Inflation and Unit Labor Cost

Transcription

1 Inflaion and Uni Labor Cos January 2012 (Revised July 22, 2012) Rober G. King Deparmen of Economics, Boson Universiy and Mark W. Wason* Deparmen of Economics and Woodrow Wilson School, Princeon Universiy Absrac We sudy wo decomposiions of inflaion,, moivaed by he sandard New Keynesian Pricing Equaion of Gali, Gerler, and Sbordone. The firs uses four componens: lagged, expeced fuure, real uni labor cos (), and a residual. The second uses wo componens: fundamenal inflaion (discouned expeced fuure ) and a residual. We find large lowfrequency differences beween acual and fundamenal inflaion. From fundamenal inflaion fell by more han 15 percenage poins, while acual inflaion changed lile. We discuss his discrepancy in erms of he daa (a large drop in labor's share of income) and hrough he lens of a canonical srucural model (Smes-Wouers (2007)). *We hank Jordi Gali, Pok-sang Lam, Michael Siemer, wo referees, and paricipans a he Sudy Cener Gerzensee 25 h anniversary conference for commens on an earlier draf. Daa and replicaion files for his research can be found a hp://

2 1. Inroducion A noable developmen of early 21s cenury macroeconomics was he rise of dynamic sochasic general equilibrium models a cenral banks around he world. Consruced along New Keynesian lines, hese DSGE models have been increasingly employed as cenral banks placed greaer weigh on inflaion argeing frameworks for moneary policy, a imes explicily as in Canada and New Zealand and a imes implicily as in he U.S. and Europe. A price equaion sressing uni labor cos, modernizing specificaions developed along he lines of Ecksein and Fromm (1968) for an earlier generaion of quaniaive models, plays a cenral role in he ransmission of shocks from he real secor o inflaion in hese models. In addiion, raional price-seer expecaions of uni labor cos also play a key role in he models inflaion dynamics. This paper provides a ransparen accouning of he sources of inflaion wihin he canonical modern macroeconomic policy model, circa 2007, using leading examples of such New Keynesian DSGE modeling. Mos modern macroeconomic models feaure a srucural equaion designed along he lines of Gali and Gerler (1999) and Sbordone (2002) ha link inflaion o flucuaions in expeced inflaion and real uni labor cos (equivalenly, labor's share), which we erm he New Keynesian Pricing Equaion (NKPE). Noably, a paricular NKPE specificaion is a componen of he seven-variable DSGE model ha Smes and Wouers (2007) developed for he Unied Saes, which we ake as our reference DSGE model. The NKPE specificaions ha we use are of he hybrid form common o Gali and Gerler (1999) and Smes and Wouers (2007), in ha hey conain an inflaion lag as well as expeced fuure inflaion. They differ in he values and inerpreaion of he NKPE coefficiens in ways ha we discuss furher below, bu are oherwise similar. Boh feaure a link o a measure of real marginal cos, wih Smes and Wouers (2007) making a model-based correcion o sandard real uni labor cos. To focus aenion on he ineracion of he uni labor cos daa and he models, we do no esimae any srucural parameers in our work, bu simply use alernaive values esimaed by Gali and Gerler (1999) and Smes and Wouers (2007). Much of our analysis focuses on he sample period because his (roughly) coincides wih he sample period used by Gali and Gerler, Sbordone, and ohers, and because i was he behavior of inflaion over his period which moivaes much of his work. Afer 1

3 reviewing he main feaures of he behavior of inflaion and he heory of he NKPE, we make four conribuions. The firs wo involve he accouning focus discussed above. Firs, we develop and use a four-way decomposiion of he hybrid NKPE o break inflaion ino inflaion expecaions, inflaion ineria, cos, and residual. We show ha inflaion over is dominaed by he inflaion expecaions componen and ha real uni labor cos accouns for only a small par. This firs finding is common o he NKPE, when we use he parameer esimaes of Gali and Gerler (1999) and hose of Smes and Wouers (2007). This decomposiion highlighs how he NKPE is a double-edged sword for an inflaion argeing cenral bank: he dominance of inflaion expecaions in inflaion shows how imporan i is o manage hese, bu he small conribuion of real uni labor cos shows ha direc managemen is difficul wih emporary changes in aggregae demand. Second, we employ a wo-way decomposiion based on solving ou he NKPE o divide inflaion ino real cos and residual componens, wih each being he evoluion of an expeced presen discouned value. Following Gali and Gerler (1999) and Sbordone (2002) who sudied similar consrucions, we use he label fundamenal inflaion for he marginal cos componen. When we implemen his decomposiion using a bivariae inflaion-real uni labor cos VAR o forecas fuure values of real uni labor cos, we find (like hese prior auhors) ha fundamenal inflaion comoves srongly wih acual inflaion. The fundamenal inflaion decomposiion shows ha, despie a modes shor-run influence of cos, an inflaion-argeing cenral bank could conrol inflaion subsanially by having sysemaic policies o conrol real aciviy which smoohed he behavior of real uni labor cos. When we apply our wo-way decomposiion o he Smes and Wouers (2007) version of he hybrid NKPE using heir full general equilibrium model for forecasing marginal cos, we find ha fundamenal inflaion behaves very differenly from acual inflaion. This decomposiion suggess ha inflaion conrol would be more problemaic, as inflaion appears dominaed by shocks o he NKPE wihin he Smes and Wouers (2007) model. More generally, he link beween inflaion and coss appears very differen from an accouning perspecive, using he wo closely relaed NKPE frameworks. Third, we underake deecive work aimed a solving his inflaion-cos puzzle. Specifically, we consider how differences in he NKPE parameer values, forecasing mehods, and real uni labor coss measures aler he behavior of fundamenal inflaion. 2

