Money in the short run: Incomplete nominal adjustment (III) 1. Sticky Prices and Wages: Calvo and alternatives

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1 Moneary Economics: Macro Aspecs, 3/ Henrik Jensen Deparmen of Economics Universiy of Copenhagen Money in he shor run: Incomplee nominal adjusmen (III) 1. Sicky Prices and Wages: Calvo and alernaives Lieraure: Walsh (Chaper 6, pp plus relevan appendix) c 2012 Henrik Jensen. This documen may be reproduced for educaional and research purposes, as long as he copies conain his noice and are reained for personal use or disribued free.

2 Inroducory remarks Sicky wage and simple wo-period saggered price seing gave subsanial real effecs of moneary policy shocks Models were simple, bu showed how presence of nominal rigidiies are promising for explaining he real effecs of moneary policy shocks seen in daa Today, we look a a very popular exension of he wo-period Taylor saggering model: The Calvo model of saggered price seing The Calvo model generaes a simple and esable Phillips-curve relaionship Cenral building block in he New-Keynesian business cycle models we cover a he end of course We conclude by a broad discussion of price (and wage-) seing models and look a some evidence for price sickiness 1

3 The Calvo model of saggered price seing Monopolisic compeiive price seers as in model of Taylor-syle saggered price seing Calvo se-up: Each period any firm faces a sae-independen probabiliy of being suck wih is price, 0 < ω < 1 This probabiliy is a naural proxy ( index ) for price sickiness The probabiliy is independen of when he firm las changed is price Hence, TDP: Time-dependen pricing Sylisic represenaion of saggering. The independence of hisory faciliaes aggregaion: When adjusing, firms choose same price in he symmeric model ω measures he fracion of firms no adjusing prices in a period 1 ω measures he fracion of firms adjusing is a period Also, he average duraion of a price is given by 1/ (1 ω) (useful when looking a daa) [ Prob. of readjusing afer one period is 1 ω; afer wo periods, ω (1 ω); afer hree periods, ω 2 (1 ω); ec. Expeced number of periods before readjusmen: (1 ω) + ω (1 ω) 2 + ω 2 (1 ω) = 1/ (1 ω) ] 2

4 Imporan implicaion of Calvo model: Expecaions abou fuure aggregae prices become of imporance (as he firm may live wih is price for several periods) Relevan maximizaion problem of inermediae goods producer i: where max E β j Π +j (i), 0 < β < 1, (6.33 ) Π (i) = P (i) Y (i) P V Y (i), and where demand for inermediae goods by final goods producers is [ ] 1 P 1 q Y (i) = Y, 0 < q < 1 (6.21) P (i) 3

5 Consider a firm ha can se a price in period. Denoe he price by P Given he Calvo srucure, i s maximizaion problem is max P E (ωβ) j [P Y +j (i) P +j V +j Y +j (i)], s.. Y +j (i) = [ P+j P ] 1 1 q Y+j Firs-order condiion: ( E (ωβ) j Y +j (i) + P Y +j (i) P ) Y +j (i) P +j V +j P = 0, Y +j (i) = [ P+j P ] 1 1 q Y+j Rewrien o bring ou he elasiciy of demand, ( Y +j (i) / P ) / (Y +j (i) /P E (ωβ) j Y +j (i) (1 + P Y +j (i) Y +j (i) P E E P +jv +j P P Y +j (i) Y +j (i) P ( (ωβ) j Y +j (i) q + P ) +jv +j 1 P = 0, 1 q ( (ωβ) j Y +j (i) 1 q 1 + P ) +jv +j = 0, E (ωβ) j Y +j (i) P ) ) = 1/ (1 q), = 0, Y +j (i) = [ P+j P ( P 1 q P +jv +j ) = 0. (6.34 ) ] 1 1 q Y+j 4

