Prof. Dr. Thomas Steger. Introduction Static Model with Market Power How to Model Price Rigidities Baseline New Keynesian Model

Transcription

1 rof. Dr. Thomas Seger Advanced Macroeconomics II Lecure SS 2 Insiu für Theoreische Volkswirschafslehre 4. New Keynesian Theory Inroducion Saic Model wih Marke ower How o Model rice Rigidiies Baseline New Keynesian Model

2 Insiu für Theoreische Volkswirschafslehre Inroducion i () A basic ene in classical macroeconomics is ha of moneary neuraliy. If nominal prices are compleely flexible (i.e. can be changed wihou coss), a change in money supply would no have real effecs. All nominal quaniies (prices and wages) would move in he same proporion and no real quaniy would be affeced. A hemicroeconomic level heimporance ofadjusmen coss seems be small. The coss of adjusing nominal prices are comparaively small. To change is prices, a firm may need o send ou a new caalog o cusomers, disribue new price liss o is sales saff, or, in he case of a resauran, prin new menus. These coss of price adjusmen, called menu coss, cause firms o adjus prices inermienly raher han coninuously. However, proponens of New Keynesian Theory believe such nominal imperfecions may have large macroeconomic consequences! The reason lies in demand exernaliies and implied coordinaion failures as will be shown below. 2

3 Insiu für Theoreische Volkswirschafslehre Inroducion i (2) These impulseresponse funcions (from an esimaed VAR), indicae ha here are emporary real effecs of money supply shocks. Source: Sims (EER, 992) 3

4 Insiu für Theoreische Volkswirschafslehre Inroducion i (3) These impulseresponse funcions (from an esimaed VAR), indicae ha here are emporary real effecs of money supply shocks. Source: Sims (EER, 992) 4

5 Insiu für Theoreische Volkswirschafslehre Saic i Model wih Marke ower: model dlseup We sar wih a simple saic model which is characerized by marke power on he side of producers (cf. o he model New Classical Macro: Case of erfec Informaion ). The economy is inhabied by a large number of idenical consumer producer households ( individuals ) indexed by i [,] and here is imperfecproducmarkecompeiion produc marke compeiion wih full price flexibiliy. The producion echnology is Q i =L i. The represenaive individual L i hires labor o produce a final oupu good Q i. Moreover, individuals supply labor o he compeiive labor marke, earning a wage rae W per hour of work. The individual producer has marke power, i.e. he can se he goods price. The demand for each good is Q η i =Y( i /) wih η>. Taking logs gives q i =y η(p i p). The uiliy funcion is again given by U i =C i L iγ /γ wih γ> and he budge consrain reads C i =( i W)Q) i+wl i. Aggregae demand is Y=M/ or y=m p. Money supply m is now publically observed. 5

6 Insiu für Theoreische Volkswirschafslehre Saic i Model wih Marke ower: individual id lbh behavior The represenaive agen solves he following opimizaion problem max Ui Ci Li i, Li ( i WQ ) i WLi s.. Ci Q Y ( / ) i i m ax Ui ( L i, i) i, Li ( i W) Y( i / ) WLi L i The firs order condiions for he wo choice variables L i and i read apply produc and chain rule U( i, Li) Y( i / ) ( i W) Y( i / ) (/ ) i W (*) i U (, ) i Li W W Li Li Li (**) The larger is η, he smaller is marke power of goods producers and hence he mark up. The larger is γ, he more imporan is disuiliy of labor and hence he less wage sensiive is he supplied amoun labor. 6

7 Insiu für Theoreische Volkswirschafslehre Saic i Model wih Marke ower: equilibrium i Since individuals are perfecly idenical each individual works he same amoun in equilibrium (L i =L for each i) and produces he same oupu (Q i =Q for each i). Aggregae oupu reads Y:= Q i di=q i =Q. From he firs order condiion for L i, noing L=Q=Y, he real wage is W/=Y γ. Subsiuing his equaion ino he price equaion (*) one ges * i Y Y Since producers are perfecly symmeric, each producer charges he same price. The price index herefore equals his common price such ha * * Y Y Finally, from =M/Y he price level reads *=M/((η )/ η) /(γ ). 7

