bank s moneary policy shocks affec hese variables, is here any lag in he policy s impac on hese variables? How does he 2 Using he same idenifying resricions, S-Aman (995) and Goschalk (200) calculaed he inflaion expecaions and ex-ane real ineres raes from nominal ineres raes. S-Aman calculaed hese raes using he U.S.A daa and Goschalk calculaed hese raes using he daa of Euro area. 3 In our model, we will use real ineres raes of differen mauriies: one-year ex-ane real ineres rae, exane real forward rae of year wo and ex-ane real forward rae of year hree o see he effecs of he cenral bank moneary policy on hem. 3

11 moneary policy shock affec he exchange raes and oher variables in he economy such as he unemploymen rae, oupu level ec.? Wha is he magniude of he policy s impac on hese variables and how long does i las? Does he cenral bank s moneary policy respond o changes in inflaionary expecaions and oher variables in he economy? To search for he answers of hese quesions, we used Canadian daa in our analysis. We find ha a posiive moneary policy shock inroduced by increasing MB (currency and all chequable deposis in charered banks) emporarily lowers he ex-ane real ineres rae and raises inflaionary expecaions. The effec of such a moneary policy shock on he nominal ineres rae, which nes he effec of he shock on real ineres rae and inflaionary expecaions, is a shor-run decline in i which is smaller in magniude han he ex-ane real rae. We find ha he impac of a given moneary policy shock is smaller on long-erm ineres rae han on shor-erm ineres rae. We also find ha a posiive moneary policy shock depreciaes he Canadian currency and generaes oher macro effecs consisen wih he convenional moneary heory. To compare our resuls wih previous sudies, we also esimae our model using he overnigh arge rae as he moneary policy insrumen. We find ha a conracionary moneary policy shock inroduced by raising he overnigh arge rae emporarily lowers inflaionary expecaions and increases he ex-ane real ineres rae wih saisically insignifican effec on he second and he hird year ex-ane real forward raes. We also find ha his ype of moneary policy shock decreases oupu, increases he unemploymen rae and appreciaes he Canadian currency. Our resuls are qualiaively beer using he overnigh arge rae insead of he moneary aggregae as he moneary policy insrumen. The remainder of he hesis is organized as follows. Chapers 2 and 3 provide esimae of he ex-ane real ineres rae and inflaionary expecaions. Chaper 2 discusses he heory behind he decomposiion of he nominal ineres rae ino he ex-ane real ineres rae and he inflaionary expecaions using he Blanchard-Quah Srucural Vecor Auo Regression (VAR) mehodology. In Chaper 3, we repor he suiabiliy of our daa for he Blanchard-Quah model, he esimaed variance decomposiion of he nominal ineres rae, he esimaed impulse responses of nominal ineres raes o ex-ane real ineres rae and 4

12 he inflaionary expecaion shocks, and we presen he esimaed series of inflaionary expecaions and he ex-ane real ineres rae. In Chaper 4, we describe he fully recursive VAR model used o esimae he effecs of moneary policy shocks on various macroeconomic variables, and we empirically idenify he feedback rule and he exogenous moneary policy shocks. Chaper 5 presens he esimaed resuls including he impulse response of various macroeconomic variables o moneary policy shocks and he analysis of heir implicaions. Chaper 6 concludes. 5

13 CHAPTER 2 2. The Theory behind he Decomposiion of he Nominal Ineres Rae ino he Ex-ane Real Ineres Rae and Inflaionary Expecaions We apply he srucural VAR mehodology developed by Blanchard and Quah (989) o decompose he Canadian one-year, wo-year and hree-year nominal ineres raes ino he expeced inflaion and he ex-ane real ineres rae componens following he approach by S-Aman (996) and Goschalk (200). The saring poin of S. Aman is he Fisher equaion ha saes ha he nominal ineres rae is he sum of he expeced inflaion and he ex-ane real ineres rae: n = r + E π ) (), k, k (, k where is he nominal ineres a ime on a bond wih k periods ill mauriy, is he n, k corresponding ex-ane real rae and E( π,k r, k ) denoes inflaionary expecaions for he ime from o +k. The inflaion forecas error, k can be defined as he difference beween he acual inflaion π and he expeced inflaion E π ) :,k =, k, k (,k π - E π ) (2) (,k Now subsiuing (2) ino (), we ge he following relaion: n, k - π = -, k r, k, k (3) Therefore, he ex-pos real rae ( - π ) is he sum of he ex-ane real rae r and he n, k, k inflaion forecas error,k. Under he assumpions ha boh he nominal ineres rae and he inflaion rae are inegraed of order one and hey are co-inegraed, and ha he inflaion forecas error is inegraed of order zero, assumpions we es and confirm in, k Secion III, hen he ex-ane real rae r,k mus be saionary.,k 6

