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1 ISSN Economics and Business Review Volume (5) Number CONTENTS ARTICLES A perspecive on leading and managing organizaional change Sanley J. Smis, Dawn E. Bowden Alernaive configuraions of firm-level employmen sysems: evidence from American companies Bruce E. Kaufman, Benjamin I. Miller How eam leaders can improve virual eam collaboraion hrough rus and ICT: A concepual model proposiion David Kauffmann Inernaional rade in differeniaed goods, financial crisis and he graviy equaion Udo Broll, Julia Jauer Tax revenues and aging in ex-communis EU counries Mihai Muascu, Maciej Cieślukowski The analyics of he New Keynesian 3-equaion Model Jean-Chrisophe Pouineau, Karolina Sobczak, Gauhier Vermandel Invesmens and long-erm real ineres rae in Poland. Sudy of invesmen srucure, curren accoun and heir correlaion wih long-erm real ineres raes Jakub Krawczyk, Szymon Filipczak BOOK REVIEWS Paweł Marszałek, Sysemy pieniężne wolnej bankowości. Koncepcje cechy, zasosowanie [Free Banking Moneary Sysems. Conceps, Characerisics, Applicaion], Wydawnicwo Uniwersyeu Ekonomicznego w Poznaniu, Poznań 204 (Bogusław Pierzak) Ewa Mińska-Sruzik, Od eksporu do innowacji. Uczenie się przez ekspor polskich przedsiębiorców [From Expor o Innovaion Learning by Exporing in Polish Enerprises], Difin, Warszawa 204 (Jan Rymarczyk) Poznań Universiy of Economics Press

2 Ediorial Board Ryszard Barczyk Wiold Jurek Cezary Kochalski Tadeusz Kowalski (Edior-in-Chief) Henryk Mruk Ida Musiałkowska Jerzy Schroeder Jacek Wallusch Maciej Żukowski Inernaional Ediorial Advisory Board Udo Broll School of Inernaional Sudies (ZIS), Technische Universiä, Dresden Wojciech Florkowski Universiy of Georgia, Griffin Binam Ghimire Norhumbria Universiy, Newcasle upon Tyne Chrisopher J. Green Loughborough Universiy John Hogan Georgia Sae Universiy, Alana Bruce E. Kaufman Georgia Sae Universiy, Alana Seve Leza Corporae Governance Business School Bournemouh Universiy Vicor Murinde Universiy of Birmingham Hugh Scullion Naional Universiy of Ireland, Galway Yochanan Shachmurove The Ciy College, Ciy Universiy of New York Richard Sweeney The McDonough School of Business, Georgeown Universiy, Washingon D.C. Thomas Taylor School of Business and Accounancy, Wake Fores Universiy, Winson-Salem Clas Wihlborg Argyros School of Business and Economics, Chapman Universiy, Orange Jan Winiecki Universiy of Informaion Technology and Managemen in Rzeszów Habe G. Woldu School of Managemen, The Universiy of Texas a Dallas Themaic Ediors Economics: Ryszard Barczyk, Tadeusz Kowalski, Ida Musiałkowska, Jacek Wallusch, Maciej Żukowski Economerics: Wiold Jurek, Jacek Wallusch Finance: Wiold Jurek, Cezary Kochalski Managemen and Markeing: Henryk Mruk, Cezary Kochalski, Ida Musiałkowska, Jerzy Schroeder Saisics: Elżbiea Gołaa, Krzyszof Szwarc Language Edior: Owen Easeal IT Edior: Pior Solarski Copyrigh by Poznań Universiy of Economics, Poznań 205 Paper based publicaion ISSN POZNAŃ UNIVERSITY OF ECONOMICS PRESS ul. Powsańców Wielkopolskich 6, Poznań, Poland phone , , fax wydawnicwo@ue.poznan.pl posal address: al. Niepodległości 0, Poznań, Poland Prined and bound in Poland by: Poznań Universiy of Economics Prin Shop Circulaion: 300 copies

3 Economics and Business Review, Vol. (5), No. 2, 205: 0 29 DOI: /ebr The analyics of he New Keynesian 3-equaion Model Jean-Chrisophe Pouineau 2, Karolina Sobczak 3, Gauhier Vermandel 4 Absrac : This paper aims a providing a self conained presenaion of he ideas and soluion procedure of New Keynesian Macroeconomics models. Using he benchmark 3 equaion model, we inroduce he reader o an inuiive, saic version of he model before incorporaing more echnical aspecs associaed wih he dynamic naure of he model. We hen discuss he relaive conribuion of supply, demand and policy shocks o he flucuaions of aciviy, inflaion and ineres rae, depending on he key underlying parameers of he economy. Keywords : dynamic IS curve, impulse response analysis, New Keynesian Macroeconomics, New Keynesian Phillips Curve, oupu gap, Taylor rule. JEL codes : C63, E2, E32, E52. Inroducion Keynesian ideas reurned o he forefron of academic research in he mid 90 s in new clohes o address quesions relaed o unemploymen, economic flucuaions and inflaion. This followed a weny year period ha winessed he dominaion of new classical ideas on boh moneary and real macroeconomics quesions. Before conribuing o he building of wha is now considered as he workhouse of modern macroeconomics [Carlin and Soskice 204], he New Keynesian School proposed in he 80 s a series of models aimed a providing microeconomic foundaions o price and/or wage rigidiy 5 and a showing Aricle received 5 April 204, acceped 9 February CREM-CNRS, Universiy of Rennes, Faculy of Economics, 7 place Hoche, Rennes cedex, France, corresponding auhor: jean-chrisophe.pouineau@univ-rennes.fr. 3 Poznań Universiy of Economics, Deparmen of Mahemaical Economy, Poznań, Poland. 4 CREM-CNRS, Universiy of Rennes, Faculy of Economics, Rennes, France. 5 On New Keynesianism, is hisory, developmen and significance for modern economics, see for example Bludnik [2009] or Romer [993].