6 Implicaions For special case of flexible prices, ω = 0, (6.34 ) becomes P P = 1 q V. Desired real price is a desired markup, 1/q > 1, over real marginal coss For general case of ω > 0, P depends of expeced fuure values of Y +j (i), P +j, and V +j The general case as an approximae Phillips-curve relaionship: Equaion (6.34 ) is rewrien as E (ωβ) j Y +j (i) ( P 1 ) P 1 q Π 1,+jV +j where Π 1,+j P +j /P 1 is gross inflaion beween 1 and + j The opimaliy condiion is log-linearized around a symmeric zero-inflaion seady sae: = 0 P P 1 = 1, Π 1,+k = 1, Y +j (i) = Y, V = q 5

7 One ges (lower-case leers are logs) (βω) j E {p p 1 v +j p +j + p 1 } = 0 where v +j v +j log q. Hence, (βω) j p = (βω) j E { v +j + p +j }, p = (1 βω) (βω) j E { v +j + p +j }. (p*) Opimal price is a funcion of expeced curren and fuure real marginal coss and aggregae prices (p*) is he unique saionary soluion o he firs-order raional expecaions difference equaion: p = βωe p +1 + (1 βω) ( v + p ). 6

8 Aggregae inflaion dynamics Remember, ω is fracion of price seers ha keeps pas period s price; 1 ω is fracion of price seers ha ses new prices By definiion of he aggregae price index, he Calvo srucure herefore implies P = [ q q 1 ω (P 1 ) + (1 ω) (P P = ) [ 1 0 q ]q 1 q q 1 ] q 1 P (i) q 1 q q di q q 1 = Π = ω + (1 ω) ( ) q 1 q P P 1 Log-linearized around he zero-inflaion seady sae: and q q 1 π = where π p p 1 is he inflaion rae q q 1 (1 ω) (p p 1 ) π = (1 ω) (p p 1 ) 7

9 Rewrie (p*) as: p = βωe p +1 + (1 βω) ( v + p ), p p 1 = βωe [p +1 p ] + (1 βω) ( v + p ) p 1 + βωp, p p 1 = βωe [p +1 p ] + (1 βω) v + π. (p*) Use aggregae inflaion dynamics, π = (1 ω) (p p 1 ), o obain: (1 ω) 1 π = (1 ω) 1 βωe π +1 + (1 βω) v + π (1 ω) (1 βω) π = βe π +1 + κ v, κ. (6.36) ω An expecaions-augmened Phillips curve wih real marginal coss as he driving variable Noe how slope of Phillips cuve depends on he measure of nominal rigidiy ω: κ/ ω < 0 Equaion (6.36) and varians hereof are cenral in New-Keynesian moneary economics Accouns for more persisence han wo-period Taylor saggering: Afer wo periods, some firms are sill suck wih he same price Despie simpliciy, he Calvo model capures many aspecs of price daa 8

10 A view a prices changes: Belgium, Source: Cornille and Dossche (2006) 9

11 A view a prices changes: France and Ialy, Source: Dhyne e al. (2005) 10

12 A view a prices changes: France, hazard raes in clohing indusry Source: Baudry e al. (2004) 11

13 A view a prices changes: France: Hazard Raes in service indusry Source: Baudry e al. (2004) 12

14 A view a prices changes: (Monhly) frequencies of price adjusmens; Euro area vs. US Source: Dhyne e al. (2005) (wih US daa based on Bils and Klenow, 2004; Nakamura and Seinsson, 2008, find longer duraion for US by excluding sales) 13

15 Summary of findings from daa: Price seing in differen secors differs; some secors exhibi long and varying periods of fixed prices some secors exhibi coninuously changing prices Price seing is asynchronized across secors In some secors, probabiliy of price adjusmen is (nearly) independen of he life-span of price Secoral rigidiies ranslae ino aggregae rigidiies While long spells of fixed prices are consisen wih he Calvo model, i does no rule ou ha prices change due o economic circumsances, raher han he arrival of some lucky draw in a loery (now known as he Calvo Fairy ) Concepually, sae-dependen price seing (SDP) seems a leas as realisic 14

