Dynamics of the price distribution in a general model of state-dependent pricing

Transcription

1 Dynamcs of he prce dsrbuon n a general model of sae-dependen prcng James Cosan non Nakov Dvsón de Invesgacón, Servco de Esudos Banco de España November 28

2 Movaon Scky prces: crucal bu conroversal!calvo (983): consan probably of adjusmen easy aggregaon: cenral o DSGE models no mcrofoundaons / many cosly msakes Lucas crque: Calvo parameer should change wh nflaon!golosov-lucas (27): menu coss as mcrofoundaon for prce sckness calbraed o mach momens n mcrodaa on prce adjusmens money shocks have much less perssen effecs han n Calvo hgher nflaon: more frequen adjusmen 2

3 Movaon Scky prces: crucal bu conroversal!calvo (983): consan probably of adjusmen easy aggregaon: cenral o DSGE models no mcrofoundaons / many cosly msakes Lucas crque: Calvo parameer should change wh nflaon!golosov-lucas (27): menu coss as mcrofoundaon for prce sckness calbraed o mach momens n mcrodaa on prce adjusmens money shocks have much less perssen effecs han n Calvo hgher nflaon: more frequen adjusmen!bu GL7 fs poorly when nesed n more general model 3

4 Ths paper Sudy dynamcs of smple sae-dependen prcng model ha ness Calvo-Yun, Golosov-Lucas and ohers 4

5 Ths paper Sudy dynamcs of smple sae-dependen prcng model ha ness Calvo-Yun, Golosov-Lucas and ohers! Esmae o mach prce adjusmens n US mcrodaa! Smulae dsrbuonal dynamcs usng mehod of Reer (28)! Repor mpulse response funcons for all hree models 5

6 Ths paper: resuls Sudy dynamcs of smple sae-dependen prcng model ha ness Calvo-Yun, Golosov-Lucas and ohers! Esmae o mach prce adjusmens n US mcrodaa! GL7 model s rejeced: no small prce changes! referred model s closer o Calvo, bu mldly sae-dependen! Smulae dsrbuonal dynamcs usng mehod of Reer (28)! Nonlnear n dosyncrac saes / lnear n aggregae sae! Repor mpulse response funcons for all hree models! Much larger real effecs of money shocks han GL7 found! lmos lke Calvo! Dfference due o (counerfacually) srong selecon effec n GL7! Effecs of auocorrelaed shocks smlar, bu sronger 6

7 Relaed leraure: dynamcs of sae-dependen prcng!aral equlbrum Caballero-Engel (993, 27), Klenow-Kryvsov (28)!General equlbrum whou dosyncrac shocks Dosey-Kng-Wolman (999)!Srong resrcons on dosyncrac processes Capln-Spulber (987), Gerler-Leahy (26) 7

8 Relaed leraure: dynamcs of sae-dependen prcng!aral equlbrum Caballero-Engel (993, 27), Klenow-Kryvsov (28)!General equlbrum whou dosyncrac shocks Dosey-Kng-Wolman (999)!Srong resrcons on dosyncrac processes Capln-Spulber (987), Gerler-Leahy (26)!Dsrbuonal dynamcs Golosov-Lucas (27): assumed money shock..d. assumed c consan Mdrgan (28): dfferen model: mulproduc frms assume mean p s suffcen sasc (Krusell-Smh mehod) Dosey-Kng-Wolman (28) flexble and scky-prce frms; normal and exreme shocks we f fner hsogram wh fewer free parameers 8

9 OUTLINE () Inroducon (2) Monopolsc compeors n paral equlbrum! Nesng varous models of sae dependence! Fne grd approxmaon (3) General equlbrum: seady sae (4) How o compue dsrbuonal dynamcs (5) Resuls: dynamcs! Impulse responses! Inflaon decomposon! Transon dynamcs 9

10 Model

11 Our model!robably of adjusmen ncreases wh he value of adjusmen: λ(l) where λ!frm-level prce adjusmens due o dosyncrac shocks!res of model: sandard New Keynesan DSGE