4 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian ha his key feaure of he real world can be explained in a seing wih opimizing agens wih marke power. An imporan breakhrough was abou 5 years ago, wih he papers of Goodfriend and King [997] and Clarida, Gali, and Gerler [999]. These conribuions inroduced a framework mixing Real Business Cycle feaures wih nominal rigidiies. This seing now forms he basic analyical srucure of conemporaneous macroeconomic models as exemplified by Woodford [2003] or Gali [2008]. Besides new ideas and a new modelling sraegy his New Keynesian Synhesis (NKS) has adoped new soluion procedures ha may appear cumbersome o non-specialiss. Because of heir recursive srucure NKS models do no admi a closed form soluion bu should be solved by borrowing procedures developed for he analysis of sochasic discree ime dynamics sysems. 6 The aim of his paper is o provide a compac and self conained presenaion of he srucure and of he sandard soluion procedure of he basic NKS framework known as he hree equaion model. We paricularly separae he main ideas conveyed by his model, using a saic version of he reference framework, from he echnical aspecs of he soluion procedure. In he presenaion we emphasise he qualiaive similariies beween he simple graphical analysis of he saic model and he Impulse Response Funcions (IRFs) of he model following he occurrence of exogenous shocks. We hen illusrae he key feaures of his model regarding he analysis of business cycles characerisics. The paper is organized as follows: In he firs secion we inroduce he general srucure of a benchmark NKS model ha combines (he log linear versions of) a Philips curve, an Euler equaion and a moneary policy (Taylor) rule. 7 In he second secion we se a simple saic version of he model o obain closed form soluions for he key macroeconomic variables and o provide he reader wih a graphical analysis of he consequences of demand and supply shocks. In he hird secion we inroduce he Blanchard-Kahn soluion procedure o ge IRFs and dynamic reacions of he model around a sable seady sae following exogenous supply demand and policy shocks. This hird secion is also devoed o a discussion of business cycles characerisics of he model. Secion four concludes.. The 3 equaion new Keynesian model The New Keynesian Synhesis (NKS) mixes he mehodology of Real Business Cycles (RBC) wih nominal and real rigidiies o characerise shor run macroeconomic developmens. More paricularly he NKS seeks o explain he macroeconomic shor run evoluion of an economy subjec o real and moneary 6 For an up o dae exhausive inroducion o his lieraure see Miao [204]. 7 In he appendix we provide he micro foundaions of he framework used in his paper.

5 2 Economics and Business Review, Vol. (5), No. 2, 205 shocks and o replicae business cycle saisics. The core represenaion of his synhesis has given rise o wha is called he 3-equaion model as he basic NKS seing reduces o a sysem of hree equaions corresponding o an AS- AD model. Firs, he AS curve is represened by he New Keynesian Phillips curve ha relaes inflaion o he oupu gap. Second, he AD componen of he model combines a dynamic IS curve (ha relaes he evoluion of he oupu gap o he ineres rae) and a MP (Moneary Policy) schedule (ha describes how he nominal ineres rae is se by he cenral bank following flucuaions in he oupu gap and in he inflaion rae. This model is based on agens micro founded decision rules where consumers maximize heir welfare subjec o an ineremporal budge consrain and where firms maximize heir profi, subjec o nominal rigidiies, characerising he imperfec adjusmen of prices on he goods marke. For convenience he micro foundaions of his model and he derivaion of he log-linear sysem are presened in appendix. These equaions in urn deermine hree main variables of ineres in a closed economy, namely he oupu gap (ˆ y ) which is he gap beween he effecive oupu and poenial oupu, he inflaion rae ( ˆ ) and he nominal ineres rae (ˆ r ). Formally, he model is defined as follows: The New Keynesian Philips Curve (PC) links curren inflaion ( ˆ ) o expeced fuure inflaion ( E { ˆ + }), o he curren oupu gap (ˆ y ) and o an exogenous supply shock ha akes he form of a cos push shock ( ε S ): 8 { } S ˆ = βe ˆ + κyˆ + ε. () + As shown in he appendix his relaionship comes from he aggregaion of he supply decision of firms ha have marke power and can re-opimize heir selling price wih disconinuiies (i.e. nominal rigidiies hey canno modify heir selling price a any poin in ime). Thus hey se he selling price of heir produc depending on hree main crieria. (i) The firs crierion is anicipaed inflaion: as firms canno re-opimize heir price, hey ake ino accoun fuure inflaion o se heir price oday. (ii) The second erm is he oupu gap: when firms se heir price hey ake ino accoun he difference beween supply and demand so ha inflaion reflecs sresses on he goods marke: firms increase heir prices during periods of expansion (ˆ y > 0) whils hey decrease i during recessions (ˆ y < 0). (iii) Finally, his relaion incorporaes a cos push erm ε S (such ha ε S > 0 may indicae an increase in raw maerials or energy price in he economy). In a sandard way we assume ha ε S is an AR() process: 9 S S S S S 2 ε = ρ ε + η wih η ~ N(0, σ ) and iid. The New Keynesian Phillips Curve is S 8 In he paper all parameers are posiive. 9 This assumpion is commonly adoped in he lieraure o characerize exogenous shocks [see for example, Gali 2008 for a discussion].

