Has the Inflation Process Changed? A Comment *

Transcription

1 Has he Inflaion Process Changed? A Commen * Jordi Galí CREI, UPF, CEPR and NBER Augus 2004 * Based on he discussion of Cecchei and Debelle s paper Has he Inflaion Process Changed? presened a he Third BIS Annual Conference, Brunnen, June 2004.

2 Inroducion The paper by Cecchei and Debelle (CD, henceforh) makes an ineresing conribuion o he growing lieraure on inflaion dynamics. The firs par of he paper is largely descripive, and complemens oher recen aemps o idenify he presence of significan changes over ime in he ime series properies of inflaion measures. CD s analysis makes use of aggregae and secor-level CPI inflaion daa for a number of OECD counries. They conclude ha he presence of a change in he mean of inflaion, observable for mos counries and CPI componens, is he dominan feaure of he daa. Once ha change in mean is accouned for, he degree of inflaion persisence is relaively small, and does no display a significan decline over ime in mos cases. Furhermore, and wih few excepions, neiher observed changes in he mean or in he persisence measures can be mapped clearly o he changes in moneary policy regime ha have aken place during he period considered for many of he counries in heir sample. The previous saisical resuls compiled by CD are a valuable addiion o he curren sock of evidence on he properies of inflaion. Mos significanly, some of CD s findings quesion boh he resuls and conclusions drawn by oher auhors. In he second par, CD ry o go beyond a simple saisical characerizaion, aiming insead a providing an assessmen of exising srucural price-seing models in ligh of he evidence of a cross-secional connecion (or lack hereof) beween CD s inflaion persisence measures and he indicaors of price rigidiies developed by several auhors in he conex of he ECB s Inflaion Persisence Nework. CD show ha no significan relaionship beween hose measures can be deeced. Independenly of he previous evidence, he finding of relaively low inflaion persisence leads CD o conclude ha he early criicisms of opimizing forward-looking price seing models ha were grounded on he apparen inconsisency of he laer wih he presence of high inflaion persisence may be misplaced.

3 My discussion below focuses on wha I view as an imporan cavea in CD s inerpreaion of he sor of reduced-form evidence found in he presen paper, a cavea ha is also found in some of he relaed lieraure. Inflaion Persisence and Opimizing Price-Seing Models Underlying much of CD s analysis and is moivaion is he noion--sressed by auhors like Fuhrer and Moore (1995)--ha he evidence poining o high inflaion persisence is inconsisen wih he opimizing price seing models ha have been widely adoped in he recen moneary business cycle lieraure. Those models, CD claim, generae high persisence in he price level (which would be increasing in he degree of sickiness), bu no in is firs difference (i.e., in he rae of inflaion). The evidence of very low persisence uncovered by CD (when proper reamen of shifs in means is made) is hus presened as reconciling (a leas parly) he univariae evidence on inflaion persisence wih he abovemenioned srucural models. Bu o wha exen do opimizing, forward looking models necessarily imply low inflaion persisence? Nex, I show by means of hree simple examples ha he connecion beween price sickiness and persisence is no an obvious one. Example #1: Inflaion Persisence wih an Exogenous Oupu Gap Consider an economy for which inflaion dynamics are described by he difference equaion { } = E + κ θ x + 1 where x is he oupu gap, β is he discoun facor, and κ θ is a coefficien inversely relaed o he degree of price sickiness (see, e.g., Galí and Gerler (1998) for a derivaion). The previous inflaion equaion, based on a price seing model originally due o Calvo

4 (1983) and usually referred o as New Keynesian Phillips curve (NKPC), is a key building block of he workhorse framework used for moneary policy analysis. I implies ha inflaion is a purely forward-looking variable, in he sense ha pas inflaion does no play an independen role in deermining curren inflaion. Insead he laer depends exclusively on curren and expeced fuure values for he oupu gap. Suppose nex ha he oupu gap follows an exogenous AR(1) process x = ρ x + u x 1 where ρx [0,1) and u is whie noise. In ha case i is easy o show ha inflaion will also follow an AR(1) process of he form κ = ρx θ 1 + u 1 βρ x In oher words, inflaion will inheri he persisence of he oupu gap. An increase in he degree of price sickiness would reduce κ θ and, as a resul, would lower he variance of inflaion. Bu i would no have any effec on is persisence. Hence, on he basis of he previous analysis, here is no reason o expec any connecion (across counries or secors) beween measures of inflaion persisence, on he one hand, and indicaors of he degree of price sickiness on he oher. Furhermore, he evenual finding of high inflaion persisence canno be inerpreed as evidence of any srucural dependence of curren inflaion on pas inflaion: as illusraed in he above example, ha dependence may be non exisen, wihou ha implying any consrains on he persisence of inflaion iself. Of course, he assumpion of an exogenous oupu gap is clearly unrealisic, so perhaps one may suspec ha any evenual influence of price sickiness on inflaion migh work hrough is effec on he oupu gap. Evaluaing he previous hypohesis requires laying down a fullfledged model, so he answer is likely o depend on some deails of he model. The following example, based on a sandard model from he lieraure, illusraes how he persisence of inflaion is no necessarily relaed o he degree of price sickiness, even when we endogenize he oupu gap.

