Sectoral Effects of Aggregate Shocks. Nathan S. Balke Southern Methodist University And Federal Reserve Bank of Dallas*

Transcription

1 Secoral Effecs of Aggregae Shocks Nahan S. Balke Souhern Mehodis Universiy And Federal Reserve Bank of Dallas* Revised July Absrac: In his paper, using a combinaion of long-run and sign resricions o idenify aggregae moneary and produciviy facors, I find ha he moneary facor is responsible for long swings in nominal variables bu has lile effec on flucuaions in oupu, real wage, or labor inpu growh. The produciviy facor in addiion o increasing oupu growh and real wage growh in he shor and long runs, also resuls in increases in labor inpu and decreases in prices, bu he quaniaive effec of he produciviy facor on labor inpu is relaively small. These resuls are robus o he number of facors included in he model and o alernaive priors abou he shor-run effecs of he moneary facor, and o he inclusion of oil prices. Oil prices, in fac, appear o be largely driven by he oher aggregae facors. * This is a much revised version of a previous paper iled Secoral Effecs of Moneary Shocks. I hank an anonymous referee, paricipans a he Advances in Economerics conference held in honor of Tom Fomby and Carer Hill as well as seminar paricipans a Souhern Mehodis Universiy, Washingon Universiy, The Federal Reserve Bank of Dallas, Texas Tech Universiy, Universiy of California a Riverside, and Sam Houson Sae Universiy for commens. Thanks o Anna Marie Herrera, David VanHoose, Jeremy Piger, Mark Wynne, and Evan Koenig for useful conversaions abou his projec. The views expressed are hose of he auhor and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.

2 . Inroducion Much of he recen lieraure on accouning for he sources of economic flucuaions have focused on moneary and produciviy shocks. Quanifying he effec of money shocks is imporan for evaluaing heories of price sickiness and for deermining he efficacy of moneary policy. Produciviy or echnology shocks have feaured prominenly in sochasic general equilibrium models of business cycles alhough recen empirical work has cas doub on he abiliy of echnology shock driven models o explain business cycle flucuaions. Mos of he lieraure use VARs o describe he daa generaing process and assume a recursive srucure o idenify economic shocks. These recursive schemes are no always well moivaed and ofen rely on ad hoc iming resricions. A few papers have applied non-recursive idenificaion schemes. For example, Gali (99) and ohers use long-run resricions o idenify moneary shocks while Gali (999) and Francis and Ramey () use long-run resricions o idenify produciviy shocks. These long-run relaionships are ofen hough o be more robus across models and policy regimes. 3 Sign resricions raher han zero resricions for impulse responses have also been used o idenify moneary shocks (Faus (998), Canova and De Nicolo () and Uhlig ()) as well as produciviy shocks (Peersman and Sraub (9)). Again, hese sign resricions migh be viewed as less sringen and more robus o alernaive economic srucures han radiional recursive zero resricions. See Chrisiano, Evans, and Eichenbaum (999) and () for an exensive review of he VAR lieraure on quanifying he effec of moneary shocks on economic aciviy. See for example, Gali (999), Francis and Ramey (), and Basu, Fernald, and Kimball (6). 3 Using long-run resricions o idenify srucural shocks is no unconroversial, see for example he criique of Faus and Leeper (997), Chari, Kehoe, and McGraan (8) and Dupor and Kiefer (8).

3 In his paper, I depar from he sandard approach aken in mos of he lieraure in several key respecs. Firs, insead of using aggregae daa, I use mached secoral daa on prices, oupu, wages, and labor inpu o idenify moneary and aggregae produciviy shocks. Using disaggregaed daa can bring addiional informaion o bear in idenificaion beyond ha in aggregae variables alone. No only are more series used, bu economic heory ofen has implicaions for secoral variables as well as for aggregae variables. For example, I use long-run moneary neuraliy o idenify a common moneary facor; moneary neuraliy implies ha relaive prices and individual secor oupus, real wages, or labor inpu are unaffeced by a one-ime change in he sock of money. Using only an aggregae price index or an aggregae measure of oupu would miss his secoral implicaion of moneary neuraliy. Similarly, aggregae produciviy shocks should have effecs across many secors, in paricular, raising real wages and oupu across secors in he long run; he iming and he exen of hese effecs, however, may vary across secors. Here, I capure hese secoral effecs of aggregae produciviy shocks in he form of non-negaiviy consrains on he long-run response of secoral real wages and oupu. Second, raher han esimae a VAR I use a common facor model o esimae moneary and aggregae produciviy shocks. A common facor model is a naural way o model he effec of a few imporan shocks on a wide cross-secion of observables. As he primary focus in he lieraure has been on a small number of aggregae shocks, focusing on a few common facors does no lessen he economic ineres of he empirical Besides helping o idenify aggregae shocks, he response of disaggregaed variables o aggregae shocks is ineresing in is own righ. Many recen heories of nominal rigidiies sugges ha relaive price effecs are cenral o he effec of money on real economic aciviy and he welfare consequences of inflaion (Woodford (3)).