6 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 3 derived from he Calvo model [983] which combines saggered price-seing by imperfecly compeiive firms. As presened in he appendix, he Calvo approach assumes ha in each period, only a fracion θ of firms, randomly chosen, can rese heir selling prices 0. Using his assumpion, Clarida, Gali, and Gerler [999] show ha he Phillips curve hen akes a paricularly simple form in which inflaion depends on he curren gap beween acual and equilibrium oupu as in he sandard Phillips curve bu on expeced fuure inflaion raher han on pas inflaion. The dynamic IS curve is a log linearizaion of he Euler bond equaion ha describes he ineremporal allocaion of consumpion of agens in he economy: D yˆ = { ˆ } ( ˆ { ˆ E y+ r E + } ) + ε. (2) σ rae ( { }), o he expeced fuure oupu gap ( { } This relaion plays he same role as he IS curve in he IS-LM model. As shown in he appendix i comes from he ineremporal opimizaion of he welfare index of a represenaive consumer subjec o is budge consrain. Once aggregaed over consumers and log-linearized around he seady sae his relaion can be expressed in erms of he oupu gap (ˆ y ). The dynamic IS curve links he curren oupu gap o he difference beween he real ineres ˆ E ˆ E y ˆ + ) and o an ex- r + D ogenous preference shock ε (ha represens a demand shock henceforh). The demand shock is described in a sandard way by AR() process of he form: D D D D D 2 ε = ρ ε + η wih η ~ N(0, σ D) and is iid. The Moneary Policy schedule (MP) is based on he Taylor rule. I links he nominal ineres rae (ha is conrolled by moneary auhoriies) o he inflaion rae and o he oupu gap: y R r ˆ = ϕ ˆ + ϕ yˆ + ε. (3) In his equaion variable ε R denoes a moneary policy shock ha follows R R R R R 2 an AR() process of he form: ε = ρ ε + η wih η ~ N(0, σ R) and iid. This shock idenifies moneary policy decisions which imply deviaions from he sandard Taylor rule such as unconvenional measures or o reshape he inflaion expecaions in he medium run. This MP schedule aims a replacing he sandard LM curve commonly found in he sandard AS-AD model. I proposes an up-o-dae descripion of he behaviour of cenral banks ha conrol a shor run nominal ineres rae insead of a moneary aggregae [Clarida, Gali, and Gerler 999]. 0 Baranowski e al. [203] propose an endogenous mechanism. In appendices, we provide an ineres rae smoohing wih smoohing parameer ρ. In his secion we neglec hese feaures such ha ρ = 0.

7 4 Economics and Business Review, Vol. (5), No. 2, 205 This 3-equaion model is a sylised shorcu ha encompasses supply and demand relaions o deermine how he hree main macroeconomic variables of ineres (he oupu gap, he inflaion rae and he nominal ineres rae) reac o exogenous supply and demand shocks. In his shor presenaion we ignore more recen developmens associaed wih he inroducion of financial fricions ha give rise o an acceleraion phenomenon [see for example Pouineau and Vermandel 205a, b]. 2. The soluion o a saic version of he model This second secion simplifies he previous sysem () (3) o convey he main ideas of he NKS model. Following Bofinger, Mayer, and Wollmershäuser [2006] and Pouineau and Vermandel [205b] we neglec he dynamic aspecs of he model and we concenrae on a saic version of he framework. 2 This is helpful o obain he reduced form for he main variables of ineres and o undersand inuiions regarding he working of he model using ools similar o he IS-LM and AD-AS frameworks. To obain he saic version of he model we firsly assume ha he moneary auhoriies are perfecly credible in he conduc of moneary policy so ha he privae secor expecs ha hey reach he argeed inflaion rae in fuure, namely ha E { ˆ + } = 0, where 0 is he long-run argeed rae of inflaion. Secondly, we assume ha he economy is very close o full employmen so ha he auhoriies are able o close he oupu gap in he fuure, namely ha E { ˆ + } = y 0. Thus he gap beween he real ineres rae and he naural ineres rae disappears. In his case we can express he moneary policy rule in erms of he real ineres rae. Imposing hese resricions, he simplified saic framework gives: = 0 + κy + ε S, (4) y = y 0 σr + ε D, (5) r = ϕ ( 0 ) + ϕ y y + ε R. (6) In equilibrium he values of he oupu gap y*, he inflaion rae * and he ineres rae r* soluion o he model (4) (6) are a linear combinaion of exogenous shocks: 2 y0 σϕ S σ R D y* = ε ε + ε, Ω Ω Ω Ω κ σκ κ Dynamic aspecs will be reinroduced in Secion 3.