14 Goschalk idenifies hree implicaions ha flow from hese assumpions. Firs, if he nominal ineres rae is non-saionary, his variable can be decomposed ino a nonsaionary componen comprised of changes in he nominal ineres rae wih a permanen characer and a saionary componen comprised of he ransiory flucuaions in he ineres rae. Second, if he nominal ineres rae and he acual inflaion rae are coinegraed, i implies ha boh variables share he common sochasic rend, and his sochasic rend is he source of he non-saionary of boh variables. On he oher hand, if he ex-ane real ineres rae is saionary, he nominal rend has no long-run effec on his variable. Third, if he nominal ineres rae and he acual inflaion rae are co-inegraed (,) and he inflaion forecas error is inegraed of order zero I(0), his implies ha changes in inflaionary expecaions are he source of hese permanen movemens in he nominal ineres rae. Therefore, he permanen movemens of he nominal ineres rae obained by using he Blanchard-Quah mehodology will be he nohing oher han hose inflaionary expecaions. Since he permanen componen of he nominal ineres rae corresponds o inflaionary expecaions, he saionary componen mus be he ex-ane real ineres rae. Therefore, using he idenifying resricions ha shocks o he ex-ane real rae have only a ransiory effec on he nominal ineres rae while shocks o inflaionary expecaions induce a permanen change in he nominal ineres rae, we can calculae inflaionary expecaions and he ex-ane real rae of ineres. 2.2 The Blanchard-Quah Srucural VAR Mehodology 4 Assuming our daa saisfies he saionariy assumpion (assumpion ha we es and confirm in Chaper 3), we urn o he srucural VAR model developed by Blanchard and Quah (989) o decompose he nominal ineres rae ino he ex-ane real ineres rae and inflaionary expecaions. As menioned earlier, our key assumpion is ha nominal ineres rae flucuaions are a funcion of wo non-auocorrelaed and orhogonal ypes of 4 The Blanchard-Quah VAR model of his chaper is based on Enders (2003). 7

15 shocks: inflaionary expecaions shocks ( p ) and ex-ane real ineres rae shocks ( r ). Our objecive is o idenify hese wo shocks and hereafer compue he empirical measures of he ex-ane real ineres rae and inflaionary expecaions componens of he nominal ineres rae. For his purpose, we use a bivariae model comprised of he firs difference of he nominal ineres rae ( n ) and real ineres rae ( r ) 5.Define he firs difference of nominal ineres rae as bivariae Blanchard-Quah VAR model can be wrien as follows: y. Now assuming a lag-lengh of q, he simple y r = b0 b2r + y + α2r +.. βy q + β2r q α... + (4) = b20 b2y + 2y + α 22r +.. β 2y q + βr22r q α... + (5) p r where p and r are uncorrelaed whie-noise disurbances wih sandard deviaions of σ p and σ r respecively. These equaions are in srucural-form and no in reduced-form as boh variables have conemporaneous effecs on each oher. As we will esimae he reduced-form VAR raher han he srucural-form VAR, our nex job is o ransform he srucural equaions ino he reduced-form equaions. To do ha, le s rewrie srucural equaions in marixform in he following way: b 2 b2 y b = r b 0 20 α + α 2 α2 y α 22 r β +... β 2 β y 2 β r 22 q q p + r and more compacly, we can wrie: Bx = Γ0 +Γ x Γp x q + (6) 5 To use he Blanchard-Quah echnique, boh variables in he VAR model mus be in a saionary form. Since he nominal ineres rae is inegraed of order one, we used i firs differenced in our model. The second variable in he VAR model- he real ineres rae- is already in a saionary form, and hence we don need o ake is firs difference. 8

16 where B = b 2 b2 b0 Γ0 = b20 α α2 Γ = α 2 α 22 β β2 Γq = β 2 β 22 y x = r p = r, we ge he VAR model in reduced- Therefore, pre muliplying boh sides of (6) by B form or in sandard-form as follows: = A0 + A x Ap x q e (7) x + where, A A e 0 p = B = B = B A = B Γ Γ Γ 0 p Defining as he elemen i of he vecor A, a as he elemen in row i and column ai0 0 of he marix A, d as he elemen in rowi and column j of he marix A, and e as he elemen i of he vecor ij e y = a0 + ay + a2r +... dy q + d2r q + e ij, we can rewrie (7) ino he following reduced-form VAR model: (8) q i j r = a20 + a2y + a22r +... d 2y q + d22r q + e2 (9) srucural shocks- p and r.since e = B (defined above), we can express e and e in erms of p and r as follows: e e 2 The error erms- and of he above reduced-form equaions are composies of he e = b ) /( b ) (0) ( p 2 r 2b2 e = b ) /( b ) () 2 ( r 2 p 2b2 2 9