5 Example #2: Inflaion Persisence under a Simple Taylor Rule Suppose ha, in addiion o he NKPC inroduced above, he economy s equilibrium is described by a new IS-ype equaion 1 x = E { x } r E { } r σ * ( ) ogeher wih a simple Taylor rule deermining he shor erm nominal rae r r = φ where φ >1 (a sufficien condiion for a deerminae equilibrium), and an exogenous process for he naural real rae degree of price sickiness and he moneary policy rule): * r (which by definiion mus be independen of boh he r = ρ r + v * * r The soluion o he model above yields he following reduced form process for inflaion: = ρ + ψ v r 1 where ψ can be shown o be a decreasing funcion of he degree of price sickiness (in addiion o showing a negaive relaion wih he inflaion coefficien φ in he Taylor rule). Bu, mos imporanly for our purposes, he persisence of inflaion is independen of he degree of price sickiness and he srengh of he cenral bank s response o inflaion. Insead, inflaion inheris he persisence of he naural real rae (given by ρ r ), which is by definiion independen of he degree of price sickiness or he moneary regime. Example #3: Inflaion Persisence wih a Hybrid NKPC Finally, le me consider an economy in which a fracion of price seers follow a simple backward-looking rule-of-humb ha makes heir newly se prices depend parly on lagged inflaion, whereas he res of firms behave in an opimizing forward-looking way as in he

6 basic Calvo model. In ha case, and as shown in Galí and Gerler (1998) he dynamics of inflaion are given by he hybrid NKPC { } = γ + γ E + λx b 1 f + 1 where γ b and γ f are, respecively, increasing and decreasing in he fracion of backward looking firms and wih he oupu gap following he same exogenous AR(1) process considered in our firs example. The reduced form process for inflaion is given by = δ + λ δγ 2 f 1 ρδ x γγ b f where δ1. In conras wih he previous examples, he persisence of 2γ f inflaion in his case does depend on characerisics of he economy oher han he persisence of he oupu gap iself. In paricular, i can be shown (afer some edious algebra) ha δ 1 is increasing in he fracion of backward-looking firms (as one would anicipae), bu decreasing in he degree of price sickiness ( somewha less inuiive resul). Hence, in he conex of he hybrid NKPC model proposed above, low levels of inflaion persisence (as deeced in he CD paper) will emerge in economies wih (i) a small fracion of backward-looking firms, and (ii) high degrees of price sickiness, a configuraion consisen wih he srucural esimaes in Galí and Gerler (1998), among ohers. Neverheless, and as illusraed by examples #1 and #2 above, ha propery is far from being robus o he specificaion of he environmen. Furher work is clearly needed in order o undersand beer he connecion beween inflaion persisence, price sickiness and oher feaures of he price seing process before we can jump o any hard conclusions in he ligh of reduced form evidence like he one presened by CD in heir paper. 1 x Inflaion Persisence and Measuremen Error Le me conclude my discussion of he CD paper wih a brief commen on an aspec of heir evidence ha could easily be missed by he casual reader. CD carry ou heir empirical analysis

7 using CPI daa for 17 counries. Wih he excepion of Ausralia and New Zealand for which quarerly daa are used, he frequency of he ime series analyzed is monhly, corresponding o monh-o-monh changes in he (log) CPI. Tha choice, which conrass wih he more common use of quarerly inflaion daa in he relaed lieraure, is poenially problemaic. The reason is simple and well-known o anyone who has ever ploed a monh-o-monh inflaion series (CD refrain from doing so): ha series is exremely volaile, possibly because of measuremen error or emporary facors unrelaed o underlying inflaion rends. The excess noise associaed wih hose series may accoun for much of he low persisence uncovered in he daa, relaive o oher sudies. A formal analysis of he implicaions for he esimaed of inflaion persisence of he daa frequency chosen lies beyond he scope of he presen paper, bu should cerainly be kep in mind, especially when aemping comparisons across sudies. References Calvo, Guillermo (1983): Saggered Prices in a Uiliy Maximizing Framework, Journal of Moneary Economics, 12 (3), pp Fuhrer, Jeffrey and George Moore (1995): Inflaion Persisence, Quarerly Journal of Economics,110, Galí, Jordi and Mark Gerler (1999): Inflaion Dynamics: A Srucural Economeric Analysis, Journal of Moneary Economics, vol. 44, no. 2,