12 Our model!robably of adjusmen ncreases wh he value of adjusmen: where λ(l) λ Inerpreaon: sochasc menu coss Inerpreaon: axom for boundedly raonal choce!frm-level prce adjusmens due o dosyncrac shocks!res of model: sandard New Keynesan DSGE Focus on dynamcs, ncludng dsrbuonal effecs 2

13 Our model!robably of adjusmen ncreases wh he value of adjusmen: where λ(l) λ Sochasc menu coss (DKW99 and Caballero-Engel) xom for boundedly raonal choce (kerlof-yellen 985) Nesed: Calvo (983) Nesed: Dosey-Kng-Wolman (999) Nesed: Golosov-Lucas (27) Nesed: Woodford (28)!Frm-level prce adjusmens due o dosyncrac shocks!res of model: sandard New Keynesan DSGE Focus on dynamcs, ncludng dsrbuonal effecs 3

14 aral equlbrum, seady sae 4

15 Monopolsc compeor rofs of frm are: Y WN Y = N Oupu s: Demand s: Y = ξ ε 5

16 Monopolsc compeor rofs of frm are: Y WN Y = N Oupu s: Demand s: Y = ξ ε s exogenous shock s scky decson 6

17 Monopolsc compeor rofs of frm are: Y WN Y = N Oupu s: Demand s: Y = ξ ε Wh scky prces, he value funcon s: V (, ) If he frm can adjus s prce, value ncreases o: * V ( ) max V (, ) 7

18 robably of adjusmen!nomnal loss from falng o adjus: D D(, ) V * ( ) V (, )!robably of adjusmen: λ λ( L) = λ ξ + ( λ)( α / L), where L D /W. We dvde by he wage o express he loss n uns of labor me. 8

19 robably of adjusmen!nomnal loss from falng o adjus: D D(, ) V * ( ) V (, )!robably of adjusmen: λ λ( L) = λ ξ + ( λ)( α / L), where L D /W.!Specal cases: ξ : equvalen o Calvo model ξ : equvalen o fxed menu cos model 9

20 Nesng alernave models! Calvo-Yun λ(l)! Golosov-Lucas λ( L) ξ = λ,, ξ L < α L α λ(l) λ λ(l) L! Cosan-Nakov λ( L) = λ + λ ( λ)( α / L) ξ λ(l) ξ < α L ξ > L 2

21 Bellman equaon a me of producon Frm ha produces a prce and producvy wll adjus prce wh probably λ nex perod: V (, ) = W ε ξ + + r {( ( D ) ( D ) ( ) } * λ V (, ') + λ V ' E W W Ths can be smplfed usng D= V * ()-V(,). 2

22 22 Smplfyng Bellman Seady sae Bellman equaon: where + = ε ξ W V ), ( { } r G V E ) ', ( ) ', ( + + ( ) ) ', ( ) ', ( '), ( W D D G λ curren profs value of no adjusng expeced gans from adjusng ). ', ( ) ' ( ) ', ( * V V D

23 23 lernave models. Calvo model: 2. Bounded raonaly: 3. Fxed menu coss: 4. Sochasc menu coss: 5. Woodford s model: ( )( ) κ Wκ D W D G = ), ( ), ( ), ( ), ( ), ( D G λ = ( )( ) ) ( ), ( ) /, ( ), ( ), ( κ κ λ W D WE D W D G = ( ) ), ( ) /, ( ), ( D W D G λ = ( ) ) ) / / exp(( ) ( ) ) / / exp(( ) /, ( θ κ λ λ θ κ λ λ + = W D W D W D

24 Dsrbuonal dynamcs and fne grd approxmaon 24

25 Fne grd of real saes! Defne grds: Γ { } { } 2 # 2 a, a,... a, Γ p, p,... p #! Grd represens real prces, deflaed by money supply: M = µ + M Begnnng-of-perod prces: ~ p ~ / M Γ rces a me of producon: p / M Γ! Real value funcon: V (, ) = M v( p, ) 25