8 Insiu für Theoreische Volkswirschafslehre Saic i Model wih Marke ower: implicaions () In his economy oupu is sub opimally low due o marke power in he produc marke. The social planner s soluion resuls from maximizing U=L L γ /γ w.r.. L. The soluion is L fb =, implying ha Y fb =>Y * =((η )/ η) /(γ ). Booms and recessions hence have asymmeric effecs on welfare since a boom brings he economy closer o is social opimum. This conforms o he pracical percepion ha a boom is good and a recession is bad. Under imperfec compeiion pricing decisions have exernaliies and hose exernaliies operae hrough he overall demand for goods. Assume ha AD falls and hence he economy runs ino a recession. The individual firm may hink abou lowering is supply price. By doing so i compares he marginal benefi wih he price adjusmen coss. I does no, however, ake ino accoun he effec ha, as all firms lower heir supply prices, he price level decreases and hence AD increases and he recession is less severe ( exernalies, coordinaon failures). Imperfec compeiion alone does no imply moneary non neuraliy. neuraliy A change in he money sock leads o proporional changes in he nominal wage and all nominal prices. Oupu and he real wage remain unchanged. 8

9 Insiu für Theoreische Volkswirschafslehre Saic i Model wih Marke ower: illusraion i 9

10 Insiu für Theoreische Volkswirschafslehre Saic i Model wih Marke ower: implicaions (2) The consequences of menu coss Suppose ha he economy is iniially in equilibrium (poin A). Nex, AD is assumed o fall. If he individual supplier holds he price fixed, poin B on he new demand curve is realized. If, insead he price is adjused opimally, he or she would realize poin C. The marginal profi from price adjusmen is given by he shaded riangle. Now, if here are coss associaed wih price adjusmen which exceedhis exra profi, he individual supplier holds he price fix. In his case, any change in nominal money supply would have real effecs!

11 Nominal lrice Rigidiies: idii Calvo (983) Approach h() Insiu für Theoreische Volkswirschafslehre ω=: flexible price case ω=: full price rigidiy Calvo (983) assumes ha firms canno adjus heir prices a each insan of ime. There are raher only infrequen opporunies a which firms can adjus heir prices ( legal and / or echnological impedimens). Each period here is a consan probabiliy ω ha he firm can adjus is price. This implies ha he expeced ime beween price adjusmens is /( ω). Assume firm i ses is price a ime o minimize a quadraic loss funcion (Roemberg, 987). 2 2 j j * 2 = E ( pi, p+ j) 2 j * 2 * 2 * 2 2 E 2 ( pi,+ j p+ j) = ( pi, p) + E( pi, p+) + E ( pi, j j j j j j price se a price se a prevails a prevails a 2 wih probabiliy 2 wih probabiliy ( a fix number a j) ( a fix number a j2) Recall: ) * 2 p i i E X E X Imagine a CEO of a company who eners his office in he morning. There are wo lighs, a red and a green one. If he green ligh is flashing, rob(green)= ω, he CEO is allowed o change he goods price. If he red is flashing, rob(red)=ω, he CEO is no allowed o change he price. This is a meaphor for saying ha here are oisson disribued opporuniies o change prices. Now, assume ha firm i can adjus is price p i,+j in period j= (green ligh flashing) and noice ha profis a some fuure dae +j are affeced by he choice of price a only if he firm has no received anoher opporuniy o adjus beween and +j. The probabiliy of his is ω j. (The CEO solves he maximizaion problem oday condiional on red ligh flashing in all periods j, which has probabiliy ω j.) p * can be inerpreed as he profi maximizing price (a ime ) in he absence of any resricions (price arge).

12 Nominal lrice Rigidiies: idii Calvo (983) Approach h(2) Insiu für Theoreische Volkswirschafslehre ω=: flexible price case ω=: full price rigidiy The firs order condiion for he opimal choice of p i may be wrien as ( ) ( )* j j * 2 j j * E pi, p+ j E pi, p+ j pi, 2 j j p j j j j * i, Ep+ j j j = Recall: E( abx) abe( X) Leing x denoe he opimal price p i se a by all firms adjusing heir price we ge x j j * =( ) Ep+ j j The price se by he firm a is a weighed average of curren and expeced fuure values of he arge price p *. If ω is small, he expeced ime unil he firm can adjus is price again is shor. In his case, less weigh is placed on fuure p * s. The preceding equaion may be rewrien as follows (see nex slide) x p E x * =( ) + + 2