8 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 5 Ω Ω Ω Ω κ σκ R κ D Ω κσϕ S * 0 = y0 ε + ε + ε, Ω Ω Ω Ω y y ( ϕ κ + ϕ ) y0 ϕ κ + ϕ D ϕ S R r* = + ε + ε + ε, Ω Ω Ω Ω where Ω = + σ(ϕ κ + ϕ y ). The adjusmen of he oupu gap, he inflaion rae and he nominal ineres rae following alernaive shocks is summarized in Table. As shown in he firs column a supply shock leads o a decrease in he oupu gap, (aciviy decreases below is naural level), and o an increase in he inflaion rae and in he ineres rae. As shown in he second column a demand shock leads o an increase in he oupu gap, (aciviy increases), in he inflaion rae and he ineres rae. As observed, he reacions of he variables of ineres o exogenous shocks are clearly affeced by he value of he parameers of he ineres rae rule of he auhoriies (ϕ and ϕ y ). Table. Reduced form of he saic model Supply Shock ε S Demand Shock ε D Moneary Shock ε R σϕ Oupu gap y / ε < 0 Ω 0 Ω > σ < Ω 0 Inflaion / ε + σϕ Ω y κ σκ > 0 > 0 < 0 Ω Ω Ineres rae r / ε y ϕ ϕ κ + ϕ > 0 > 0 Ω Ω Ω > 0 To undersand more clearly he reacion of he economy o supply and demand shocks we refer he reader o figures and 2. Graphically he model can be represened as consising of wo panels: in he lower panel of each figure, he IS-MP block (equaions (5) and (6)) presened in he (y, r) space focuses on demand side aspecs and can be reaed as a New Keynesian represenaion of he IS-LM framework; in he upper panel he AD-PC block presened in he (y, ) space deermines he global equilibrium of he economy and can be reaed as a New Keynesian represenaion of he AD-AS framework. The PC curve is given by equaion (4) and he AD curve is obained by combining equaions (5) and (6) and is defined in equaion (7), y0 σϕ D y = ( 0) + ε y y y. (7) + σϕ + σϕ + σϕ

9 6 Economics and Business Review, Vol. (5), No. 2, 205 The consequences of he demand shock are presened in Figure. The firs panel displays he adjusmen of he inflaion rae and he oupu gap. The second panel displays he adjusmen of he demand side, accouning for he reacion of he cenral bank o he shock. PC B C 0 A C AD AD y 0 y C y B y r MP r C C MP B IS r 0 A IS y 0 y C y B y Figure. Demand shock To undersand he main differences beween he wo panels one has jus o remember ha he IS curve (5) moves one for one wih a demand shock whils he demand curve moves by less han one. Thus, aking poin A as he iniial equilibrium of he model a posiive demand shock moves he IS curve from IS o IS in he lower panel, which in urn, ignoring he reacion of he cenral bank, moves he demand schedule o he doed line. As he emporarily equilibrium B implies an increase in he inflaion rae he cenral bank reacs by increasing he ineres rae for any value of he oupu gap. Thus, he MP curve in he lower panel moves lef from MP o MP. This, in urn, leads he aggre-

10 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 7 gae demand curve o move o he lef from he doed line o AD. In he final equilibrium C, he evoluion of aggregae demand from AD o AD, ha combines boh he iniial demand shock and he moneary reacion, is less han proporional o he demand shock. Furhermore, wih he reacion of he cenral bank he increase of inflaion is dampened. Finally he posiive demand shock leads o an increase in he oupu gap, an increase in inflaion and a rise in ineres rae, as summarized in Table. PC PC B 0 B A y B y 0 AD y r MP MP r B r 0 B A IS y B y 0 Figure 2. Supply shock y The consequences of he supply shock are presened in Figure 2. In his example he supply shock is a posiive inflaion shock (ha corresponds o a decrease in he supply of goods ). Following his supply shock he Phillips curve moves upwards o he lef in he (y, ) space. This shock leads o an increase in he rae of inflaion and he cenral bank reacs by raising he ineres rae. Graphically he reacion of he cenral bank means increasing he ineres rae for any value of he oupu gap so ha he MP curve moves lef o MP in he

11 8 Economics and Business Review, Vol. (5), No. 2, 205 lower panel of Figure 2. Once all he adjusmens have been implemened he final equilibrium lies a poin B which is characerized by a negaive oupu gap (namely aciviy falls below is naural value), an increase of he inflaion rae over is argeed value and a poin B an increase in he ineres rae (needed o dampen par of he inflaion consequences of he supply shock). Finally, he balance beween he consequences of he shocks on aciviy and inflaion depends on he slope of he demand curve which, in urn, is affeced by he reacion of he cenral bank o inflaion rae and oupu gap developmens. A more conservaive cenral bank (namely a cenral bank ha pus a higher weigh on inflaion and a lower weigh on he oupu gap) makes he slope of he demand curve of he economy flaer in he upper panel of figures and 2, which ranslaes ino lower flucuaions in he ineres rae bu o a higher variabiliy of he oupu gap. Conversely if he sance of he cenral bank reacion is more sensiive o he oupu gap and less sensiive o inflaion hen he MP and AD curves become seeper and shocks have a lower impac on aciviy and a higher impac on inflaion. 3. The fully-fledged model In he dynamic version of he model () (3), each period corresponds o a quarer. As he fully fledged model does no have a closed form soluion i mus be simulaed around a sable seady sae. The soluion procedure, based on he Blanchard-Kahn [980] approach, 3 requires he choice of numerical values for he parameers of he model in order o compue Impulse Response Funcions (IRFs hereafer ) and he corresponding variance decomposiion of he hree variables of ineres of he model. 3.. The soluion procedure The soluion procedure inroduced by Blanchard and Kahn [980] is based on marix calculus and is aimed a selecing a unique sable dynamic pah o describe he reacion of he variables following he occurrence of exogenous shocks. The Blanchard-Kahn condiion defines a necessary crierion o ge his resul hrough he equaliy beween he number of forward variables and he number of unsable eigenvalues. Pracically he problem of he eigenvalues ranslaes ino he problem of appropriae values of he srucural parameers of he model or heir combinaions. To be solved he model firs has o be 3 In his paper we adoped he Blanchard-Kahn approach for solving he model, given is anerioriy and populariy in lieraure. However, he reader should be aware of he exisence of oher mehods inroduced by Klein [2000] and Sims [2000]. Miao [204] offers a nice comparison beween hese hree approaches.