17 According o he sandard assumpion of VAR, since p and r are whie-noise process, e and e 2 mus have zero means, consan variance, and are individually serially uncorrelaed. The imporan poin o noe here is ha alhough each e and have zero auocovariances, hey are correlaed wih each oher unless here is no conemporaneous effec of on r and r on, ha is, unless he coefficiensb = b 0 6. y y 2 2 = Now if we ignore he inercep erms, following Enders (2003), he bivariae moving average (BMA) represenaion of { y } and { r } sequences can be wrien in he following form: e 2 y r = = c ( k) p k + c2 ( k) k= 0 k= 0 (2) c2 ( k) p k + c22 ( k) k= 0 k= 0 r k (3) r k Using marix noaion, in a more compac form, we can rewrie he above equaions as follows: y C = r C 2 ( L) ( L) C C 2 22 ( L) p ( L) r (4) where he C (L) are polynomials in lag operaor L such ha he individual coefficien of ij C ij (L) are denoed by c (k). For example, he second coefficien of C ( ) is c (2) 2 and ij he hird coefficien of C ( ) is c 2 (3). Le s drop he ime subscrips of he variance and 2 L he covariance erms and normalize he shocks for our convenience so ha var( ) = and var( r ) =. If we name he variance-covariance marix of he innovaions (srucural shocks), we end up as follows: 2 L p 6 A deailed discussion of he properies of he srucural shocks- p and r and he composie errors erms of he reduced-form equaions- and e are in Enders (2003). e 2 0

18 var( p ) = cov( p r ) cov( p, r ) var( ) r = 0 0 As menioned earlier, he key o decompose he nominal ineres rae n ino is rend and irregular componen is o assume ha ex-ane real ineres rae shocks emporary effec on he { n r have a } sequence. In he long run, herefore, if he nominal ineres rae n is o be unaffeced by he ex-ane real ineres rae shock, i mus be he case ha he cumulaed effec of r coefficiens in (2) mus be such ha shocks on he y sequence mus be zero. So he r k= 0 c 2 ( k) r k = 0 (5) Our nex job is hen o recover ex-ane real ineres rae shocks r and inflaionary expecaion shocks p from he VAR esimaion. The reduced-form equaions (8) and (9), in lag operaor, can be wrien in he following marix form: y A = r A 2 ( L) ( L) A A 2 22 ( L) y ( L) r e + e 2 (6) In a more compac noaion, we can rewrie he above equaions as follows: x A( L) x + e (7) = where x = he column vecor ( y, ) r e = he column vecor ( e, 2 ) e A(L) = he 2Χ 2 marix wih he elemens equal o he polynomials (L) and he A ij

19 coefficiens of A ij (L) are denoed by (k). a ij As shown earlier, he VAR residuals in model (6) are composies of he pure innovaions p and r. Therefore, we can relae he VAR residuals and he pure innovaions as follows. We know e is he one-sep ahead forecas error of y i.e., e = y E y. On he oher hand, from he bivariae moving average (BMA) represenaion (equaions (2) and (3)), one-sep ahead forecas error can be defined as ( 0) 2 (0) 2 c + c. Therefore, we can wrie as follows: e e = c + (0) (8) ( 0) p c2 r Similarly, for we can wrie: e 2 e 2 = c2 + (0) (9) ( 0) p c22 r Combining (8) and (9), we ge he following relaionship in marix noaion: e e 2 c = c 2 (0) (0) c c 2 22 (0) p (0) r (20) I is now eviden ha once we have he values of c 0), c2 (0), c2(0) andc ( 22 recover he pure innovaions- p and r from he regression residuals- e and (0), we can of our esimaed VAR model. To do his, we follow he Blanchard-Quah VAR echnique. Following hem, we use he relaionship beween (6) and he BMA model (4) plus he long run resricion ha nominal ineres is unaffeced by he ex-ane real ineres rae i.e., he cumulaive effec of r e 2 shock on { } sequence is zero (equaion (5)). We, herefore, end up wih he following four resricions from which we calculae he numerical values of he coefficiens: c c (0),c 2 0) andc (0) which, in urn, we use o recover he pure innovaions- p and r. y (0 ), 2 ( 22 2

20 Resricion : Given (8) and using he assumpion ha he inflaionary expecaion shock p and he ex-ane real ineres rae shock r are uncorrelaed i.e., E p r = 0, we see ha he normalizaion Var( ) Var( ) = means ha he variance of e is as follows 7 : p = r 2 2 Var ( e ) = c (0) + c (0 (2) 2 ) Resricion 2: Using he similar concep used in resricion, we ge: Resricion 3: 2 2 Var ( e ) = c (0) + c (0 (22) ) The produc of e and = e 2 is [ c ( 0) p + c2(0) ] [ c2 ( 0) p + c22(0) r ] e 2 r e Taking he expecaion, he covariance of he VAR residuals is: Ee Resricion 4: = c 0) c (0) c (0) (0) (23) e2 ( c22 The fourh resricion is he assumpion ha he ex-ane real ineres rae shock r has no long-run effec on he nominal ineres rae sequence n which is equaion (5). Now our 7 We can easily figure ou resricion and resricion 2 using he following marix algebra. Dropping he ime subscrips of he variables in (20), we can wrie i more compacly as follows: e = c i. e., ee = c c i. e., Eee = cic Var( e ) i. e., 0 0 Var( e 2 c = ) c 2 (0) (0) c c 2 22 (0) (0) 0 0 c c 2 (0) (0) c c 2 22 (0) (0) 3