13 Insiu für Theoreische Volkswirschafslehre Nominal lrice Rigidiies: idii Calvo (983) Approach h(2 (2a) x j j * =( ) Ep+ j j * * 2 2 * =( ) Ep + Ep + + Ep * * 2 2 * =( ) p + Ep+ + Ep * * * =( ) p + E p+ + p Ex + ( ) * =( ) p + E x + x + is iself an expeced value (i.e. a number). The expeced value of an expeced value is sill a number; E (E + (x))=e + (x). 3

14 Nominal lrice Rigidiies: idii Calvo (983) Approach h(3) Insiu für Theoreische Volkswirschafslehre ω=: flexible price case ω=: full price rigidiy If he price arge p * depends on he aggregae price level p and oupu y such ha p * = p +γy +ε we have + x =( ) p + y + + E x (*) Moreover, wih a large number of firms, a fracion ω will acually adjus heir price each period. Hence, he aggregae price level can be expressed as p =( ) x + p (**) - Equ. (*) and (**) imply ha inflaion π =p p is hen given by (Walsh, 23, p. 227) ( )( ) = E++ y+ This represens a posiively sloped sloped AS curve in (y, π ) plane. A rise in ω (i.e. he average me beween price changes increases) causes he coefficien π / y o decrease. Oupu movemens have a smaller impac on curren inflaion, holding E π + consan. 4

15 Insiu für Theoreische Volkswirschafslehre Nominal lrice Rigidiies: idii Convex rice Adjusmen Cos As an alernaive o he Calvo (983) approach, we consider convex price adjusmen cos (Hairaul and orier, EER, 993). Consider a firm ha produces a differeniaed good X j under monopolisic compeiion. If he firm adjuss is supply price, i mus bear convex price adjusmen cos (AC j ) of he form AC j p j = 2 p j Leing λ denoe he real marginal producion coss, each firm solves he following dynamic opimizaion problem 2 p j D max E X j AC p j = s.. X D j p j Y j Assignmen Skech he opimal soluion {p j } of his dynamic opimizaion problem (you may wano o check he lieraure). Discuss he similariies and he differences beween his convex price adjusmen seup and he Calvo (983) approach. AC j p j = 2 p j 2 5

16 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Non echnical ldescripion Households. There is mass oneofidenicalof households (HH). Each HH supplies labor, purchases goods for consumpion, and holds money and bonds. Firms. There is mass one of idenical firms. Each firm hires labor o produce a differenaed good, which is sold in monopoliscally compeve markes ( Dixi Sigliz (977) seup). Nominal price rigidiies. Each firm ses he price of he good i produces, bu no all firms rese heir prices in each period. There are nominal price rigidies ( Calvo (983) approach). Behavioral assumpions. Households maximize heir ineremporal welfare, while firms maximize hepresen discouned value ofaninfinie profi sream. There is also a cenral bank ha conrols he nominal ineres rae according o a Taylor rule. 6

17 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Households () There is mass one of idenical households each of which maximizes welfare given by E b C M N b The composie consumpion good C is given by The budge consrain is given by j C c dj wih This funcion can be inerpreed as a subuiliy funcion. Alernaively, i can be inerpreed as a producion funcion. In his case, he c j denoe differeniaed inermediae goods and here is a CRS secor producing he consumpion good C. C M B W M N real consumpion expendiures expendiures on real real expendiures on real labor income real money balances money balances financial invesmens carried over from he (bond purchases) previous period B bond repaymens plus ineres (in real erms) profis (in real erms) 7

18 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Households (2) The household s decision problem: Sage The Lagrangian g funcion reads min c j p s.. jcjdj c j dj C LA: p jc jdj c j dj C LA p j p j c j dj c j p j c j dj c j c j C c j inner derivaive ouer derivaive From he definiion of C one ges p j : j j j C C dj p dj C p dj p dj c j p j C C The price elasiciy of demand for any good c j is given by θ. If θ, he individual goods become closer and closer subsiues, and, as a consequence, individual firms have less marke power. 8

19 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Households (3) The household s decision problem: Sage 2 b C M N max E,, b C M N M B W M B s.. C N The reduced form sysem (shadow price eliminaed) of firs order condiions reads wih : C E C FOC: Euler equaion M C b FOC2: Inraemporal opimaliy condiion seing he MRS beween M and C equal o he opporuniy cos of holding money. N C W FOC3: Inraemporal opimaliy condiion seing he MRS beween leisure and C equal o he W/. 9