12 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 9 wrien in a sae-space represenaion. For our linear model () (3), defining Ξ = ( + y σ ϕ + κ ϕ ), his represenaion is: { } S yˆ ˆ Ξ σ βϕ E y βσ + + { Ξ σε + = ˆ y ( ) ˆ +. (8) D S R σκ κ β σ ϕ E + } βσ σβε + βε βε The Blanchard-Kahn condiion saes ha here are as many eigenvalues of σ βϕ he marix Z T = greaer han one in modulus as here are y σκ κ + β( σ + ϕ ) non-predeermined variables. Since here are wo forward-looking variables in he model () (3) (ˆ y and ˆ ), we know ha here should be exacly wo eigenvalues ouside he uni circle o ge one unique sable rajecory of each of he model s variable around he seady sae. Given he form of he marix Z T, he Blanchard-Kahn condiion for he model () (3) reduces o he following relaion: κ(ϕ ) + ( β)ϕ y > 0. Table 2. Calibraion of parameers Parameer Value Descripion β 0.99 discoun facor σ relaive risk aversion ε 6 elasiciy of subsiuion amongs goods φ elasiciy of marginal disuiliy wih respec o labour ϕ.5 influence of inflaion rae in he ineres rae rule ϕ y 0.5/4 influence of oupu gap in he ineres rae rule ρ S 0.90 persisency of supply shock ρ D 0.90 persisency of demand shock ρ R 0.40 persisency of moneary policy shock θ 3/4 probabiliy of reaining old price Source: Auhors synhesis. This condiion reduces o he choice of appropriae values for he parameers of he model. A sufficienly relevan condiion for he previous one o be hold is ha he moneary auhoriies should respond more han proporionally o inflaion developmens (namely, ϕ > ) according o he Taylor principle. In his case a rise in inflaion leads o a more han proporional rise in nominal ineres causing an increase in real ineres raes ha affecs agens economic decisions and hus he real macroeconomic equilibrium of he model. The

13 20 Economics and Business Review, Vol. (5), No. 2, 205 choice of parameers is herefore a main feaure of he analysis as i mus boh represen economic feaures and conribue o he Blanchard-Kahn condiion. As presened in Table 2, following Galí [2008], we use a calibraion of he model parameers ha is commonly seleced in he lieraure. The inra-emporal elasiciy beween inermediae goods is se a 6 which implies a seady sae mark-up of 20 % in he goods marke corresponding o wha is observed in main developed economies. The sensiiviy of he inflaion rae o changes in he marginal cos is equal o 0.3 roughly. The value of he discoun facor se a 0.99 implies he seady sae quarerly ineres rae equal o one and he seady sae real reurn on financial asses of abou 4 percen per year. Average price duraion amouns o hree quarers which is consisen wih empirical evidence. 4 The values of coefficiens in he ineres rae rule (3) are consisen wih variaions observed in he daa on inflaion and he ineres rae given in he annual raes. 5 Because in our model periods are inerpreed as quarers he oupu gap coefficien has o be divided by Impulse-response analysis The mechanisms by which random innovaions change ino endogenous variables flucuaions may be illusraed by impulse response funcions (IRFs). Each IRF isolaes he impac of a paricular shock hroughou he economy. To documen he response of aciviy, inflaion and nominal ineres we sequenially describe he consequences of a supply, demand and ineres rae shock. The demand shock: Figure 3 documens he consequences of a % posiive demand shock. As observed he increase in goods demand for leads o an in- Benchmark regime is: ϕ =.5, ϕ y = 0.5/4, inflaion arge regime: ϕ =.7, oupu gap regime: ϕ y = 0.8/4 Figure 3. Effecs of a % demand shock 4 Galí, Gerler, López-Salido [200] and Sbordone [2002] provide esimaions based on aggregae daa. Galí [2008] poins also o some micro evidence. 5 These values were originally proposed by Taylor [999] as a good approximaion of he moneary policy conduced by he Federal Reserve in years when he head of he USA cenral banking sysem was Alan Greenspan. His moneary policy decisions largely followed sandard Taylor rule recommendaions.