21 job is o ransform his resricion ino he VAR represenaion so ha we can use his resricion o calculae he coefficiens we need. We will proceed as follows. We can rewrie he reduced form VAR, equaion (7), as follows: x = A( L) Lx + e i. e.,[ I A( L) L] x = e i. e., x = [ I A( L) L] e (24) For noaional convenience, le s denoe he deerminan of [I A(L)L] by D. Therefore, doing some algebra furher equaion (24) can be wrien as follows 8 : y A22 ( L) L = (/ D) r A2( L) L A2 ( L) L e A L L ( ) e 2 Using he definiion of A ij (L), we ge: y Σa22 ( L) L = (/ D) r Σa 2( L) L Σa2 ( L) L e Σa L L ( ) e 2 Now he soluion for y in erms of he curren and lagged values of { e } and { } is: e 2 y = (/ D){[ k+ k+ a22 ( k) L ] e + [ a2 ( k) L ] e2} k= 0 k= 0 (25) Replacing e and e 2 in he (25) wih and r from equaions (8) and (9), we ge he following equaion: p y = (/ D){[ k+ k+ a22 ( k) L ]( c(0) r + c2(0) r ) + [ a2 ( k) L ]( c2(0) p + c22 (0) r} k= 0 k= 0 8 The deails of he algebra are available in Enders (2003, p.334). 4

22 i. e., y [ = (/ D){[ k + k+ a22 ( k) L ] c(0) p + [ a2 ( k) L ]( c2(0) k= 0 k= 0 k+ k+ a22 ( k) L ] c2(0) r + [ a2 ( k) L ] c22 (0) r} k= 0 k= 0 (26) p + Therefore, using (26), he resricion ha he ex-ane real ineres rae shock { r } has no long-run effec on he nominal ineres rae n is: [ k+ k+ a22 ( k) L ] c(0) r + [ a2 ( k) L ] c2(0) r = 0 k= 0 k= 0 So our fourh resricion ha for all possible realizaions of he { r } sequence, ex-ane real ineres rae shocks { r } will have only emporary effec on he y sequence (he firs difference of nominal ineres rae) and n iself (he nominal ineres rae) is: [ k+ k+ 22 ( k) L ] c(0) + [ a2 ( k) L ] c2(0) = 0 k= 0 k= 0 a (27) We now have four equaions: (2), (22), (23) and (27) o ge four unknown values: c( 0), c2 (0), c2(0) andc22 (0). Once we have hese values of c ij (0) and he residuals of he VAR { } and { e }, he enire { e idenified using he following equaions: 2 p } and { r } sequences can be e = (0) (28) i c( 0) p i + c2 r i and e 2 i = c2( 0) p i + c22 (0) r i (29) As our objecive is o decompose he nominal ineres ino he ex-ane real ineres rae and inflaionary expecaion, we will sop a his poin. Since hroughou he model we assume ha he source of he change in he nominal ineres rae is he inflaionary 5

23 expecaion shock { p } and he ex-ane real ineres rae shock { r }, he cumulaion of hese effecs yields he level of he nominal ineres rae as a funcion of inflaionary expecaions and ex-ane real ineres rae shocks. This means ha he cumulaion of he effecs of hese srucural shocks give he permanen and he saionary componens of he nominal ineres raes. Adding he calculaed saionary componens o he mean of he ex-pos real ineres rae (mean of he difference beween he observed nominal ineres rae and he conemporaneous inflaion rae), herefore, gives us he ex-ane real rae. Once we have he ex-ane real ineres rae, inflaionary expecaions esimaes can be obained by subracing he esimaed ex-ane real ineres rae from he nominal ineres rae as he nominal ineres rae is he sum of hese wo raes. 2.3 Impulse Response Funcions 9 The impulse response funcions give us he opporuniy o visually observe he behavior of he nominal ineres rae in response o he inflaionary expecaion shock p and he ex-ane real ineres rae shock r. The pracical way o derive he impulse response funcions is o sar wih he reduced-form VAR model. Our wo-variable VAR model in sandard-form (reduced-form) wih he nominal ineres rae n and he real ineres rae r in marix noaion can be wrien as follows: n a = r a 0 20 a + a 2 a a 2 22 n r e + e 2 (30) Using he concep of Vecor Moving Average Represenaion (VMA), (30) can be wrien as follows: n n = + r r a a a a 2 i= i e e2 i (3) 9 For his economeric presenaion, we heavily depend on Enders (2003). 6

24 Now for our purpose, we will rewrie (3) in erms of p and r sequences. From he relaionship ha e e = B, we find: = ( n b2 r ) /( b2 2) b e2 = ( r b2 n ) /( b2b2) In marix noaion, we can rewrie he above equaions as follows: e e 2 = [/( b2b 2 )] b 2 b 2 n r (32) Combining (3) and (32), we ge: n n = + [/( b2 b r r 2 )] a a a 2 i= 0 2 a22 i b 2 b 2 n r For noaional convenience and simplificaion, as argued by Enders, (2003, p 305.), we can define he 2X2 marix φ i wih elemens φ jk (i) : φ i = [ A i /( b 2 b 2 )] b 2 b 2 Therefore, he moving average represenaion (3) can be wrien in erms p and r sequences as follows: n n = + r r φ( i) φ 2( i) i= 0 22 φ2 ( i) n φ ( i) r i i More compacly, we can wrie x = µ + i= 0 φ i i (33) 7