4 Fourh, we explore how his inflaion-cos puzzle manifess iself in he srucural inerpreaion of inflaion dynamics wihin he Smes and Wouers DSGE model. Specifically we highligh how he srucure of heir model implies ha inflaion mus be explained primarily by he model's price shocks and also ha hese shocks mus have opposie effecs on inflaion and marginal cos. Simply pu, an imporan par of inflaion in he model arises from exogenous price shocks ha drive up inflaion and drive down labor cos. Bu he inflaion generaed by hese shocks is fairly emporary given he moneary policy rule, while he price markup shocks and he labor cos responses are highly persisen and move in opposie direcions. We describe why his negaive comovemen is an ineviable par of basic "firs generaion" sicky price DSGE models driven by highly persisen markup shocks and find i ineresing ha i also appears in he much more elaborae Smes and Wouers model. We hen look forward from he end of he basic daa inerval in 1999 o examine he inflaion cos puzzle in more recen imes, finding ha i inensifies, and hen look back o consider how he evolving behavior of uni labor coss undermines a key moivaion for he NKPE. When we exend he sample hrough 2010, he real uni labor cos series used by Gali, Gerler, and Sbordone -- as well as he measure used by Smes and Wouers -- exhibi large rend declines a he end of he sample. This leads o a collapse in fundamenal inflaion on he order of 15 percenage poins in he 2000s, a period in which acual inflaion is essenially unchanged. Sepping back, we recall ha he NKPE focus on cos measures was developed parly o avoid challenges raised by he modeling of capaciy oupu for empirical analysis of price dynamics: uni labor cos could poenially be unaffeced by real rends, while oupu would no be. 1 Ironically, i seems ha he marginal cos approach now faces he same issues of idenifying he effecs of rends and produciviy shocks ha were a major reason for modern pricing analysis o move away from oupu gaps. Our findings highligh he fac ha 1 Fuhrer (1997) argues ha he NKPE fails badly when a convenional oupu gap is employed. However, a class of modern macroeconomic models hose ha add nominal fricions o a real business cycle core framework imply a ime-varying level of capaciy oupu due o changes in produciviy and oher real facors ha would make convenional oupu gaps a poor proxy for pricing pressures, while a measure of real marginal cos (or average markup) would be an appropriae indicaor (see, for example, Goodfriend and King (1997)). Gali and Gerler (1999) make an explici empirical comparison beween marginal cos and oupu gap models of inflaion dynamics. 3

5 convenional uni labor cos measure is no longer a useful consrucion for inflaion dynamics and has no been a leas since he early 2000s. The organizaion of he paper is as follows. In secion 2, we briefly review he inflaion dynamics developed by Gali and Gerler (1999) and Sbordone (2002), which focuses on he comovemen of inflaion and real uni labor cos. In secion 3, we describe he wo accouning decomposiions discussed above for inflaion. In secion 4, we consider he implicaions of he NKPE using he parameer values and forecasing mechanisms previously developed in Gali and Gerler (1999) and hen we do he same for he Smes and Wouers (2007) framework. This isolaes he inflaion-cos puzzle discussed above: a SW fundamenal inflaion measure is very differen from boh acual inflaion and a GG fundamenal inflaion measure. 2 In secion 5, we conduc our deecive work and solve he puzzle, a leas in a mechanical empirical sense, and hen we describe how i is manifesed in he srucural impulse response of he Smes and Wouers DSGE model. In secion 6, we briefly look a inflaion and labor cos over he longer inerval. We documen ha a GG fundamenal inflaion measure displays he same aberran behavior over his exended inerval ha he SW fundamenal inflaion measure did earlier (and coninues o in recen years). The basic difficuly is ha real uni labor cos or, equivalenly, labor's share has declined dramaically since he mid 1990s wih lile accompanying change in inflaion. In secion 7, we provide a summary, conclusion, and discussion of direcions for furher work. 2 In his sudy, which involves replicaion and exension of prior work, here is poenial confusion beween he resuls of he original sudies and he resuls of replicaions/exensions developed along he lines of he sudies. We use full names o indicae maerial which is exacly aken from prior sudies, such as he parameer values esimaed by Gali and Gerler (1999) and Smes-Wouers (2007). When we refer o daa, we use he auhor's full names because we have carefully reconsruced and exended he daa employed hese auhors, so ha he series closely mach over he esimaion inervals for boh prior sudies wih some small excepecions discussed below (see Appendix A for some addiional deails). Thus, when we discuss he Gali-Gerler and Smes-Wouers measures of labor cos, we are referring o heir concepual consrucions and our daa se. Fundamenal inflaion (FI) plays an imporan role in our sudy, as i did in Gali and Gerler (1999) and Sbordone (2002). We use abbreviaions o indicae our FI consrucions. When we refer o GG fundamenal inflaion, his is our FI consrucion along Gali-Gerler lines bu i differs in some deails ha we discuss below. The SW fundamenal inflaion is our consrucion using Smes-Wouers parameer esimaes and our replicaion/exension of heir daa se. We hink i is an informaive consrucion, bu i is no one which hey used. 4

6 2. The New Keynesian price equaion We sar by providing a brief accoun of he moivaions for he New Keynesian pricing equaion (NKPE) sudied in his paper Forward-Looking Pricing The sandard New Keynesian modeling of price dynamics is aracive on wo dimensions. Firs, as widely noed, i is an implicaion of opimizaion in he Calvo seing, sressing he impac of curren and expeced fuure marginal cos on pricing. 4 Imporanly, i capures key dynamic inflaion implicaions of more elaborae models in a racable manner: here are a small number of parameers o esimae. 5 Second, i provides a near-neural linkage beween rend inflaion and real marginal cos. 6 The NKPE may be wrien as = be +1 + (1) where is a measure of real marginal cos, b is a discoun facor and is a nonlinear combinaion of he discoun facor, he expeced frequency of price adjusmen opporuniies, and oher srucural parameers in various versions of (1). Afer discussing his benchmark specificaion, Gali and Gerler (1999) develop a more general hybrid model of inflaion ha incorporaes a backward-looking componen o inflaion, = b 1 + f E z (2) raionalized by he inroducion of some price-seers who adop imiaive sraegies. In his expression, z is a residual erm, wih radiional ambiguiy in inerpreaion. 3 This specificaion is someimes called he "New Keynesian Phillips Curve." As i links inflaion o marginal cos raher han oupu or unemploymen, we prefer he erminology of Kurmann (2005). This erminology accuraely capures is role in NK-DSGE models as one equaion in a wage-price block. 4 Texbook reamens are provided by Gali (2008), Walsh (2010), and Woodford (2003). 5 See Robers (1995) for a comparison of specificaions. 6 This near-neuraliy propery is shared by many models, as noed, for example, by Robers (1995) and Goodfriend and King (1997)). I holds for sae dependen pricing models (see, Dosey, King and Wolman (1999). More recenly, Cogley and Sbordonne (2008) have considered he consequences of ime-varying rend inflaion wihin a higher order approximaion of he Calvo (1983) model. 5