26 Fne grd of real saes! Defne grds: Γ { } { } 2 # 2 a, a,... a, Γ p, p,... p #! Grd represens real prces, deflaed by money supply: M = µ + M Begnnng-of-perod prces: ~ p ~ / M Γ rces a me of producon: p / M Γ! Real value funcon: V (, ) = M v( p, ) Nex perod: V (,, + ) = M + v( µ p,, + ) 26

27 Dsrbuonal dynamcs Tme lne: shocks, derendng Ψ ~ Ψ Ψ + + producon shocks, derendng adjusmens ~ Ψ + producon adjusmens shocks, derendng Begnnng of perod: Tme of producon: ~ Ψ : ~ ψ = prob ~, = N x N N x N jk jk ( j k p = p a ) ( j k p = p a ) Ψ : ψ = prob, = 27

28 Marx noaon! Defne grds: Γ { } { } 2 # 2 a, a,... a, Γ p, p,... p #! roducvy shocks : jk j k S s = prob( a a )! djus real prces: Defne R wh ones n column j, row j-#µ, zeros elsewhere! Curren profs : jk U ( j k ) ξ ( j ) u = p w / a p ε Now rewre Bellman... 28

29 Marx noaon! Defne grds: Γ { } { } 2 # 2 a, a,... a, Γ p, p,... p #! roducvy shocks : jk j k S s = prob( a a ) N x N! djus real prces: Defne R N x N! Curren profs : Now rewre Bellman... wh ones n column j, row j-#µ, zeros elsewhere Deflaes real prce from p j o p j /µ = p j-#µ jk U ( j k ) ( j ) u = p w / a ξ p ε N x N 29

30 Backwards nducon n marx noaon Guess V wh elemens v jk j k j v( p, a ) : p Γ, a k Γ. Opmal value: v * = max V 2. Loss from no adjusng: D = * v * V 3. Expeced gans: G = λ( D / w) *. D 4. Work backwards: V = U + β R' *( V + G) * S and reurn o. 3

31 Backwards nducon n marx noaon Guess V N x N wh elemens v jk j k j v( p, a ) : p Γ, a k Γ. Opmal value: 2. Loss from no adjusng: 3. Expeced gans: D v max V * = x N N x N = * v * V G = λ( D / w) *. N x N D 4. Work backwards: V = U + β R' *( V + G) * S and reurn o. u jk = (p j -w/a k )ξ(p j ) -ε Relaes p j o p j-#µ Markov process for shocks 3

32 Dsrbuonal dynamcs n marx noaon Shocks and derendng: roducvy follows Markov process, prce p j deflaed o p j /µ : ~ Ψ S = R* Ψ * S' rce adjusmens: Λ λ( D / w) Change o opmal prce wh probably : ~ ~ Ψ = ( Λ) *. Ψ + *. ( *( Λ *. Ψ )) 32

33 Dsrbuonal dynamcs n marx noaon Shocks and derendng: roducvy follows Markov process, prce p j deflaed o p j /µ : rce adjusmens: = R* Ψ * S' Change o opmal prce wh probably : ~ Ψ S ~ ~ Ψ = ( Λ) *. Ψ + *. ( *( Λ *. Ψ )) Λ R deflaes and rounds up or down o grd λ( D / w) selecs opmal prce and rounds o grd 33

34 General equlbrum: seady sae resuls 34

35 35 Households, frms, cenral bank Uly of households:, dscoun facor erod budge consran: Consumpon aggregaon: Money supply: ) / log( M N C ν χ γ γ + β r B T M W N B M C Π = = ε ε ε ε d C C C C ε = ) / (... ~, ) ( ) (, d M M = = ε ε µ µ φ µ µ µ

36 General equlbrum: Seady sae fxed pon! Guess: p! Euler, FOC: C! Solve Bellman: γ = ( βµ ) / p,! Calculae dsrbuons: p w = χc! Calculae and reurn. γ V = U + β R' *( V + G) * S { } jk j ε ψ ( p ) ε = j k u jk = p j w k a C ~ Ψ = R* Ψ * S' ~ ~ Ψ = ( Λ).* Ψ +.*( *( Λ.* Ψ) p p j ε 36