14 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 2 crease in aciviy so ha he oupu gap becomes posiive. However, as producion overshoos is naural value his rise in aciviy increases he inflaion rae. Since boh he oupu gap and inflaion rae increase he cenral bank should reac by raising he nominal ineres rae. According o he Taylor principle he nominal ineres rae increases more han proporionally o inflaion developmens o affec real exchange raes. This policy however is no sufficien o close he posiive oupu gap immediaely or o dampen he inflaion rae. The effec of moneary policy should be assessed over ime on he oupu gap (aciviy goes back o is naural value as ime passes) and on he rae of inflaion (ha converges owards is naural value). The adjusmen ime pah is affeced by he parameer value of he Taylor rule. As presened in Figure 3 a higher concern for inflaion or oupu gap reduces he volailiy of boh aciviy and inflaion. Thus, sricer moneary policy leads o more moderae responses of variables o he demand shock. The supply shock: Figure 4 represens he consequences of a % increase in inflaion (i.e. he negaive supply shock acs as an increase in he price of raw maerials or energy ha increases he real marginal cos of producion). This shock has a direc impac on inflaion ha rises and overshoos is argeed value. As a consequence moneary auhoriies should reac according o he Taylor principle by raising he ineres rae. Since he increase in he nominal ineres rae is higher han he rae of inflaion, he real rae rises. This, in urn, negaively affecs oupu ha decreases under is naural value. However, as ime passes, he increase in he ineres rae dampens inflaion. Finally, he oupu gap goes back o is seady sae value whils he inflaion rae reaches is argeed value. As previously for he demand shock, he ime pah of variables is affeced by he parameer values of he Taylor rule. A higher concern for oupu gap (as represened wih inflaion arge IRF) leads o weaker responses of real variables and sronger responses of nominal variables. Inversely a higher concern for inflaion leads o sronger responses of real variables and weaker responses of inflaion and nominal ineres rae. Benchmark regime is: ϕ =.5, ϕ y = 0.5/4, inflaion arge regime: ϕ =.7, oupu gap regime: ϕ y = 0.8/4 Figure 4. Effecs of a % supply shock

15 22 Economics and Business Review, Vol. (5), No. 2, 205 Benchmark regime is: ϕ =.5, ϕ y = 0.5/4, inflaion arge regime: ϕ =.7, oupu gap regime: ϕ y = 0.8/4 Figure 5. Effecs of % a moneary policy shock The moneary policy shock: Figure 5 documens he consequences of a % increase in he nominal ineres rae (corresponding o a 25 basis poin increase in he exogenous shock measured in quarerly erms as presened in he figure). Because of sicky prices he iniial increase in he nominal ineres rae implies a corresponding increase in he real ineres rae a he iniial period. This depresses demand in he economy as i leads households o delay heir consumpion hrough ineremporal consumpion smoohing as repored in he Euler condiion. Since aciviy is demand deermined, firms producion decreases. In he meanwhile he drop in demand generaes deflaion. The economy recovers overime, since, according o he Taylor rule, a decrease in boh aciviy and in he inflaion rae leads o a reducion in he nominal ineres rae afer he iniial period Business cycle saisics IRF analysis aims a isolaing he effec of a paricular shock on he dynamics of endogenous variables. However, in real life siuaions, shocks occur boh randomly and joinly o affec he macroeconomic equilibrium. The combined effec of supply and demand shocks over ime is capured by hisorical variance analysis. The aim of his exercise is boh o evaluae he relaive conribuion of each ype of shock on he moion of macroeconomic variables over ime and o appreciae how a paricular design for economic policy may dampen he effec of one paricular ype of shock. Table 3 shows he variance decomposiion of aciviy, inflaion and he nominal ineres rae under he benchmark calibraion of Table 2 and evaluaes he sensiiviy of he benchmark resuls o alernaive values of key behavioural and policy parameers of he model. In he firs panel of Table 3 (Benchmark calibraion), supply side shocks (namely price mark- up shocks) explain mos of he oupu variabiliy leaving only a marginal conribuion (around 4%) o demand and ineres rae shocks. In conras he variabiliy of he inflaion rae is mainly explained by demand and moneary policy innovaions. Finally, around 2/3 of ineres rae variabiliy is explained by real supply side shocks.

16 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 23 Table 3. Variance decomposiion (in %) Supply Demand Moneary Policy Benchmark Producion Inflaion Ineres rae Sicky economy θ = 0.95 Producion Inflaion Ineres rae Quasi-flexible economy θ = 0.0 Producion Inflaion Ineres rae Aggressive Moneary Policy ϕ = 2.5 Producion Inflaion Ineres rae Oupu-oriened moneary policy ϕ y = Producion Inflaion Ineres rae In panel 2 (sicky economy) and panel 3 (quasi flexible economy) we evaluae he sensiiviy of he benchmark resuls o alernaive assumpions regarding nominal rigidiies. In he sicky economy only 5% of he oal number of firms can rese heir price each period. Whils in he quasi flexible siuaion 99% of he oal number of firms rese heir prices each quarer. The main consequences can be assessed wih regard o he conribuion of supply side shocks o inflaion and ineres raes. Remarkably supply side shocks have no effec on eiher inflaion or ineres raes when prices are flexible. In conras he flucuaions of he oupu gap are more sensiive o ineres rae shocks whils he effec of demand shocks on aciviy is almos unobsevable. In panel 4 and 5 we evaluae he sensiiviy of he benchmark resuls o alernaive assumpion regarding he conduc of moneary policy. When a moneary policy is more aggressive in erms of inflaion (panel 4) i dampens he effec of demand shocks on aciviy (and in conras makes oupu developmen