7 There is an exensive lieraure on idenificaion, esimaion and esing of (2). Macroeconomiss are widely divided on wheher he fricions embedded in (2) are he mos imporan ones for undersanding he ineracion of inflaion and real variables, as well as on parameer esimaes and resuls of model specificaion ess. While his lieraure is valuable, is concerns are no ours: we simply ake he parameer esimaes in wo influenial sudies and underake accouning exercises based on hese parameer values. These exercises highligh dimensions of success, as in he prior lieraure, bu also subsanial empirical difficulies ha have no been sressed in he lieraure. 2.2 Decomposing inflaion In our analysis of he links beween pricing and real uni labor cos, we consider wo decomposiions of he sources of inflaion. Decomposiion 1 involves he elemens of (2) direcly, which we erm ineria ( b 1 ), expeced inflaion ( f E 1 ), real uni labor cos ( ) and he residual (z ). For his, we need an esimae of E +1 which we consruc using wo models: (1) an esimaed bivariae vecor auoregression using and and (2) he esimaed Smes-Wouers DSGE model. Decomposiion 2 involves he raional expecaions soluion of (2) i i 1 E j z Ez j j0 j0 (3) Given he parameers b, f, and he soluion parameers (,,, z ) are readily and uniquely deermined. 7 To make his decomposiion operaional, we need esimaes of he expecaion erms E +j and E z +j which are compued using a vecor auoregression and he Smes- Wouers model. The full ime series decomposiion ha we presen involves only wo componens, 7 This a second-order expecaional difference equaion familiar from Sargen (1978). For he specific formulas applicable in his case, see Gali and Gerler (1999, page 217). 6

8 z = + (4) in ha we solve for he pah of inflaion aribuing he 1 separaely o and z. Tha is: (5) i 1 i 1 E j (1 L) E j j0 j0 z z i 1 1 (1 L) i z Ez j z Ez j j0 j0 (6) We label as fundamenal inflaion, using he erminology of Campbell and Shiller (1998) and Gali-Gerler (1999) A preview of he daa and our main resuls Armed wih his framework, we can summarize he main resuls in he paper before going ino he deails of he models and our analysis. Decomposiion 2 uses fundamenal inflaion ( ) o summarize he relaion beween real uni labor coss () and inflaion (). Because is he discouned sum of expeced fuure, and because is highly serially correlaed (as we will see), he low frequency movemens in mimic he low frequency movemens in. Thus, an implicaion of he NKPE is ha inflaion inheris he low frequency movemens of real uni labor coss. The model is useful, in he sense ha i explains inflaion using real uni labor coss, if hese wo ime series share he same low-frequency behavior. Pu differenly, if he low-frequency behavior of inflaion differs markedly from he low frequency behavior of real uni labor coss, hen variables oher han real uni labor cos (z in equaion (2)) mus be imporan for explaining inflaion. 8 Our measure of fundamenal inflaion differs slighly from he measure used by Gali and Gerler. Their measure i is 1 E j 0 j i while our measure is 1 E j 0 j which differ in he value of lagged inflaion. We solve ou for he effecs of pas inflaion so as o make our resuls more concepually comparable o hisorical shock decomposiion such as hose employed in Smes and Wouers (2007). Generally, he Gali-Gerler measure will rack inflaion more closely, as i incorporaes he effecs of lagged z. Bu given ha he value of he persisence parameer is low (abou one-hird), he differences beween heir fundamenal inflaion and ours is pracically small. Furher, boh measures share he same low frequency properies sressed below. 7

9 Figure 1 plos inflaion and Gali and Gerler s measure. The wo series move ogeher over low frequencies, and he implied fundamenal inflaion series in Figure 3 capures imporan movemens in inflaion. Figure 4 plos inflaion and he Smes-Wouers measure. They have differen low-frequency behavior, and he fundamenal inflaion which we consruc for he Smes-Wouers model and displayed in Figure 7 differs markedly from acual inflaion. Thus, Gali and Gerler s model suggess ha real uni labor coss are he main drivers of inflaion, while Smes and Wouer s model suggess ha oher facors (z) play a dominan role. These figures cover he , he (approximae) sample period of ineres in early work on he NKPE. Figure 12 exends boh measures hrough 2010, and shows large pos declines in boh measures. Figure 13 shows ha hese declines in led o large falls in he corresponding measures of fundamenal inflaion, bu ha acual inflaion changed lile. Thus, he NKPE implies ha hese measures of have imporan low-frequency movemens unrelaed o he real marginal coss imporan for aggregae inflaion or ha oher facors (z) conspired o preven a dramaic fall in inflaion during he 2000s. This preview raises many quesions. Why do he measures used by Gali and Gerler and Smes and Wouers differ? Wha role do he specific parameer values in (2) play in hese conclusions? Do hese differences in fundamenal inflaion (decomposiion 2) lead o differen conclusions abou he imporance of expeced inflaion (decomposiion 1) in he inflaion process? Wha is he srucural inerpreaion of he z-variable in he Smes and Wouers model and how does i inerac wih? Why have real uni labor coss fallen so dramaically over he pas decade? And finally, given hese resuls, is he NKPE a useful empirical model for inflaion? The remainder of he paper akes up hese quesions. 8