37 arameers s n Golosov and Lucas (27):!Dscounng: β=.99 quarerly!crr: γ=2!labor supply coeffcen: χ=6!money demand coeffcen: ν=!elascy of subsuon: ε=7!money growh: % (as n C Nelsen daa) djusmen probably: λ λ( L) = λ + ( λ)( α / L) ξ!roducvy process: wh sd(ε )=σ log + = ρ log + ε +, Smulae a monhly frequency. 37

38 arameers s n Golosov and Lucas (27):!Dscounng: β=.99 quarerly!crr: γ=2!labor supply coeffcen: χ=6!money demand coeffcen: ν=!elascy of subsuon: ε=7!money growh: % (as n C Nelsen daa) djusmen probably: λ λ( L) = λ + ( λ)( α / L) ξ!roducvy process: wh sd(ε )=σ log + = ρ log + ε +, Smulae a monhly frequency. Esmae free parameers 38

39 Esmaon!Esmaed parameers: log ρ = σ + = log + ε+, sd( ε+ ) λ( L) = λ + λ ( λ)( α / L) ξ!mcrodaa on prce adjusmens: C Nelsen supermarke daa (Mdrgan 28)!Mnmze objecve funcon wh wo erms: Mean adjusmen frequency n model vs. daa Hsogram of prce adjusmens n model vs. daa 39

40 rce changes: models vs. evdence.25.2 cual and smulaed dsrbuon of prce changes C Nelsen Model MC.25.2 cual and smulaed dsrbuon of prce changes C Nelsen Model Calvo Densy of prce changes.5. Densy of prce changes Sze of prce changes cual and smulaed dsrbuon of prce changes Sze of prce changes C Nelsen Model SDS Densy of prce changes Sze of prce changes 4

41 rce changes: models vs. evdence.25.2 cual and smulaed dsrbuon of prce changes C Nelsen Model Mdrgan cual and smulaed dsrbuon of prce changes C Nelsen Model W oodford Densy of prce changes.5. Densy of prce changes Sze of prce changes.25.2 cual and smulaed dsrbuon of prce changes Sze of prce changes Top 3 CI areas Model KK-GL67 Densy of prce changes Sze of sandardzed prce changes 4

42 rce changes: models vs. evdence GL7 Calvo CN Daa Monhly frequency of changes % % % Mean absolue prce change Sandard devaon Changes less han 5% % 49.7% 25.2% % (NS7).5 (VM8) 3.2 (VM8) 25% (VM8) Varance of λ relave o GL

43 Benchmark calbraon: probably of adjusmen λ λ ( L) = ( λ)( α / L) ξ + λ ( 2 σ ε, ρ, λ, α, ξ ) = (.5,.88,.9,.3,.29) Lambda as a funcon of he loss from nacon.6.4 robably of adjusmen Loss from nacon (n % of frm's medan value) 43

44 Benchmark calbraon: dsrbuons and prce polcy Opmal prce polcy.6.4 Log arge relave prce Log (nverse) producvy 44

45 Compung general equlbrum: dynamcs 45

46 Is Krusell-Smh mehod suable for menu cos model? Consder Golosov-Lucas (27) menu cos model... Suppose frm adjuss f devaes from opmum by 5%. Two possble nal condons:!ll frms devae by % from opmal prce Resul: % of frms adjus!% of frms devae by % from opmal prce Resul: % of frms adjus!krusell-smh mehod assumes omorrow s mean vares smoohly wh oday s mean!fals o predc omorrow s mean n menu cos model because ndvdual choces are hghly nonlnear 46