25 The coefficiens of φ i shows he effecs of inflaionary expecaions shocks, p, and exane real ineres rae shocks, r, on he enire ime pahs of nominal ineres rae sequences { n } and real ineres rae sequences { r }. More precisely, he elemens φ (i) are he impac mulipliers of he shocks of n i and r i on { n } and { r } sequences. For example, he coefficien φ (0) 2 is he insananeous impac of a one-uni change in he ex-ane real rae shock r on he nominal rae n. In he same way, updaing by one period, he elemens φ () and φ ( 22 ) represens he effecs of one uni change in he inflaionary expecaion shock p on he nominal ineres rae n and one uni change in jk he ex-ane real ineres rae shock r on he real ineres rae r respecively. The cumulaed effecs of he impulses in p and r can be obained by summing up he coefficiens of he impulse response funcions. For example, afer m periods, he effec of he ex-ane real ineres rae shock r on he nominal ineres rae n + m is φ 2 ( m ). Therefore, he cumulaed sum of he effecs of r on he { n } sequence is: m i= 0 φ2 ( i) As m approaches infiniy, he above summaion yields he long-run muliplier. Therefore, hese four se of coefficiens: φ i), φ ( i), φ ( i) andφ ( ) are called he impulse response ( i funcions, and ploing hese impulse response funcions agains ime gives us he behavior of nominal ineres rae series { n } and real ineres rae series { r } in response o inflaionary expecaions and he ex-ane real ineres rae shocks. 2.4 Variance Decomposiion Variance decomposiion is anoher very pracical way o ake a closer look a he behavior of he variables we used in he VAR model. In our model, wih he knowledge of he variance decomposiion, we will be able o figure ou he proporion of he 8

26 movemens in he nominal ineres rae sequence { n } and he real ineres rae sequence { r } due o he inflaionary expecaion shocks and he ex-ane real ineres rae shocks r. To calculae he variance decomposiion, we need o calculae he forecas errors of he VAR model in reduced-form. The sandard-form VAR in (30) can be wrien more compacly as follows: p x + e = A0 + A x Updaing he above equaion by one period and aking he condiional expecaion of, we ge: x + E x+ = A0 + A x One-sep ahead forecas error, herefore, can be defined as: x E x + = e+ Similarly, he wo-sep ahead forecas error ise Ae +, and in he same way, he m- sep ahead forecas error is: 2 n e + m + A e+ m + A e+ m A e+ (34) Nex we will describe hese forecas errors in erms of { } sequences raher han{ sequences. Using (33) o condiionally forecas isφ 0 +. In he same way, m-sep ahead forecas error x + m E x + m is: m + m E x m = φ i x + i= 0 + m i x +, he one-sep ahead forecas error e } Considering only on he { n } sequence, he m-sep ahead forecas error becomes: 9

27 n + m En+ m = φ ( 0) y+ m + φ() y+ m φ( m ) y+ + φ2 (0) z+ m + φ2 () z+ m φ2 ( m ) z+ 2 Therefore, denoing he m-sep forecas error variance of y + by σ n (m), we ge: m σ ( m) = σ [ φ (0) + φ () φ ( m ) ] + σ [ φ (0) n n r φ () φ ( m ) ] 2 Since all he values of φ jk (i) are necessarily nonnegaive, i is eviden from he above equaion ha he variance of he forecas error increases as he forecas horizon m 2 increases. Now decomposing he m-sep ahead oal forecas error σ n (m) due o he inflaionary expecaion shocks p and he ex-ane real ineres rae shocks r respecively, we ge: Proporion of forecas error due o shocks in p sequence: σ n [ φ(0) + φ() φ( m ) ] 2 σ ( m) n and he proporion of forecas error due o shocks in r sequence: σ n [ φ2 (0) + φ2 () φ2 ( m ) ] 2 σ ( m) n If ex-ane real ineres rae shocks r explain none of he forecas error variance of he nominal ineres rae { n } a al forecas horizons, we can say ha he { } sequence is exogenous o he ex-ane real rae. In such a siuaion, he nominal ineres rae { sequence would evolve independenly of he ex-ane real ineres rae shock and he real ineres rae { r } sequence. On he oher hand, if n r shocks explain all he forecas error variance in he { } sequence a all forecas horizons, he nominal ineres rae { would be enirely endogenous. In our bivariae VAR model, since we assume ha he ex- n r n n } } 20

28 ane real ineres rae shock r does no have a long-run effec on he nominal ineres rae, i is expeced ha in laer periods, he relaive conribuion of his shock on he nominal ineres rae will be almos zero. On he oher hand, he relaive proporion of inflaionary expecaions shocks p in explaining he flucuaion of he nominal ineres rae in subsequen periods will end o one. 2