10 3. Accouning wih jus he NKPE We now invesigae how he hybrid NKPE (2) accouns for inflaion during he period, using our wo decomposiions. For his purpose, we use he parameer values from Gali and Gerler (1999) displayed in Table Inflaion and RULC The cenral feaure of he New Keynesian pricing heory is a link o real marginal cos, mos frequenly proxied by real uni labor cos in applied work. Figure 1 shows he comovemen of GDP deflaor price inflaion () and log real uni labor cos (measured as he logarihm of he raio of nominal compensaion per hour o nominal oupu per hour in he nonfarm business secor). The real uni labor cos series moves ogeher wih inflaion, noably during he 1970s and 1980s. To operaionalize our decomposiions, we need o consruc E +1 for he firs and for he second. In each case, we follow Gali and Gerler (1999) and use a i E j 0 j bivariae VAR ha includes four lags of and o forecas he relevan variables. We consequenly call hese GG-VAR decomposiions. Addiional compuaion deails on he fundamenal inflaion decomposiion are provided in secion 5 below. 3.2 Resuls from Decomposiion 1 The resuls of decomposiion 1 are displayed in Figure 2. We find ha expeced inflaion is he dominan source of acual inflaion in Figure 2 ( f E +1 ). A smaller par of inflaion is due o inerial effecs ( b 1 is shown in panel A). Because he coefficien on real uni labor cos is small ( = 0.15), he real uni labor cos componen ( ) accouns for lile of he variaion in inflaion. Finally, residual influences (z = [ f E +1 + b 1 + ]) are quaniaively imporan. 3.3 Resuls from Decomposiion 2 While curren real uni labor coss accouned for lile of he variaion in inflaion using decomposiion 1, maers are very differen when expeced fuure real uni labor coss are included using decomposiion 2. Figure 3 displays he fundamenal componen of inflaion 9

11 over (he comparable Figure 2 in Gali and Gerler (1999) is for a slighly shorer z sample period, ). Given (4), he residual componen is jus he difference beween he inflaion and is fundamenal componen ( = ). Our GG fundamenal inflaion series does a reasonable job of racking acual inflaion during he inerval ha such expecaions-augmened pricing equaions were designed o explain: he rise in inflaion during he lae 1960s, he susained high inflaion of he 1970s, and he unwinding of inflaion in he early 1980s. Indeed, i is he close correspondence of fundamenal inflaion wih acual inflaion over hese periods ha many researchers found inriguing when hey were firs displayed in Gali and Gerler (1999) and Sbordone (2002). 9,10 z 3.4 Implicaions for modeling The racabiliy and empirical success of he NKPE led i o become a sandard, if conroversial, elemen of exbook presenaions of he New Keynesian approach o macroeconomics. 11 More imporan for our purposes, he NKPE was impored ino modern DSGE models employed by cenral banks around he world, as discussed in he inroducion. Wih many cenral banks underaking some version of inflaion argeing, Figures 2 and 3 capure why he NKPE approach was aracive as par of a larger model. Figure 2 is in line wih he idea ha inflaion conrol requires he managemen of expecaions, while Figure 3 suggess ha aggregae demand policies -- which affec inflaion hrough real marginal cos in hese models -- could be used for his purpose. A he same ime, he parameer esimaes of 9 The relaionship is less srong in he early and lae periods of our sample, wih much of poor performance in he laer period arising from revisions in he real uni labor cos daa ha were no available o Gali, Gerler, and Sbordone. 10 The esimae of fundamenal inflaion is subjec o subsanial sampling variabiliy ha is, appropriaely compued confidence bands in figure 3 are wide. Because fundamenal inflaion is a discouned sum of expeced fuure values of, he sampling variabiliy arises from uncerainy in he discoun facor and he parameers used o consruc he forecass. Because is large, uncerainy abou he long-run properies of he forecasing model are paricularly imporan. Characerizing his uncerainy is complicaed because he variables in he model, and, are highly serially correlaed so he VAR has roos near he uni circle, i.e., approximae uni roos. We have herefore no aemped o compue appropriae confidence bands. However, o give you some sense of he uncerainy, consider a simple version of he model in which follows a univariae AR(1), i = 1 + u, in which case fundamenal inflaion is given by (1 ) 1 (1 L) 1 u. Considering uncerainy in he firs erm, (1 ) 1, he 95% confidence inerval for compued using Sock s (1991) mehod ranges from o 1.012, and using he poin esimae of from able 1 ( = 0.876) yields a 95% confidence inerval for (1 ) 1 ha ranges from 4.1 o 8.8, so ha he scale varies by a facor of model ha 2. Addiional uncerainy arises from he esimaed values of and, and he persisence in. 11 See Gali (2008), Walsh (2010), and Woodford (2003). 10

12 Table 1 indicae ha major movemens in real marginal cos mus arise because he parameer is small (a 0.15 for he Gali-Gerler sudy) 12. Wih expeced inflaion held consan, cuing annualized inflaion by one percen in he curren quarer hus requires ha real marginal coss fall by 6 percen. The NKPE hus incorporaed he idea of a challenging shor-erm rade-off if expecaions are fixed, while having lile long-run rade-off wih changing expecaions. Sbordone (2002) highlighs he promise of he NKPE single equaion esimaes as follows: nominal rigidiies are a reasonable componen of a complee macroeconomic model. The failure of exising general equilibrium models which incorporae nominal rigidiies o accoun for all feaures of observed ime series (see King and Wason (1996); Chrisiano e al. (1997)) may no be due o a misspecified pricing equaion, bu raher o oher feaures of hese models (ha hey share wih sandard real business cycle models). We now urn o he analysis of a rich DSGE model. 4. Accouning wih he canonical NK-DSGE model While we can learn much abou inflaion and is relaion o uni labor cos from analyzing he NKPE in isolaion, i mus be imbedded in a complee srucural economeric model o answer quesions abou ineracions of inflaion and oher variables (oupu, ineres raes, employmen, ec.) and quesions abou he srucural sources of variabiliy and covariabiliy. In his paper, we sudy DSGE inflaion dynamics using he model of Smes and Wouers (2007). Along wih many oher builders of modern DSGE models, Smes and Wouers employ an alernaive roue o a hybrid NKPE han ha provided by Gali and Gerler (1999): hey assume ha a fracion of firms can dynamically index heir prices o he inflaion rae, raher han keeping hese fixed in nominal erms, a mechanism popularized by Chrisiano, Eichenbaum and Evans (2005) and developed in deail by Eichenbaum and Fisher (2007). 13 While his sory provides a differen moivaion for lagged inflaion in he NKPE, he resul also akes he form (2), albei wih a differen link beween ha equaion's coefficiens and srucural parameers. The Smes-Wouers sudy also employs a differen sample period, differen daa, 12 Noe ha heir esimae is jus under.04, bu is for a quarerly inflaion rae. As we are using annualized inflaion raes, we muliply by 4 o obain he.15 value referenced in he ex. 13 The fac ha acual micro prices are held fixed in nominal erms raher han adjused mechanically according o an index has led o subsanial criicism of he indexaion mechanism (see, for example, Collard and Dellas (2006)). 11