16 Sae-dependen price seing In SDP models, some fixed menu cos prevens firms from changing prices every period Mankiw (1985) demonsraed how small (second-order) menu cos could preven price adjusmen in equilibrium Laer models of he Ss varian showed how prices would remain unchanged, as long as variaions in opimal (flexible) price remained inside a band; when opimal price wen ouside he band, a firm would adjus SDP models are diffi cul o handle in macroeconomic models: he probabiliy of a price change becomes endogenous, and any differences beween firms creae aggregae price disribuions ha are diffi cul o analyze (in TDP models, firm heerogeneiy can be handled by differen exogenous probabiliies of adjusmen) 15

17 Main implicaion of SDP models: Less overall nominal rigidiy: Firms ha choose o adjus are he ones farhes away from he opimal price; hence a moneary shock will have smaller effec as hose who adjus, make a larger adjusmen (decisions are on boh he exensive and inensive margin) Caplin and Spulper (1987) was early exreme illusraion: Under SDP wih menu coss, money could be neural: Those adjusing, adjused so much so as o cause aggregae price changes o mach nominal shocks (and increased variabiliy of nominal shocks lead o more ofen adjusmens Gerler and Leahy (2008) presens a less exreme case, where he Ss decision rules across secors lead o an inflaion adjusmen equaion like π = βe π +1 + κ v, κ > κ less nominal rigidiy han in Calvo (6.36) (6.38) Dosey, King and Wolman (1999) assume ha firms face differen, random menu coss; aggregaion faciliaed by he propery ha hose adjusing will choose same price: Compared wih Calvo model, simulaions show ha he aggregae differences are no big on impac afer a moneary shock; bu he fracion of firms changing prices will increase over ime in conras wih he consan fracion under Calvo = Effecs of a moneary shock die ou faser While diffi cul o dispue ha firms in real life decide boh on he exensive and inensive margin, many argue ha he Calvo model in several dimensions provides a saisfacory modelling o inflaion deerminaion (when exended appropriaely) 16

18 Exensions on Calvo model: Inflaion persisence The basic Calvo model predics ha inflaion is enirely forward looking; pas inflaion does no maer for curren inflaion A odds wih convenional Phillips-curves of he NAIRU ype π = π 1 + ky, k > 0 where y is oupu or some oupu gap measure o capure real marginal coss Ulimaely an empirical issue wha is imporan. Recen exensions of he Calvo model, feaures lagged inflaion in he specificaion (called Hybrid New-Keynesian Phillips curves): and gives various reasons: π = (1 φ) βe π +1 + κ v + φπ 1, 0 < φ < 1, (6.42) Rule-of-humb behavior by hose adjusing prices; Galí and Gerler (1999) Deviaions from raional expecaions; Robers (1997) Indexaion of prices o pas inflaion; Chrisiano, Eichenbaum and Evans (2005) Mos empirical specificaions incorporae inflaion persisence o fi daa, bu evidence on he moivaions are weak [hence, he microfoundaions of (6.42) are no srong] 17

19 Hybrid Calvo Phillips curves: Time-series evidence (Are prices forward looking and wha are implied price sickiness?) Galí and Gerler (1999), Sbordone (2000): US pos-war daa; φ around and κ esimaed o imply expeced duraion of prices of 9 monhs (ω 0.66) Galí e al (2001): (pre-) Euro daa: φ very small Jensen (2010): Euro area : φ around 0.4 (paper/noe can be found on my websie; was background for my blog pos on he Phillips curve in February 2011 a alandelige.dk) Unseled issue: How o measure marginal coss? Oupu gap (and measured how?)? Labor share? Capaciy uilizaion? Very lively empirical area; in boh micro- and macroeconomerics Very imporan when we move o design of opimal moneary policy as he rade-off beween economic aciviy and inflaion is cenral o undersand Are inflaion expecaions imporan or no? (Will credibiliy issues maer or no?) Are dispersion among firms in he economy imporan for aggregae inflaion? 18

20 Concluding remarks: Wage and price rigidiies are real Source: Knell (2010, ECB WP) 19

21 Plan for nex lecures Tuesday, April 10, Exercises Exercise published on he web Thursday, April 12, Lecures Moneary credibiliy problems 1. Inflaion and discreionary moneary policy 2. Repuaional soluion o credibiliy problems Lieraure: Walsh (Chaper 7, pp ) 20