20 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Households (3a) The Lagrangian funcion for he problem a sage 2 reads A = we have b C M N W M B : M B LA E N C b W M B M B W M B M B LA : E u C, M, N N C u C, M, N N C... LA E C C C LA W W E N N N b b LA M M E M LA E B Repeaing he same seps for = and hen generalizing one ges M E W N W C C N W C N b M b b C, E M E C E E C C E C 2

21 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Firms () There is mass one of idenical c firms each of which is producing a variey of consumpion goods. Each firm has access o he following producion echnology c j =A N j wih E(A )=. Firms have marke power and can hence se he goods price. Given he demand for each c j his implies a specific producion quaniy and via c j =A N j a specific amoun of labor demand. rices canno be se, however, perfecly flexible, i.e. here are nominal price rigidiies. Nominal price rigidiies are modeled according o Calvo (983). Each period, he firms ha are allowed o adjus heir prices are randomly seleced. The fracion ω of all firms adjus ( green ligh flashing ), while he fracion ω do no adjus ( red ligh flashing ). The parameer ω is a measure of he degree of nominal price rigidiies: a lager ω implies ha fewer firms adjus each period and ha he expeced ime beween price changes is longer. Those firms ha do adjus heir price a ime do so o maximize he expeced presen discouned value of curren and fuure profis. rofis a some fuure dae +s are affeced by he choice of price a only if he firm has no received anoher opporuniy o adjus beween and +s. The probabiliy of his is ω s. 2

22 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Firms (2) The problem of he ypical firm p j max E, cj cj p j real producion real revenues in period cos in period Using c j =(p j / ) θ C he preceding problem may be expressed as max (assuming ha no price changes occured) p j p j obj: E, C E, C p j Euler equaion /, E A C W C wih ; The firs order condiion for he opimal price a =,, denoed as p * j =p *, is given by * * p E, C p E, C j obj ( ) p *, E, pe real discoun facor in expeced value erms p * E, (*) E, This equaion shows how adjusing firms se heir nominal goods price. Because he firm canno adjus every period, i mus ake ino accoun curren and expeced fuure marginal cos (λ ) as well as he curren and expeced fuure aggregae price level ( ). 22

23 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Flexible rice i Case (ω=) Assuming ω= ( all firms are allowed o adjus heir prices ), he opimal supply price is E,, * (flexible price case) * generalizing * p p p opimal nominal E,, supply price mar facor When prices are flexible, all firms charge he same price, and herefore p * =. Hence, one ges W / W A A Moreover, from χn η /C σ =W / (see FOC 3 above) we ge N A C Equ. (**) and he producion funcion Y =A N (noice ha Y =C ) may be expressed as (**) real marginal price level k up producion cos Aˆ Nˆ Yˆ, Yˆ Aˆ Nˆ Cˆ Noice ha X denoes he proporional deviaion of variable X ˆ f Y ˆ from is seady sae value X. A See he mehodical slide roporional Deviaion from SS Linearizaion Technique a he end of his lecure noe. 23

24 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Sicky i rices (<ω<) () The price index in period may be expressed as * p j dj p j dj priceof adjusing firms in priceof non-adjusing firms in (all idenical due o symmery) (differen across firms) Imagine an economy wih, say, firms. A each period here are wo ypes of firms: adjusers (p * ) and nonadjusers (p ). The price index is calculaed by aggregaing hese prices. If we now pick, say, 2, firms in a random fashion, he resuling sample comprises adjusers and non adjusers. Non-adjusers were randomly seleced. * p pj (***) Hence, on average,. Linearizing equ. (*) and (***) around he seady sae by means of firs order Taylor approximaion ( mehodical slide below and appendix in Walsh(23)) yields j ˆ = E + + wih : expeced real marginal cos fuureinflaion fl i (proporional ldeviaion i from SS) ( )( ) The curren inflaion rae π is accordingly deermined by wo erms (compare o equ. (*)) The expeced fuure inflaion rae (E π + ), i.e. he inflaion process is forward looking. The real marginal cos,in erms of he proporional deviaion from SS, (λ ). This equaion is ofen ermed New Keynesian hillips curve. I differs from he radiional hillips curve since i has been derived from a model of opimizing behavior on he par of price seers, condiional on he assumed economic environmen. I shows how he impac of real marginal cos on inflaon ( κ) depends on srucural parameers, like ω and β. 24