13 and a differen esimaion procedure. However, from he srucural parameers esimaed by Smes and Wouers esimaes (2007, able 1), we can calculae he implied values of, f, and b : we lis hese in Table 1 and use hem hroughou he paper. The Smes and Wouers (2007) model for he U.S. economy is a medium scale DSGE model. I feaures a neoclassical flexible price core ha is a real business cycle model augmened wih real fricions in invesmen (cos of changing he rae of invesmen) and consumpion (habi persisence) ha is subjeced o shocks o general producion and invesmen-specific echnology. 14 Monopolisic compeiion elemens are presen in boh labor and produc markes, wih variable elasiciy aggregaors of he Kimball (1995) form and wih overhead coss absorbing profis. Nominal sickiness along Calvo (1983) lines is inroduced ino boh produc and labor markes as in Erceg, Henderson, and Levin (2000). As previously discussed, here are addiional price and wage ineria mechanisms -- parial indexaion -- embedded in earlier DSGE models. Finally, he model is closed wih an ineres rae rule for moneary policy in he radiion of Taylor (1993). The Smes-Wouers model is esimaed using Bayesian mehods along he lines advocaed by An and Schorfheide (2007). A major impeus o DSGE model developmen was provided by he Smes and Wouers (2007) finding ha he model was compeiive in fi and forecasing wih sandard and Bayesian VAR models. As a medium scale DSGE model, he Smes and Wouers framework model conained predicions for a subsanial number of macroeconomic variables (abou 40). In esimaion, he auhors sough o mach 7 series of major ineres o macroeconomiss and policymakers: he growh raes of oupu, consumpion, and invesmen; he growh raes of nominal prices and wages; he level of labor inpu (aggregae hours); and he shor-erm nominal ineres rae. The auhors inroduced he minimum number of srucural shocks necessary o avoid a sochasic singulariy. They specified hese as a shock o oal facor produciviy, an invesmen specific echnology shock, a governmen purchase shock, an ineres rae spread shock, shocks o price and wage markups, and a moneary policy shock. Imporanly for our analysis, Smes and Wouers rea z differenly from Gali and Gerler along wo dimensions. Firs, hey give z a srucural inerpreaion as he exogenous 14 Variable depreciaion arising from endogenous capaciy uilizaion and overhead producion coss also augmen he core neoclassical model. 12

14 componen of a ime-varying markup of price over marginal cos. Second, hey specify is evoluion as z = p z 1 + p p p 1 (7) wih p = 0.89, and p = Processes wih subsanial moving average parameers have been used exensively in he lieraure on forecasing inflaion wih univariae ime series models (see, for example, Nelson and Schwer (1978) and Sock and Wason (2007)). The MA componen of he specificaion allows a forecasing model o capure he fac ha here are imporan high frequency componens of inflaion since a value of p = 0.69 means a curren forecas error induces a forecas revision ha is only abou 0.2 of he error (E z +1 E 1 z +1 = ( p ) p = 0.21 p ). Neverheless, since E z +j E 1 z +j = j ( p ) p, he implied price markup variaions are highly persisen. 4.2 Inflaion and Modified RULC The overhead srucure of producion in Smes and Wouers (2007) means ha sandard real uni labor cos does no accuraely measure real marginal cos. However, i can be measured by modified real uni labor cos, = (W P ) + n 1 y (8) where is he raio of oal cos (including overhead cos) o oal oupu. 16 The value of esimaed by Smes and Wouers implies ha he ypical firm has overhead cos ha are approximaely 60% of is oal cos, so ha 1.6. The Gali and Gerler measure of real uni labor cos akes he form as (8), bu wih = 1. As a pracical maer, he Smes and Wouers uni labor cos is hus less responsive o movemens in oupu relaive o real compensaion. 15 These numbers are he poserior means of he parameers, provided in Table 2 of Smes and Wouers (2007). In heir work, he parameer is called p o disinguish i from he AR parameer of oher shock processes. 16 While he Smes-Wouers -DSGE model was no direcly fi o mach modified real uni labor cos, i was fi o mach he join behavior of is ingrediens (W,n,P,y) and modified real uni labor cos is one of he many variables provided by he Smes-Wouers Dynare code ha is employed o esimae and simulae he Smes-Wouers -DSGE model. 13

15 The inflaion dynamics of he DSGE model obey he NKPE (2) using his modified uni labor cos consrucion. Figure 4 shows he inflaion and modified real uni labor cos series which we employ in our analysis of he Smes and Wouers DSGE model. Noe ha GDP inflaion is he same as in Figure 1; i is he labor cos series which is differen Decomposing inflaion in he Smes-Wouers model Smes and Wouers (2007) do no use eiher of our decomposiions, bu raher provide a hisorical decomposiion of inflaion ino componens arising from he various shocks, as in sandard vecor auoregression analysis. Figure 5 displays he DSGE model's decomposiion of he hisorical behavior of inflaion ino price markup shocks, wage markup shocks, moneary policy shocks, and all oher shocks. 18 The DSGE framework allows a furher breakdown of he las panel ino consequences of shocks o governmen purchases, general produciviy, invesmen-specific produciviy, and an ineres rae spread. However, given he focus of he presen sudy and o avoid unwieldy figures, we oped for a more limied breakdown. Some macroeconomiss would surely be surprised by his decomposiion, which aribues mos of he variaion in inflaion o price and wage shocks. Bu Keynesian economiss have long suggesed ha mos of inflaion is due o such facors. Oher macroeconomiss would poin o he fac ha he DSGE model indicaes ha moneary policy exered an imporan effec on inflaion -- firs posiive and hen sharply negaive -- during he lae 1970s and early 1980s. We now urn o he resuls of our decomposiions. 17 Gali-Gerler and Smes-Wouers also differ in some deails of heir measuremens of he componens of real marginal cos (W,P,n, and y). Gali and Gerler use measures for he non-farm business secor for all of hese componens. Smes and Wouers use full-economy measures for y and P (real GDP and he GDP deflaor), nominal compensaion per hour in he non-farm business secor for W, and compue n (oal hours of employmen) using average weekly hours in he non-farm business secor muliplied by employmen in he oal economy (from he U.S. household survey). Finally, because n and y are in per-capia erms, Smes and Wouers divide hours and oupu by a measure of populaion; his adjusmen is no necessary for Gali and Gerler (because =1 for heir measuremen of ). Edge and Gurkaynak (2010) discuss measuremen problems wih he populaion series used by Smes and Wouers. Our analysis is based on a modified version of he series ha eliminaes hese problems. See Appendix A for deails. 18 Our Figure 5 conveys similar conen o Figure 4 in Smes and Wouers (2007), bu is ailored o our purposes. Smes and Wouers (2007) combine price and wage markup shocks in providing he hisorical decomposiion of inflaion. 14