17 24 Economics and Business Review, Vol. (5), No. 2, 205 more sensiive o supply shocks) and reinforces he impac of demand shocks on inflaion (whils, conversely, i dampens he impac of supply side shocks on his variable). Finally, his policy has almos no noiceable effec on he relaive conribuion of shocks on ineres rae developmens. In panel 5 an oupu oriened moneary policy increases he effec of supply shocks on inflaion and ineres rae whils leaving he relaive conribuion of shocks on aciviy almos unchanged. The resuls obained in hese las wo panels may serve as simple guideline o deermine he naure of moneary policy depending on boh is objecive and he origin of shocks. If an economy is mainly affeced by price mark-up shocks moneary policy should be more closely oriened owards oupu developmens. As his policy is able o dampen he effec of supply shocks on inflaion, whils having no noiceable effec on aciviy, moneary auhoriies are able o sabilise prices more easily. In conras if he economy is affeced by demand shocks he auhoriies have o use arbirage because a more aggressive policy agains inflaion dampens he impac of demand shocks on aciviy whils i increases he impac of demand shocks on inflaion. Conclusions In his paper we have described in a concise way he main ideas conveyed by he 3 equaion New Keynesian model and he main elemens of he soluion procedure required o analyse he dynamics of he model. To inroduce he reader o his class of models we have presened a simple saic version of he model ha gives boh direc reduced forms and provides he basis for a simple graphical analysis of he macroeconomic equilibrium. We have hen inroduced he Blanchard-Kahn soluion procedure and repor IRFs o describe he dynamic adjusmen of he economy over periods. Finally we have used he hisorical variance analysis o evaluae how a modificaion of values of he key parameers of he model affec he relaive conribuion of supply side and demand side shocks. Our aim was no o provide he reader wih a comprehensive and up o dae caalogue of all he resuls obained by his New Keynesian lieraure bu raher o offer a clear and simple presenaion of he basic ideas and he required echnical ools needed o solve his class of models ha have become he convenional workhorse of oday s macroeconomics.

18 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 25 Appendix A. Micro-foundaions A.. Households There is a coninuum of households j [0; ] wih a uiliy funcion σ + φ C H U( C, H ) = χ, he represenaive household maximizes is welfare, defined as he expeced sream of uiliies discouned by β (0, σ + φ ): C ( j), H ( j), B ( j) Under he budge consrain: + τ ( + ( ) + ( )) max E β U C j, H j τ τ τ = 0. (A.) D PC ( j) + e B ( j) = R B ( j) + W H ( j), (A.2) σε where σ > 0 and φ > 0 are shape parameers of he uiliy funcion wih respec o consumpion and o labour supply whils χ is a shif parameer which scales he seady sae labour supply o realisic values. As in Smes and Wouers [2005] we inroduce an AR() demand shock process in he budge consrain of he represenaive household denoed by ε D. Afer replacing he Lagrange muliplier he firs order condiions are defined by he Euler bond condiion: σ E C E + ( j) β R = D, (A.3) ε C ( ) j e + P + where + = is he inflaion rae and he labour supply equaion is deermined P by: W χc ( ) σ ( ) φ j H j =. (A.4) P These equaions define he opimal pahs of labour and consumpion and maximize he welfare index of he represenaive household. A.2. Firms The represenaive firm i maximizes is profis: { P } ( i Y i W H i ( i), Y ( i) max ) ( ) ( ), (A.5) H

19 26 Economics and Business Review, Vol. (5), No. 2, 205 under he supply consrain: Y (i) = H (i). (A.6) We suppose ha firms solve a wo-sage problem. In he firs sage, firms choose labour demand in a perfecly compeiive marke. The firs order condiion is: W MC ( i) = MC =, (A.7) P where MC denoes he nominal marginal cos of producing one uni of goods. In he second sage problem he firms canno opimally se prices. There is a fracion of firms θ ha are no allowed o rese prices. Prices hen evolve according o P (i) = P (i). The remaining share of firms θ can se heir selling price such ha P (i) = P *(i), where P *(i) denoes he opimal price se by he represenaive firm given he nominal rigidiy. The maximizaion programme is hus defined as: + c λ + τ τ max E ( βθ) P* ( ) MC ( ) i τ Y τ( ) c + i + i P* ( i) λ, (A.8) τ= 0 under he downward sloping consrain from goods packers: where: = S γε μ + τ μ + *( ) τ P i E { Y + τ( i) } = E Y + τ, τ > 0, P + τ (A.9) μ e he ime-varying mark-up, denoes he imperfec subsiuabiliy beween differen goods varieies, S ε denoes he mark-up shock, γ a shif parameer ha normalizes he shock o uniy in he log-linear form of he model as in Smes and Wouers [2005]. Since firms are owned by households hey discoun he expeced profis using he same discoun facor as households (β τ λ c +τ /λc ). The firs order condiion is hus: E + c τ λ + τ ( βθ) P* ( i) μ ( i) ( i) 0 c + MC + Y + =. (A.0) λ μ τ τ τ τ= 0 + τ

20 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 27 A.3. Auhoriies To close he model he moneary policy auhoriy ses is ineres rae according o a sandard Taylor Rule: ρ ϕ R R Y = R R Y y ϕ ρ e R ε, (A.) where: R he nominal ineres rae, he inflaion rae, Y he level of oupu, ε R an AR() moneary policy shock. Finally, parameers R, and Y are seady sae values for he ineres rae, he inflaion rae and GDP 6. The cenral bank reacs o he deviaion of he inflaion rae and he GDP from heir seady sae values in a proporion of ϕ and ϕ y, he cenral bank also smoohes is rae in a proporion of degree ρ. A.4. Equilibrium condiions Afer aggregaing all he supplies by firms he resource consrain for he economy is defined by: Y = C. (A.2) Whils he aggregaion beween consrained firms and non-consrained firms leads o he following equaion for aggregae prices: μ μ μ ( P ) = θ( P ) + ( θ)( P* ). (A.3) B. Linearizaion To obain he seady sae of he model, we normalize prices i.e. P = whils we assume ha households work one hird of heir ime H = /3. Then we find: C = Y = H, W = MC =, μ = σ φ χ WC H. 6 Under a credible cenral bank, and Y also can be inerpreed as he arges of he cenral bank in erms of inflaion rae and GDP.