29 CHAPTER 3 3. The Saionariy Properies of he Daa We use Canadian monhly daa for he nominal ineres rae ( n ) wih one-year, wo-year and hree-years o mauriy, and he seasonally adjused consumer price index (CPI) from 980: o 2002:2. The inflaion rae is calculaed as he annualized monhly rae of change of he CPI. Our required assumpions are ha he nominal ineres rae and he inflaion rae are boh inegraed of order one and ha he wo variables are co-inegraed (,-). The saionary properies of he nominal ineres rae, he real ineres rae and he inflaion rae are invesigaed using he Phillips-Perron es, he Augmened Dickey Fuller es (ADF), and he KPSS es. Boh he ADF es and he Phillip-Perron ess have he null hypohesis of non-saionariy (uni-roo) and he KPSS es has he null hypohesis of saionariy. The resuls of uni-roo ess are repored in Table and Table 2, and he resuls of co-inegraion es are repored in Table 3. Table : Uni-roo ess of he CPI and he Inflaion Rae. Variable ln(cpi) Uni Roo Tess ADF Tes Phillips-Perron Tes KPSS Tes (c,, 4) (c,, 5).7265(5) ln(cpi) (c,, 3) (c,, 4).674(4) 2 ln(cpi) (c,2 ) (c,3 ) (3) is he firs difference operaor and 2 is he second difference operaor. The bracke indicae he inclusion of a consan, c, rend,, and lag lengh. Lag lenghs for he ADF es are chosen by he Ng- Perron(995) recursive procedure and lag lenghs for he Phillips-Perron and KPSS es are chosen by he Schwer (989) formula. Consider he CPI firs. The Augmened Dickey Fuller (ADF) es canno rejec he null of uni roo a 0 percen level bu he Phillips-Perron (PP) es rejecs he null hypohesis of uni roo a % level of significance. The KPSS es rejecs he null hypohesis of saionariy a % level of significance. Therefore, we conclude his variable is non- 22

30 saionary. For he inflaion rae, he ADF es canno rejec he null hypohesis of uni roo a 0% level of significance and he KPSS es rejecs he null hypohesis of saionariy a % level of significance. However, once again he Phillip-Perron es rejecs he null of uni roo a he % level. The saionariy of he firs difference of he inflaion rae is suppored by all hree es procedures. Given hese mixed resuls, we do no rejec he mainained hypohesis ha he inflaion rae is inegraed of order one. To explore he saionary characerisic of he inflaion rae, we also check is auo correlaion funcions. We find ha he auo correlaion coefficien sars a a reasonably high value and i drops off as he lag lengh increases which suggess ha his ime series is non saionary. Table 2: Uni-roo ess of Nominal and Real Ineres Raes Variable One Year Raes Nominal Rae (n, ) Nominal Rae Real Rae ( n π, k ) Two- Year Raes Nominal Rae (n,2 ) Nominal Rae n π (, k ) Three- Year Raes Nominal Rae (n,3 ) Nominal Rae Real Rae( n π, k ) Uni Roo Tess ADF Tes Phillips-Perron Tes KPSS Tes (c,, 7) (c,, 7) 2.76 (7) (c, 6) (c, 6) (6) (c, 6) -4.80(c, 6).202 (6) (c,, 7) (c,, 7) (7) (c, 6) (c, 6) (6) (c, 4) (c, 4) 2.0 (4) (c,, 7) (c,, 7) (7) (c, 6) (c, 6) (6) (c, 4) (c, 4).862 (4) The brackes indicae he inclusion of a consan, c, rend,, and lag lengh. The resuls are robus o he c and assumpions. Lag lenghs are chosen by he Ng-Perron(995) recursive procedure. Recall ha i is assumed ha here is a uni roo in he nominal rae ( ). Table 2 indicaes ha for he one- year nominal ineres rae, neiher he ADF es nor he Phillips- n, k 23

31 Perron (PP) es can rejec he null hypohesis of uni roo a 5% level of significance, and he KPSS es rejecs he null hypohesis of saionariy a % level of significance. Therefore, we conclude his variable is non-saionary. For he wo-year nominal rae, he ADF canno rejec he null of uni roo a 0 percen, bu he PP rejecs he null a percen. The KPSS es rejecs he null hypohesis of saionariy a % level of significance. For he hree-year nominal rae, he ADF canno rejec he null hypohesis of uni roo a 0% bu he PP rejecs a percen while he KPSS rejecs he null hypohesis of saionariy a percen. The es procedures also suppor he hypohesis ha he firs difference of he nominal ineres raes is saionary for nominal ineres raes of all mauriies. As wih he inflaion daa, given he mixed resuls we do no rejec he hypohesis ha he nominal ineres raes are inegraed of order one Finally consider he real rae of ineres. We es his assumpion by esing he equivalen assumpion ha n, k π is saionary. Boh he ADF es and he Phillip- Perron es rejec he null hypohesis of uni roo a % level of significance for real ineres raes of all mauriies alhough he KPSS es does no suppor he null hypohesis of saionariy for any of hese real ineres raes. Since boh he ADF es and he Phillip- Perron es srongly suppor he hypohesis of saionariy, we conclude ha he real ineres rae is saionary. From he above findings we can conclude ha he nominal ineres rae and he inflaion rae are co-inegraed. To double check our conclusion, however, we also confirm ha he nominal ineres raes of all mauriies and he inflaion rae are co-inegraed in Table-3. We use he Johansen co-inegraion es for his purpose. The firs row presens he likelihood raio es for which he null hypohesis is ha hese variables are no coinegraed. The second row presens he es ha hese variables share a mos one coinegraing equaion. Table-3 demonsraes ha for all mauriies, he likelihood raio es saisic indicaes he variables are co-inegraed (, -). 24