16 4.3 Decomposiion 1 Jus as we did for he Gali-Gerler NKPE parameer values, we can use (2) and he Smes-Wouers NKPE parameer values o decompose ino a componen associaed wih lagged inflaion ( ineria ), expeced fuure inflaion, real uni labor cos (, now using he modified uni labor cos series), and residual (z in equaion (2)). However, o generae inflaion expecaions, we now use he inflaion forecas from he full Smes and Wouers (2007) DSGE model, so ha we label he decomposiions as SW-DSGE. The resuls are shown in Figure 6. Comparing hese o he corresponding figure for our replicaion of Gali and Gerler (Figure 2) leads o he same finding: expeced inflaion is he dominan force in curren level of inflaion. Evidenly his conclusion is robus o he range of parameer values encompassed by Gali-Gerler and Smes-Wouers as well as o he differences in he way real marginal cos () is measured. 4.4 Decomposiion 2 Similarly, we can use (5) and (6) o break ino a marginal cos componen ( fundamenal inflaion, ) and price mark-up componen ( z ) for he DSE model. Each componen depends on curren and expeced fuure values: we use he full Smes and Wouers DSGE model o consruc he forecass, for example j0 j E j in fundamenal inflaion. Figure 7 provides acual inflaion and our consruced SW-DSGE fundamenal inflaion. While Figure 3 shows a plausibly close relaion beween he acual inflaion and he GG- VAR over much of he sample period, no such relaion is eviden in Figure 7. Noably, since = + z, Figure 7 insead suggess ha over he period, inflaion was he resul of wo counervailing rends: a large downward rend in he marginal cos componen,, ha was essenially cancelled ou by an upward rend in he price markup componen, z. 4.5 The Inflaion-Uni Labor Cos Puzzle The behavior of inflaion wihin he DSGE seup hus provides a puzzle, which we can pose as a series of quesions. Why are he single equaion and DSGE resuls for fundamenal inflaion so differen? Is i because he NKPE parameers in Table 1 are no he same? Is i because uni labor cos, as modified by Smes-Wouers, is a poor proxy for marginal cos, while 15

17 he GGS consrucion beer capures marginal cos? Is i because, as wih Sbordone's (2002) appraisal of an earlier generaion of sicky price DSGE models, here is somehing crucially wrong wih he res of he Smes and Wouers model as a driving process for inflaion? Or is i somehing else abou he comovemen of inflaion and real uni labor cos? We now urn from being accounans o being deecives. 5. Undersanding fundamenal inflaion As we have seen, he esimae of fundamenal inflaion based on he GG-VAR model indicaes ha much of he variaion in inflaion over was associaed wih variaion in expeced fuure marginal cos (i.e., fundamenal inflaion shown in Figure 3). By conras, our SW-DSGE consrucion of fundamenal inflaion is no close o variaions in acual inflaion. In his secion, we invesigae why he wo models yield such dramaically differen fundamenal inflaion series over Common compuaional framework To sor hrough he sources of differences in he wo fundamenal inflaion measures, i is useful o inroduce some noaion and a common compuaional framework. For boh he GG fundamenal inflaion consrucion (based on a VAR) and he SW consruc (based on he DSGE model), fuure values of are forecas using a sae-vecor, say d which evolves as d = Md 1 + u (9) where u is an unforecasable error vecor. For he GG measure of fundamenal inflaion, d conains curren and lagged values of inflaion and real uni labor, when we place heir VAR in he companion form (9). For he SW measure, d is he sae-vecor for he DSGE model. In boh models is linearly relaed o d, ha is = d (10) 16

18 where, for he GG-VAR model is a selecion vecor ha exracs from he sae vecor d, and for he Smes-Wouers-DSGE model is a vecor of coefficiens. Thus, each version of fundamenal inflaion can be wrien as ' [ I M] d (1L) ' [ I M] d (11) where he expression uses he definiion of fundamenal inflaion in (5) ogeher wih he formula for compuing expeced discouned familiar from Campbell and Shiller (1988). Equaion (11) highlighs wo imporan differences in he GG-VAR and SW-DSGE measures of fundamenal inflaion. The firs is ha here are a differen se of parameers for he hybrid NKPE, ha is he values of,, and in (11). 19 In wha follows we denoe he hybrid NKPE parameers by = (,, ), wih GG and SW denoing he parameer values implied by he Gali-Gerler and Smes-Wouers srucural parameer esimaes. The second difference is ha here is a differen forecasing model, ha is he values of M and d in (11). Finally, a hird imporan difference is ha he daa used for forecasing (d) is no he same across he wo sudies, as we discuss furher below. More absracly, based on (11) we can represen fundamenal inflaion as (, M, ), indicaing is dependence on NKPE parameers, on he forecasing model, and on he empirical measure of marginal cos employed. (Inflaion eners, oo, bu i is a common ime series and canno be he source of any differences given hese oher elemens). Using his noaion, we have so far looked a ( GG, M GG-VAR, GG ) in Figure 3 and ( SW, M SW-DSGE, SW ) in Figure Differen cos measures As discussed above, one source of he difference beween he fundamenal inflaion measures is he empirical measure of. Figure 8 plos he sandard real uni cos measure used by Gali and Gerler and he modified version used by Smes and Wouers. A sriking feaure of he plo is he differen low-frequency behavior of he wo series, paricularly pos-1980, wih he Smes-Wouers modified measure showing a more pronounced decline from 1980 unil he 19 Recall from secion 2 above ha hese parameers are funcions of b, f, and : he implied values of,, and are lised in Table 1. In urn, for he Smes-Wouers model, b, f, and are funcions of deeper srucural parameers. 17