21 28 Economics and Business Review, Vol. (5), No. 2, 205 Firs, combining he Euler bond equaion (A.3) and he resources consrain (A.2), i.e. yˆ = cˆ, we ge producion deermined by: ( ˆ ) D E + E+ ε yˆ = yˆ rˆ +. (A.4) σ The labour supply equaion (A.4) in log-deviaion is: wˆ = σcˆ + φhˆ, (A.5) where w ˆ denoes he variaions of he real wage. Up o a firs order approximaion of he firm price opimizaion soluion (A.0) and he aggregae price equaion (A.3), he linearized new Keynesian Phillips curve is: ( θ)( θβ) S ˆ = ˆ βe + mc ˆ + + ε. (A.6) θ Thus he real marginal cos is: mc ˆ = wˆ and he producion funcion y = h, hen from he labour supply equaion, he marginal cos can be simplified as: mc ˆ = ( σ + φ) yˆ. Then he Philips curve is: ( θ)( θβ) S ˆ ˆ ˆ = βe+ + ( σ + φ) y + ε. (A.7) θ Finally, he moneary policy is deermined by: ( ) rˆ ρrˆ ρ ϕ ϕ yˆ ε. (A.8) y R ˆ = + ( ) + + To summarize, our model is deermined by he following se of hree equaions: D yˆ = ˆ ( ˆ ˆ E y+ r E + ) + ε, σ ( θ)( θβ) S ˆ = ˆ + ( + ) ˆ βe+ σ φ y + ε, θ y Δy R rˆ = ˆ + ( )( ˆ + ˆ ) + ( ˆ ˆ ρr ρ ϕ ϕ y ϕ y y ) + ε. Where shock processes are deermined by: i i i i ε = ρ ε + η, i = D, S, R. (A.9)

22 J.-C. Pouineau, K. Sobczak, G. Vermandel, The analyics of he New Keynesian 29 References Baranowski, P., Gałecka-Burdziak, E., Górajski, M., Malaczewski, M., Szafrański G., 203, Inflacja a mechanizmy akualizacji cen. Sudium dla Polski, Łódź, Wydawnicwo Uniwersyeu Łódzkiego, Wydawnicwo Naukowe PWN. Blanchard, O., Kahn, C.M., 980, The Soluion of Linear Difference Models under Raional Expecaions, Economerica, vol. 48, no. 5: Bludnik, I., 2009, The New Keynesianism Proclamaion of a Consensus?, Poznań Universiy of Economics Review, vol. 9, no. : Bofinger, P., Mayer, E., Wollmershäuser, T., 2006, The BMW Model: A New Framework for Teaching Moneary Economics, Journal of Economic Educaion, vol. 37, no. : Carlin, W., Soskice, D., 204, Macroeconomics: Insiuions, Insabiliy, and he Financial Sysem, Oxford Universiy Press. Clarida, R., Galí, J., Gerler, M., 999, The Science of Moneary Policy: A New Keynesian Perspecive, Journal of Economic Lieraure, vol. 37, no. 4: Galí, J., 2008, Moneary Policy, Inflaion, and he Business Cycle: An Inroducion o he New Keynesian Framework, Princeon Universiy Press, Princeon. Galí, J., Gerler, M., López-Salido D., 200, European Inflaion Dynamics, European Economic Review, vol. 45, no. 7: Goodfriend, M., King, R., 997, The New Neoclassical Synhesis and he Role of Moneary Policy, NBER Macroeconomics Annual, vol. 2: Klein P., 2000, Using he Generalized Schur Form o Solve a Mulivariae Linear Raional Expecaions Model, Journal of Economic Dynamics and Conrol 24(0), Sepember: Miao, J., 204, Economic Dynamics in Discree Time, MIT Press. Pouineau, J.C., Vermandel, G., 205a, Cross-border Banking Flows Spillovers in he Eurozone: Evidence from an Esimaed DSGE Model, Journal of Economic Dynamics and Conrol, no. 2: Pouineau, J.C., Vermandel, G., 205b, A Primer on Macroprudenial Policy, The Journal of Economic Educaion, forhcoming. Romer, D., 993, The New Keynesian Synhesis, Journal of Economic Perspecives, vol. 7, no. : Sbordone, A.M., 2002, Prices and Uni Labor Coss: Tesing Models of Pricing Behavior, Journal of Moneary Economics, vol. 45, no. 2: Sims, C., 2000, Solving Linear Raional Expecaion Models, Working Paper, Deparmen of Economics, Princeon Universiy. Smes, F., Wouers, R., 2005, Comparing Shocks and Fricions in US and Euro Area Business Cycles: a Bayesian DSGE Approach, Journal of Applied Economerics, 20(). Taylor, J. B., 999, A Hisorical Analysis of Moneary Policy Rules, in: Taylor, J.B. (ed.), Moneary Policy Rules, Universiy of Chicago Press, Chicago. Woodford, M, 2003, Ineres and Prices: Foundaions of a Theory of Moneary Policy, Princeon Universiy Press, Princeon.

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