32 Table 3: Coinegraion ess of Nominal Ineres Raes and Inflaion raes Variables Eigen value Likelihood Raio 5 Percen Criical Value Percen Criical Value Inflaion Rae Year Nominal Rae Inflaion Rae Year Nominal Rae Inflaion Rae Year Nominal Rae Variance Decomposiion and Impulse Responses As we have confirmed he daa saisfies all he required saionariy assumpions, our nex sep is o esimae he VAR model. We esimae hree differen reduced-form VAR models for 3 differen nominal ineres raes and corresponding real ineres raes 0. The wo key oupus of VAR esimaion ha are of ineres are he variance decomposiions and impulse response funcions. The decomposiion of variance presened in Table 4 allows us o measure he relaive imporance of inflaionary expecaions and he ex-ane real ineres rae shocks ha underlie nominal ineres rae flucuaions over differen ime horizons. I is eviden from Table 4 ha he proporion of he variance of nominal ineres raes of all mauriies explained by ex-ane real ineres rae shocks gradually approaches zero in he long-run which is he resul of he resricion ha ex-ane real ineres rae shocks have no permanen effec on he nominal ineres rae. As in S. Aman (996), boh ypes of shocks have been imporan sources of nominal ineres rae flucuaions. 0 We used he RATS program (Doan, 2000) o esimae he VAR models. In all he models we use a laglengh of 20 which was deermined on he basis of Likelihood Raio crierion and he Akaike Informaion crierion. 25

33 Table 4: Variance Decomposiion of Nominal Ineres Raes (in percen) Horizons One-Year Rae Two- Year Rae Three- Year Rae (Monhs) Inflaionary Ex-ane Real Inflaionary Ex-ane Real Inflaionary Ex-ane Expecaion Ineres Rae Expecaion Ineres Rae Expecaion Ineres shock shock shock shock shock shock Long-erm Real Rae Nex we presen he impulse responses of nominal ineres raes o he srucural shocks in Figure wherein he horizonal axis measures he number of monhs. Figure demonsraes ha he effec of ex-ane real ineres rae shocks disappear gradually while he effecs of inflaionary expecaions shocks on nominal ineres raes of all mauriies are fel more dominanly in he laer periods. This, as argued by S-Aman (996, p.2) may reflec he dynamics of he adjusmen of expecaions o a change in he rend inflaion. Our impulse response funcions are similar o hose of Goschalk (200) and S-Aman (996). 26

34 [[ Impulse Response of -Year Nominal Rae Inflaion Exp. Shock Ex-ane Rae Shock Impulse Response of 2-Year Nominal Rae Inflaion Exp Shock Ex-ane Rae Shock Impulse Response of 3-Year Nominal Rae Inflaion Exp. Shock Ex-ane Rae Shock Figure : Impulse Responses of Nominal Ineres Raes 3.3 The Ex-ane Real Ineres Rae and Inflaionary Expecaions To review, we esimae he ex-ane real ineres rae and inflaionary expecaions by firs compuing he effecs of ex-ane real rae shocks and inflaionary expecaions shocks on he nominal ineres rae. The cumulaion of hese shocks provides he saionary and permanen componens of nominal ineres raes. An esimae of he ex-ane real ineres rae is hen obained by adding he saionary componens o he mean of he difference beween he observed nominal ineres rae and he conemporaneous rae of inflaion i.e., 27

35 he mean of he ex-pos real ineres rae. Then, he measure of inflaionary expecaions One-Year Nominal Rae and Componens Nominal Rae Ex-ane Inflaion Expecaions M 983M0 984M03 985M05 986M07 987M09 988M 990M0 99M03 992M05 993M07 994M09 995M 997M0 998M03 999M M07 200M M Two-Year Nominal Rae and Expecaions Nominal Rae Ex-ane Inflaion Expecaions M03 985M03 986M03 987M03 988M03 989M03 990M03 99M03 992M03 993M03 994M03 995M03 996M03 997M03 998M03 999M M03 200M M03 Three-Year Nominal Rae and Componens Nominal Rae Ex-ane Inflaion Expecaions M03 985M03 986M03 987M03 988M03 989M03 990M03 99M03 992M03 993M03 994M03 995M03 996M03 997M03 998M03 999M M03 200M M03 Figure 2: Nominal Ineres Rae and Is Componens is calculaed by subracing he ex-ane real ineres rae from he nominal ineres rae. The esimaed ex-ane real ineres rae and he inflaionary expecaions of one-year, wo-year and hree-year along wih he corresponding nominal ineres raes are shown in Figure 2. We also repor he esimaed series of he one-year inflaionary expecaion wih he corresponding realized inflaion rae in Figure 3. I is clear from he figure ha he 28