19 mid 1990s. Derended values of he series are shown in Appendix B; he derended series generally move ogeher: he correlaion beween he derended series is Evidenly, differences in low-frequency behavior of GG and SW are poenial souces of he differences in he wo fundamenal inflaion series. 5.3 An approximaion o fundamenal inflaion To simplify maers, we find i useful o inerpre he various versions of using an approximaion and a relaed pair of approximaion coefficiens. To moivae his approximaion, consider he GG-VAR forecasing model in which d conains curren and lagged values of and. From (11), fundamenal inflaion will hen depend on a disribued lag of and, (L) (L) (12) where he polynomials in he lag operaor, (L) and (L), depend on and M. By rearranging he sae vecor (which one can always do wihou changing any implicaions of he model (12)) we creae an alernaive equivalen form, (1) (1) (L) (L) (13) This new formulaion (13) pulls ou a single level of and ogeher wih lags of he firs differences = 1 and = 1. In (13) he coefficiens on he levels of and are he sums of he coefficiens in disribued lag in he original equaion (12) so hey can be wrien as (1) and (1). The rearrangemen yielding (13) les us break up ino a level componen, (1) + (1), and an addiional componen ha is a disribued lag of changes ( (L) + (L) ). Because and are persisen and because depends on long-run forecass of fuure mos of he variabiliy in arises from he level componen, (1) + (1), and 18

20 he disribued lag of changes, (L) + (L), has relaively lile effec on. Thus, we will approximae by, where = (1) + (1) (14) The advanage of his approximaion is ha i allows us o characerize differences in fundamenal inflaion using only he coefficiens (1) and (1), as well as he measure of real marginal cos,. This approximaion canno be direcly used for he SW-DSGE measure of because i is based on a sae vecor d ha conains variables oher han and, so ha (12) does no hold. To overcome his problem, we compue an approximaion in wo seps for he SW fundamenal inflaion. In he firs sep, we use he DSGE model o compue he model-implied populaion values of he auocovariances and cross-auocovariances for and : from hese, we compue he implied bivariae VAR coefficiens for and wih he same number of lags used in he GG-VAR fundamenal inflaion. In he second sep, we compue he approximaion (12) using he model-based bivariae VAR coefficiens and daa on and. Figure 9 shows he GG-VAR and SW-DSGE measures of fundamenal inflaion (, from Figures 3 and 7) ogeher wih heir approximaions ( using (14)) and where each approximaion is based on a bivariae VAR, as discussed above. The GG approximaion uses he Gali-Gerler measure of (real uni labor cos) and he SW approximaion uses he Smes- Wouers measure of (modified real uni labor cos). In panel A of Figure 9, we see ha he GG consrucs, and, essenially coincide: GG GG hus, we can capure mos of he variaion in using o coefficiens (1) and (1) along wih he levels of GG and. In panel B of Figure 9, we see ha he approximaion is less han perfec for he SW consrucs, bu does capure much of variaion in (he correlaion beween he wo series is 0.97). So, we view he approximaion as reasonable in each case. How does he approximaion help us in our deecive work? We wan o learn abou he relaive imporance of NKPE model parameers he forecasing model parameers M, and 19

21 he empirical measure of marginal cos in generaing he sriking difference beween he GG- VAR and SW-DSGE measures of fundamenal inflaion. Firs, we can see ha he disribued lag weighs (L) and (L) in (12) depend only on (he parameers in he NKPE) and M (he sae-ransiion marix ha governs he forecasabiliy of fuure values of real marginal cos), equaions (12) and (14): we can hus change and M separaely and deermine he effec on jus wo numbers, (1) and (1) Secondly, we see ha he paricular measure of marginal cos plays a role. Taking hese poins ogeher, any differences in measures of fundamenal inflaion can be aribued o he choice of, M, and a paricular empirical measure of real marginal cos. This allows us o invesigae he source of he differences beween he wo fundamenal inflaion measures by changing he values of, M, and Mixing and Maching, M, and Table 2 summarizes he behavior of (, M, ), for various values of, M, and. Five summary saisics are shown for each measure of fundamenal inflaion: (1) and (1) are he coefficiens from (14), ( sample period, cor(, approximaion in (14), and cor(, ) is he sandard deviaion of over he ) is he correlaion beween fundamenal inflaion and he ) is he correlaion of acual inflaion wih. The able highlighs wo ses of benchmark resuls, presened in he boldfaced rows 1 and 6. These abulae informaion on he fundamenal inflaion and approximaion series displayed in Figure 9. Firs, row 1 of he able shows resuls for he GG-VAR fundamenal inflaion and is approximaion, based on (14) and ploed in Panel A of Figure 9. Row 1 indicaes ha he approximaion depends posiively on boh and wih weighs (1) = 1.30 and (1) = 0.26; ha i has a volailiy jus slighly higher han acual inflaion (( ) = 2.90 versus () = 2.53); ha he approximaion is nearly perfec cor(, ) = 0.99); and ha i capures many of he movemens in acual inflaion (cor(, ) = 0.61) over he sample period. Second, row 6 shows he resuls for he SW-DSGE series ploed in Panel B of Figure 9. In conras o he resuls jus discussed, row 6 shows ha he SW-DSGE approximaion places a larger posiive weigh on ( (1) = 1.89), bu a negaive weigh on 20