47 Mehod of Reer (28) Reer (28, forhcomng JEDC):!Ofen, ndvdual shocks bgger han aggregae shocks.!therefore: ndvdual choce needs nonlnear soluon, bu lnear soluon suffces for aggregae dynamcs.!sep : dealed nonlnear soluon of seady sae on grd Solve ndvdual choces by backwards nducon on grd!sep 2: Lnearze dynamcs a every grd pon Vewed pon by pon, he Bellman equaon s jus a sysem of frs-order expecaonal dfference equaons Many equaons, bu sandard oolks applcable (Sms, Klen, ec)!surprse: I s easy!!! 47

48 Is Reer s mehod suable for menu cos model? Consder Golosov-Lucas (27) menu cos model... Suppose frm adjuss f devaes from opmum by 5%. Two possble nal condons:!ll frms devae by % from opmal prce Resul: % of frms adjus!% of frms devae by % from opmal prce Resul: % of frms adjus!reer s mehod can capure hs dfference: % and % from opmal prce are dfferen grd pons!each grd pon reaed by a dfferen equaon... coeffcens of hese equaons no lnearly relaed 48

49 Sep : seady sae (already done)! Guess: p! Euler, FOC: C! Solve Bellman: γ = ( βµ ) / p,! Calculae dsrbuons: p w = χc! Calculae and reurn. γ V = U + β R' *( V + G) * S { } jk j ε ψ ( p ) ε = j k u jk = p j w k a C ~ Ψ = R* Ψ * S' ~ ~ Ψ = ( Λ).* Ψ +.*( *( Λ.* Ψ) p p j ε 49

50 Dynamcs. F.O.C. labor: C / γ = χ w 2. Euler equaon: p C γ = βe µ p C γ + γ p+ C + 3. Labor demand: N = j k Ψ jk ( p j / p ) ε C a k C 4. rce ndex: { } jk j ε ( ) ε p p = j k Ψ 5

51 Dynamcs ~ U, V, D, G, Ψ, Ψ,, Marces haveszen p x N. 5. Bellman s: { } p C R *( V G ) S + V = U + βe * p + γ C γ + ' Dsrbuons sasfy: Begnnng of perod: ~ Ψ R * Ψ * S' = + + Tme of producon: ~ ~ Ψ = ( Λ ) *. Ψ + *. ( *( Λ *. Ψ )) JUST HUGE SYSTEM OF ST-ORDER DIFFERENCE EQS... CN BE LINERIZED! (Reer 28) 5

52 Sep 2: Lnearzed dynamcs ˆ µ + = φµ ˆ + ε+ ε + Suppose wh d, mean zero. Defne row vecor: X lengh: 2N N π +2 ( vec( V )', C, p, vec( Ψ )') Equlbrum dynamcs can be summarzed by: ( X X, µ, ) E F +, ˆ+ ˆ µ = 2N N π +3 frs-order expecaonal dfference equaons n 2NNπ +3 seres. 52

53 Sep 2: Lnearzed dynamcs ˆ µ + = φµ ˆ + ε+ ε + Suppose wh d, mean zero. Defne row vecor: X lengh: 2N N π +2 ( vec( V )', C, p, vec( Ψ )') Equlbrum dynamcs can be summarzed by: ( X X, µ, ) E F +, ˆ+ ˆ µ = 2N N π +3 frs-order expecaonal dfference equaons n 2NNπ +3 seres. (We ve elmnaed w, N, and Ψ ~.) 53

54 Sep 2: Lnearzed dynamcs ˆ µ + = φµ ˆ + ε+ ε + Suppose wh d, mean zero. Defne row vecor: X lengh: 2N N π +2 ( vec( V )', C, p, vec( Ψ )') Seady sae sasfes: F ( X*, X*,,) = We ve already solved for he seady sae ( sep ). 54

55 Sep 2: Lnearzed dynamcs ˆ µ + = φµ ˆ + ε+ ε + Suppose wh d, mean zero. Defne row vecor: X lengh: 2N N π +2 ( vec( V )', C, p, vec( Ψ )') Lnearzaon around seady sae: E X + B X + CE µ + D ˆ µ + ˆ+ = Can be solved by aul Klen s QZ algorhm. lernaves: Chrs Sms algorhm, ec. 55