25 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: Sicky i rices (<ω<) (2) The real marginal cos (λ ) can be relaed o an oupu gap measure (as i usually occurs in he radiional hillips curve). The firm s real marginal cos equals he real wage divided by he ML, i.e. λ =(W / )/A. (The number of working hours required o produce one addiional oupu good (/A ) imes he real cos of a working hour (W / ).) W / linearizing ˆ ˆ ˆ ˆ W A A Y AN Yˆ Aˆ Nˆ W linearizing N linearizing Wˆ ˆ ˆ ˆ N C C ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ Y A Y A A Y Y A Nˆ Cˆ ˆ ˆ ˆ f A Y Y ˆ Yˆ Hence, he New Keynesian hillips cure may be expressed as follows ˆ ˆ f = E++ Y Y oupu gap Terminology is used a bi sloppy here. Usually, a hillips curve is a relaion of he form π =f[e π +,(u u)]. u)]. Y Y f is he difference beween he acual oupu gap (under price rigidiies) and he flexible price equilibrium oupu gap. 25

26 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: General Equilibrium i () The reduced form of his simple general equilibrium model consisen wih opimizing behavior on he par of households and firms can be wrien as follows: x E x E u (#) Equ. (#) resuls from linearizing he Euler ˆ ˆ f Y Y + = E + x (##) This reduced form sysem appears similar o radiional AS AD models. equaion and noing ha, in his model, Y =C (see he nex slide). The s equaion describes he demand side of he economy (an expecaional, forward looking IS curve). The 2 nd equaion (New Keynesian hillips curve) describes he supply side. Models in he AS AD radiion are ofen criicized as saring from curves raher han saring from he primiive ases and echnology from which behavioral relaionships can be derived, given maximizing behavior and marke srucure. The parameers appearing in he above sysem are explici funcions of he underlying srucural parameers of producion and uiliy funcions and he assumed process of price adjusmen. The sysem conains expecaions of fuure variables. The absence of his ype of forward looking behavior is a criical shorcoming of older AS AD models. This reduced form sysem conains hree variables, namely x, π, and γ. The model can be closed by assuming ha he cenral bank implemens moneary policy hrough conrol of he nominal ineres rae. 26

27 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: General Equilibrium i (a) Linearizaion of he Euler equaion ( slide roporonal deviaon from SS linearizaion echnique ) is done as follows may be expressed as C E EC f C g, E, EC LHS : ˆ C CC C C f () (.) C ˆ in SS E RHS: C ˆ C g (.) ˆ in SS E in SS E ˆ C CEC g EC E g (.) (.) E E E E C ˆ C C ˆ C E C ECˆ Cˆ ˆ E EC Yˆ ˆ ( SS) ( SS) Y EY E x EY Y EY E Yˆ using x ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ f Y Y f f f Y E x E x E u EYˆ EYˆ EYˆ Yˆ f f f 27

28 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: General Equilibrium i (2) As regards cenral bank behavior, one obvious possibiliy would be o assume ha he cenral bank ses he nominal ineres rae according o a Taylor rule: x v wih v v (###) x v We simplify by assuming ha δ x =, ie i.e. he cenral bank only arges inflaion and does no care abou he economy s posiion in he business cycle. Consider he reduced form model (#), (##), and (###). The impac of moneary policy on oupu and inflaion operaes hrough he real ineres rae. As long as he cenral bank is able o affec he real ineres rae hrough is conrol of he nominal ineres rae, moneary policy can affec real oupu. Changes in he real ineres rae aler he opimal ime pah of consumpion ( Euler equaon). An increase in he real ineres rae, for insance, leads HH o pospone consumpion. Curren consumpion, hence oupu, falls relaive o fuure consumpion. 28