36 [[ esimaed inflaionary expecaion series is less volaile han he realized inflaion rae. I is also noiceable ha expecaions lag he urning poins of acual inflaion. Inflaion Expecaions Vs Realized Inflaion Rae Inflaion Expecaions Inflaion M 983M0 984M03 985M05 986M07 987M09 988M 990M0 99M03 992M05 993M07 994M09 995M 997M0 998M03 999M M07 200M M Figure 3: Inflaionary Expecaions and he Inflaion Rae Recall ha we assume ha he inflaion forecas errors are inegraed of order zero I(0). As repored in Table 5, he ADF es saisic suppor his hypohesis a he one percen level of significance while he Phillips-Perron es suppor his hypohesis a he five percen level of significance respecively. Table 5: Uni Roo Tes of Inflaion Forecas Errors Variable Uni Roo Tess Inflaion Forecas Error ADF Tes Phillips-Perron Tes We use a lag-lengh of 3 for he ADF and he Phillips-Perron ess of he inflaion forecas error which was deermined on he basis of he Ng-Perron(995) recursive procedure. We did no add any consan or rend he regression. 29

37 CHAPTER 4 4. A Framework for Analyzing he Effecs of Moneary Policy Shocks We use a fully recursive VAR model o esimae he effecs of moneary policy shocks on various macroeconomic variables. The firs sep is o idenify policy shocks ha are orhogonal o he oher shocks in he model. To do his, we follow he approach of Kahn e al. (2002) and Edelberg and Marshall (996) o caegorize all he variables in our model ino hree broad ypes. The firs ype of variable (Type I variable) is he moneary policy insrumen. We use boh he moneary aggregae, MB, and he overnigh arge rae (OT) as he moneary policy insrumens. The second ype of variable (Type II variable) is he conemporaneous inpus o he moneary policy rule, ha is, he variables he cenral bank observes when seing is policy. In he basic model, we will include only one variablehe measure of inflaionary expecaions (EI) as he conemporaneous inpu o he policy process. In he diagnosic model, however, in addiion o EI, we will include oher variables, such as oupu (Y), he exchange rae (E) and unemploymen rae (UNPR) as conemporaneous inpus o moneary policy. The hird ype of variable (Type III variable) in he basic model is a variable ha responds o he change in policy. Since convenional heory reas he ex-ane real ineres rae as he channel hrough which changes in policy are ransmied o policy arges, we use hree alernaive ineres raes,, he one-year ex-ane real ineres rae, F, he wo-year forward ex-ane real ineres rae and F, he 2 3 hree-year forward ex-ane real ineres as our Type III variables 2. R 2 Assuming ha R and R2 are he one-year and he wo-year ex-ane real ineres raes, and F2 is he exane real forward rae of year wo, he relaionship beween hem (Bodie e. al., 2003) will 2 be ( + R 2) = ( + R)( + F2). From his equaion, he ex-ane real forward of year wo can be calculaed as ( + R2) F 2 = ( + R) 2. Using he similar echnique, he ex-ane real forward rae of year hree 2 ( + R3) can be calculaed as F 3 =, where R3 is he hree-year ex-ane real ineres. ( + R2) 30

38 Therefore our basic model includes hree differen variables:[ EI, M, R ]. We assume ha he cenral bank s feedback rule is a linear funcion of conemporaneous values of Type II variables (inflaionary expecaions) and lagged values of all ypes of variables in he economy. Tha means ha ime s change of moneary policy of he Bank of Canada is he sum of he following hree hings: he response of he Bank of Canada s policy o changes up o ime - in all variables in he model (i.e., lagged values of Type I, Type II and Type III variables), he response of he Bank of Canada s policy o ime changes in he non-policy Type II variable (inflaionary expecaions in he basic model), and he moneary policy shock. Therefore, a moneary policy shock a ime is orhogonal o: changes in all variables in he model observed up o ime -, and conemporaneous changes in he Type II nonpolicy variable (inflaionary expecaions in he basic model). So, by consrucion, a ime moneary policy shock of he Bank of Canada affecs conemporaneous values of Type III variables (i.e., he real ex-ane ineres raes of differen mauriies in he basic model) as well as all variables in he laer periods 3. The nex wo secions of his chaper describe he deails of he fully recursive VAR model, he echnique of how o idenify he wo porions of moneary policy- he feedback rule and exogenous moneary policy shocks, and how o ge he impulse responses of moneary policy shocks. 4.2 The Recursive VAR Model o Esimae he Moneary Policy Shock Our basic VAR sysem consiss of hree equaions, and each equaion in he sysem akes one of he hree variables- inflaionary expecaions (EI), money supply (M) and he exane real ineres rae (R) o be is dependen variable. In he srucural VAR sysem, for 3 This framework assumes ha he cenral concern of he Bank of Canada in he seing of policy is inflaionary expecaions because of he lag beween changes in is insrumen and he impac on is objecive. Unless he bank arges inflaionary expecaions direcly, i canno hope o conrol inflaion effecively. 3