56 General equlbrum: dynamc resuls 56

57 Impulse responses: d money growh shock.5 Money growh process SDS Calvo Menu cos.5.25 Inflaon. Nomnal neres rae Inensve margn Exensve margn Selecon effec Consumpon Real neres rae Labor Real wage rce dsperson Real money holdngs Monhs Monhs Monhs 57

58 Inflaon decomposons! Inflaon deny jk jk ~ π = λ Ψ x j, k jk x jk log p ( a p * k = j ) where s he desred prce adjusmen, n logs 58

59 Inflaon decomposons! Inflaon deny Desred prce change jk jk ~ π = λ Ψ x j, k jk robably of adjusmen Dsrbuon afer shock 59

60 Inflaon decomposons! Inflaon deny Desred prce change jk jk ~ π = λ Ψ x j, k jk robably of adjusmen! Klenow and Kryvsov! Inensve and exensve margn Dsrbuon afer shock π ~ x λ Ψ = jk jk jk j, k jk ~ jk jk ~ λ jk j k Ψ, λ j k Ψ, = av fr π fr av + av fr 6

61 Inflaon decomposons! Inflaon deny Desred prce change jk jk ~ π = λ Ψ x j, k jk robably of adjusmen! Klenow and Kryvsov! Inensve and exensve margn Dsrbuon afer shock π ~ x λ Ψ = jk jk jk j, k jk ~ jk jk ~ λ jk j k Ψ, λ j k Ψ, = av fr π fr av + av fr Inensve margn Exensve margn 6

62 Inflaon decomposons! Inflaon deny Desred prce change jk jk ~ π = λ Ψ x j, k jk robably of adjusmen Dsrbuon afer shock 62

63 Inflaon decomposons! Inflaon deny Desred prce change jk jk ~ π = λ Ψ x j, k robably of adjusmen! Cosan and Nakov! Inensve margn, exensve margn, and selecon effec jk Dsrbuon afer shock π ~ ~ ~ ~ x λ Ψ ) Ψ = av fr + = jk jk jk jk jk jk Ψ λ Ψ + x ( λ j, k j, k j, k jk jk jk * sel π fr av * + av * fr + sel 63

64 Inflaon decomposons! Inflaon deny Desred prce change jk jk ~ π = λ Ψ x j, k robably of adjusmen! Cosan and Nakov! Inensve margn, exensve margn, and selecon effec jk Dsrbuon afer shock π ~ ~ ~ ~ x λ Ψ ) Ψ = av fr + = jk jk jk jk jk jk Ψ λ Ψ + x ( λ j, k j, k j, k jk jk jk * sel π fr av * + av * fr + sel Inensve margn Exensve margn Selecon effec 64

65 Why he dfference wh GL7? x -4 Dsrbuon Menu Cos Model of frms Dsrbuon of prce changes 8 Golosov- Lucas (27) Densy of frms Densy of frms wh SS producvy Ideny of adjusng frms Densy of adjusers SS densy of frms Densy of prce changes Before moneary shock fer moneary shock Dsance from opmal prce Dsance o opmal prce Sze of prce changes (log)!fxed menu coss mply srong selecon effec: Frms ha adjus are far from opmal prce.!shock redsrbues mass from prce decreases o prce ncreases Large change n average adjusmen, av......even f small change n average desred adjusmen, av *!Depends on frms jumpng from λ jk = o λ jk = Such srong sae dependence rejeced by esmae of λ(l) 65

66 Why he dfference wh GL7? 8 x -4 Dsrbuon SDS Model of frms Dsrbuon of prce changes 7 Cosan- Nakov (28) Densy of frms Densy of frms wh SS producvy Ideny of adjusng frms Densy of adjusers SS densy of frms Densy of prce changes Dsance from opmal prce Dsance o opmal prce Sze of prce changes (log)!in esmaed model, many adjusers are near opmal prce!selecon effec smaller (/3 of change n nflaon) verage adjusmen smlar o average desred adjusmen: av av *!Shock falls less on nflaon, more on oupu 66