22 ( (1) = 0.89); ha i has a volailiy much higher han acual inflaion (( is a good, bu no perfec approximaion (cor(, uncorrelaed wih acual inflaion (cor(, ) = 0.02). ) = 0.97); and ha i is essenially ) = 5.22); ha i To look behind hese sark differences, he oher rows of he able summarize he behavior of compued using differen permuaions of, M, and. For example, row 2 shows resuls for ( SW, M GG-VAR, GG ), i.e., an approximaion compued using he GG measure of real uni labor cos ( GG ) and forecasing model (M GG-VAR ) bu using he Smes- Wouers NKPE parameer values ( SW ). Comparing he various rows in he able leads o he conclusion ha all of he (, M, ) ingrediens play complemenary roles in explaining he differences beween he GG and SW measures of fundamenal inflaion. We discuss each ingredien in urn. To undersand he role of he parameer values, compare he row 2 informaion on ( SW, M GG-VAR, GG ), and he benchmark in deail. Noe ha he Smes-Wouers esimaes in Table 1 pu more weigh on expeced fuure inflaion (higher ) in he NKPE. In urn, his leads o more weigh placed on expeced fuure values of in fundamenal inflaion. (From Table 1, he Smes-Wouers discoun facor is SW =.998 while he corresponding Gali-Gerler value is GG = 0.876). Turning o our approximaion, wih M and held consan (based on GG), (1) is slighly smaller and (1) is subsanially larger (rising from 0.26 in row 1 o 0.99 in row 2) compued using SW raher han wih GG. Bu i canno be he Smes-Wouers parameers alone ha lead o he difference, as row 2 of Table 2 also shows ha (i) he approximaion becomes more highly correlaed wih acual inflaion; and (ii) i also becomes oo volaile relaive o acual inflaion. To undersand he role of he forecasing model M, sar by looking a he firs hree rows of he able: each uses M GG-VAR i.e, forecass consruced using a VAR esimaed using he GG measure. These measures are differen on some dimensions (such as volailiy and correlaion wih acual inflaion), bu hey all place a weigh on he measure ha is posiive and less han he corresponding values using M SW-VAR or M SW and a weigh on ha is posiive ( (1) = 0.26 in rows 1 and 3 and is 0.99 is row 2). By conras, here is a very differen paern in all of he oher rows of he able: he weigh placed on is posiive and large, and he weigh 21

23 placed on is negaive ( (1) < 0). Said differenly, wih fixed, increases in predic decreases in fuure when he SW forecasing model is used, bu predic increases in when he GG forecasing model is used. This finding holds robusly: (i) i occurs when he forecasing model is esimaed using he Smes-Wouers measure of, eiher direcly in a VAR in rows 4 and 5 (M SW-VAR ) or indirecly using he complee Smes-Wouers DSGE model in rows 6 and 7 (M SW ) and (ii) i occurs when he parameers are hose of Gali-Gerler (lines 4 and 7) or Smes- Wouers (lines 5 and 6). 20 Finally, o undersand he role of he empirical measure of in fundamenal inflaion, noice ha cor(, ) is close o one for all rows in he able (ha is for boh he GG and SW measures). This is consisen wih he approximaion equaion (14) ha shows, for a given value of (1), he measure of has a direc effec on he approximae measure of fundamenal inflaion. Taken ogeher hese resuls sugges a wo-par explanaion for he rending behavior of in he SW-DSGE fundamenal inflaion consrucion displayed in Figures 7 and 9. In he firs half of he sample period ( ), he seep decline in arises largely from upward rend in acual inflaion via he (1) componen of our approximaion o fundamenal inflaion. This curious resul arises because here is a negaive value of (1) = 0.89 in line 6 of Table 2. In he second half of he sample period, here is lile low frequency variaion in inflaion. However, he Smes-Wouers modified real uni labor cos measure shows a marked decline which, when amplified by (1) = 1.89 in line 6 of Table 2, leads o a seep decline in he measure of fundamenal inflaion ha we have consruced for he Smes-Wouers model and daa. A pronounced decline does no arise in he benchmark GG-VAR measure (displayed in Figure 9A) of fundamenal inflaion, because our approximaion indicaes ha heir forecasing model does no imply a negaive relaionship beween and fundamenal inflaion (ha is, 20 To help undersand he role of M for he sign of (1) consider he VAR(1) model, y = y 1 +, where y = ( ). In his case, he discouned sum of fuure expecaions of y is given by Ay, where A = (I ) 1, so ha (1) is proporional o A 12. When A is posiive, he sign of (1) is deermined by he sign of 12. When 12 is posiive, high values of inflaion oday predic high values of in he fuure; when 12 is negaive, high values of inflaion oday predic low values of in he fuure. In he general VAR(p) model y = (L)y 1 +, he same resul holds as an approximaion wih (1) (he sum of he coefficiens) replacing. In he VAR represened by M GG-VAR, (1) 12 is posiive ( (1) 12 = 0.03), while i is negaive in he approximae VAR consruced using M SW ((1) 12 = 0.15) and when using he VAR esimaed direcly using he Smes-Wouers daa, M SW VAR ((1) 12 = 0.03). 22

24 (1) > 0) and because he Gali-Gerler measure of real uni labor cos does no show he same rend decline eviden in he Smes-Wouers cos measure. 5.4 DSGE srucural inerpreaion We now urn o undersanding aspecs of he comovemen of inflaion and cos wihin he DSGE model Why does high inflaion forecas low cos? While his forecasing exercise explains he empirical mechanics underlying he lowfrequency behavior of SW fundamenal inflaion, i doesn' explain how his behavior is manifesed in he Smes and Wouers srucural DSGE model. For example, wha is i in he srucural model ha explains why high inflaion oday predics low fuure values of marginal cos? Tha is, wha is i in he Smes-Wouers model ha leads o a negaive value of (1)? This negaive value is paricularly puzzling because he underlying economics of he NKPE indicae jus he opposie: if oday's inflaion arises from expeced fuure values of real marginal cos, hen high inflaion predics high (no low) values of fuure marginal cos. To see how he model can generae a value of negaive value of (1), recall ha inflaion is compleely decomposed ino a componen (fundamenal inflaion, specified in (5)) associaed wih expeced fuure and a componen z associaed wih expeced fuure price markup variaions (specified in (6)). The Smes-Wouers model conains seven exogenous shocks. One of hese, p, is a price-markup shock and he six ohers, which we'll collec in a vecor oher, represen shocks o produciviy, ineres raes, and so forh. The NKPE makes a srong resricion, ha oher affecs only hrough is effec on. In conras, he pricemarkup shock, p, affecs in wo ways: firs direcly hrough he effec of p on curren and expeced fuure values of z (z = (1 p L) 1 (1 p L) in he Smes-Wouers DSGE model), and indirecly hrough he general equilibrium effecs of hese shocks on curren and fuure values of. Thus, consider a oher shock ha leads o an increase in. Because his arises hrough, he shock induces a posiive correlaion beween and. Indeed, if was affeced only by oher shocks, hen =, so ha in he forecasing exercises in he las secion (1) = 0 and p 23