29 Insiu für Theoreische Volkswirschafslehre Baseline New Keynesian Model: General Equilibrium i (3) Source: Walsh 23, p The figure illusraes he impac of a moneary policy shock, i.e. an x increaseinhe nominal ineresrae rae. Ex E u The rise in he nominal ineres rae (Δγ >), given E π +, causes he oupu gap x o decrease = + conemporaneously y( (consumpion E+ x demand falls and some prices are sicky). se of parameers: β=.99, σ=η=, δ π =.5, ω=.8, ρ v =.5 As he oupu gap falls, he inflaion rae π decreases conemporaneously. As a resul, he real ineres rae increases. (I increase sronger han he nominal ineres rae.) As before, an increase in he real ineres rae causes consumpon ( Euler equaion) and hence oupu o fall. The basic ineres rae ransmission mechanism for moneary policy could be exended o include effecs on invesmen spending if capial were inroduced ino he model. All he persisency displayed by he responses arises solely from serial correlaion in he moneary rule (i.e. ρ v >). 29

30 Insiu für Theoreische Volkswirschafslehre Summary and Conclusion New Keynesians argue ha some kind of nominal price / wage rigidiies cause moneary neuraliy o break down. There are also models which are based on real wage rigidiies ( Chaper on Unemploymen). These models (also ermed New Keynesian DSGE models) represen he sae of he ar when i comes analyzing business cycles in indusrialized counries. The reduced form of New Keynesian models resembles radiional AS AD models. The difference is, however, ha (i) New Keynesian models are based on opimizing behavior and (ii) () incorporae forward looking elemens in a naural manner. So far, mos heoreical models have separaed he long run (economic growh) from he shor run (economic flucuaions). I would be insrucive o combine endogenous growh heory (R&D based growh models) wih New Keynesian models o invesigae he ineracions beween crisis and long run growh. 3

31 Insiu für Theoreische Volkswirschafslehre roporional ldeviaion from SS Linearizaion i Technique (mehodical li issue) This slide shows how a (non linear) funcion y=f(x,z) can be linearized by means of a firs order Taylor approximaion around he seady sae. As a resul, he variables are ransformed ino proporional deviaions from he seady sae. y f( x, z) f( x, z) f( x, z) y y RHS: f ( xz, ) f( xz, ) xx zz; LHS: y y ( y y) y y y yy ˆ x xx z xx y zz f( x, z) f( x, z) f( x, z) f( x, z) y yy ˆ f( x, z) xx zz f( x, z) x xˆ z zˆ x xx z xx x xx x x f( x, z) x f( x, z) z yˆ xˆ zˆ x xx y z xx y zz zz zz zz zz zz xx x z zz zz z Example : y ax bz yy ax xx bz zz ax x x bz z z ˆ ˆ ˆ xx x zz z x z yˆ a xˆb zˆ y y Example 2 : y ax bz yy ax bz xx ax bz zz ˆ ˆ ˆ yˆ xˆzˆ Alernaively (example 2): y ax bz ; y ax bz y x z y x z ln yln y ln xln x ln zln z yˆ xˆzˆ 3

32 Insiu für Theoreische Volkswirschafslehre Noaion i () Saic Model C i individual consumpion i [,] producer consumer households L i individual labor supply M nominal money balances price level i individual price i / relaive price Q i individual id good U i uiliy of individual i W nominal wage W/ real wage X* equilibrium value of X x:=ln(x) naural logarihm of he corresponding upper case variables Calvo approach E (X) expeced value of X condiional on informaion known a i [,n] represenaive firm i p i, * p x y firm s iacual price in period firm s profi maximizing arge price aggregae price level opimal price se a by all firms oupu ß> discoun facor γ> consan parameer π inflaion (p p ) <ω< measure for degree of nominal price rigidiy Y real Income γ> consan parameer η> consan parameer 32

33 Insiu für Theoreische Volkswirschafslehre Noaion i (2) New Keynesian Model B C c j E (X) L j M N p j W X j nominal sock of bonds composie consumpion good differeniaed inermediae goods expeced value of X labor demand of firm j nominal money balances labor supply price of good j aggregae price level nominal wage differeniaed good x oupu gap (Y Y f ) Y Y Y f A aggregae oupu oupu gap labor produciviy erm β> discoun facor γ nominal rae of ineres δ x > policy parameer δ π > policy parameer η> consan parameer θ> elasiciy of demand for individual goods λ real marginal cos μ shadow price <ρ v < parameer (auocorrelaion coefficien) π seady sae inflaion rae π Π inflaion rae real profi χ> consan preference parameer Ψ <ω< Lagrangian muliplier measure for degree of nominal price rigidiy 33