67 Impulse responses: auocorrelaed money growh.5 Money growh process Inensve margn Consumpon Real neres rae SDS Calvo Menu cos Inflaon Exensve margn Labor Real wage.2. Nomnal neres rae Selecon effec rce dsperson Real money holdngs Monhs Monhs Monhs 67

68 Real mpac of money growh shocks hllps curve : log( C ) = α + β log( µ ) Uncorrelaed shocks ( φ µ = ) GL7 Calvo CN Sd dev money growh shock (x) Sd dev quarerly nflaon (x) % explaned by nomnal shock % % % Sd dev quarerly oupu growh (x) % explaned by nomnal shock 26% 42% 96% Slope of he hllps curve (β ) Sandard error..3.2 R

69 Real mpac of money growh shocks hllps curve : log( C ) = α + β log( µ ) Correlaed shocks ( φ µ =.8) GL7 Calvo CN Sd dev money growh shock (x)..2.6 Sd dev quarerly nflaon (x) % explaned by nomnal shock % % % Sd dev quarerly oupu growh (x) % explaned by nomnal shock 29% 3% 9% Slope of he hllps curve (β ) Sandard error..3. R

70 Transonal dynamcs: shf n p 6 Money growh process Inflaon Nomnal neres rae Inensve margn Exensve margn Selecon effec Consumpon Real neres rae Monhs Labor Real wage Monhs rce dsperson Real money holdngs Monhs 7

71 Transonal dynamcs: shf n Money growh process Inflaon Nomnal neres rae Inensve margn Consumpon Real neres rae Monhs Exensve margn Labor Real wage Monhs Selecon effec rce dsperson Real money holdngs Monhs 7

72 Transonal dynamcs: pos-euro Money growh process.2 Inflaon Nomnal neres rae Inensve margn Exensve margn Selecon effec Consumpon Real neres rae Monhs Labor Real wage Monhs rce dsperson Real money holdngs Monhs 72

73 Effec of sarng condons: IRFs afer producvy shock Money growh process.2 Inflaon.2 Nomnal neres rae Inensve margn Exensve margn Selecon effec Consumpon Real neres rae Labor Real wage rce dsperson Real money holdngs Monhs Monhs Monhs 73

74 Conclusons!Now feasble o compue DSGE dsrbuonal dynamcs wh sae-dependen prces Reer (28)!Benchmark calbraon: money growh shocks no neural!uocorrelaed shocks: effecs smlar, bu sronger!near-neuraly n GL7 calbraon due o srong selecon effec srong selecon effec and lack of small prce changes boh due o counerfacual degree of sae dependence!ddonal fndngs: rce dsperson quanavely mporan (unlke sandard NK DSGE) Increased aggregae producvy causes labor o fall (lke NK DSGE) 74

75 Conclusons!Now feasble o compue DSGE dsrbuonal dynamcs wh sae-dependen prces Reer (28)!Benchmark calbraon: money growh shocks no neural!uocorrelaed shocks: effecs smlar, bu sronger!near-neuraly n GL7 calbraon due o srong selecon effec srong selecon effec and lack of small prce changes boh due o counerfacual degree of sae dependence!ddonal fndngs: rce dsperson quanavely mporan (unlke sandard NK DSGE) Increased aggregae producvy causes labor o fall (lke NK DSGE)!hllps curve s alve and well! 75

76 Some exensons: Taylor rules 76

77 Shock n Taylor rule.5 Shock process SDS he Calvo he -.2 Inflaon.5 Nomnal neres rae Inensve margn Exensve margn Selecon effec Consumpon Labor rce dsperson Real neres rae Monhs Real wage Monhs Real money holdngs Monhs 77

78 Taylor rule: ermanen dsnflaon Shock process Inflaon Nomnal neres rae.5 Calvo SDS Inensve margn Consumpon Real neres rae Monhs Exensve margn Labor Real wage Monhs Selecon effec rce dsperson Real money holdngs Monhs 78

79 James Cosan THNK YOU FOR YOUR TTENTION