4 analysis. In addiion o aggregae moneary and produciviy facors, I include a hird facor ha while no having a clear a priori inerpreaion will end up looking like a radiional aggregae demand facor. Also, I consider a model ha includes oil prices and an addiional facor ha is inerpreed as an oil facor. Third, I use Bayesian mehods o esimae he common facor model. While Bayesian mehods are no crucial for he implemenaion of long-run or sign resricions, in his applicaion hey grealy simplify he empirical analysis. Furhermore, a Bayesian approach allows one o se priors over shor-run responses and use hose, in addiion o long-run resricions, in he idenificaion of aggregae shocks. I find ha he esimaed moneary facor is responsible for much of he long swings in secor price growh, M growh, and he nominal ineres rae, suggesing ha his facor is capuring underlying inflaionary pressure in nominal variables. Taking he unweighed average across secors o be a measure of aggregae aciviy, he moneary facor, on he oher hand, explains lile of he hisorical flucuaions in aggregae oupu growh, real wages, or labor growh. Impulse response analysis for he moneary facor is somewha sensiive o he prior assumpions ha one makes abou he shor-run responses of secoral variables o a moneary shock; suggesing ha he daa are no oo informaive abou hese shor-run effecs. Produciviy shocks, on he oher hand, are esimaed o increase aggregae oupu, real wages, and labor inpu in boh he shor-run and long-run bu he size of he increases varies subsanially across secors. These resuls are robus o alernaive priors abou he shor-run effec of moneary shocks. Tha produciviy shocks are associaed wih increases in labor inpu boh a he aggregae and secoral level are in conras o he 3

5 resuls of Gali (999) and Francis and Ramey (). Neverheless, while hisorical decomposiions for oupu and real wages sugges ha he aggregae produciviy facor is an imporan source of flucuaions in hese variables, he aggregae produciviy facor has only a small impac on labor flucuaions over our sample. When I include oil prices and an oil facor in he analysis, he findings for he moneary or produciviy facors are no subsanially changed. The oil facor conribues only modesly o flucuaions in aggregae oupu, inflaion, labor, and real wages. Ineresingly, he oil facor seems o affec aggregae and secoral economic aciviy primarily hrough a demand channel raher han hrough supply-side channel. Finally, a large fracion of oil price flucuaions appears o be driven by he aggregae demand facor, suggesing ha oil prices are responding endogenously o overall economic aciviy. Several previous papers have applied facor models o disaggregaed daa in a macroeconomic conex. Explici dynamic common facor models have been employed o explain cyclical behavior of secoral oupu (Quah and Sargen (99) and Forni and Reichlin (998)), world and regional growh raes (Kose, Orok, and Whieman (3)), and disaggregaed prices (Bryan and Cecchei (993) and Nah ()). Sock and Wason (), Bernanke, Boivin, and Eliasz (), among ohers, employed facor models where he facors are based on he principal componens of disaggregae daa. There is also an empirical lieraure ha examines he relaive price implicaions of moneary shocks. Hercowiz (98) examined how he dispersion in cross-secion disribuion of prices changed in response o anicipaed and unanicipaed money changes. Bils, Klenow, and Krysov (3) examined how he response of prices differs depending on wheher he price is classified as being in a flexible price versus a sicky price. Balke and Wynne (7) find using 8 digi monhly PPI daa ha moneary shocks have subsanial relaive price effecs. Lasrapes (6), using more aggregaed price indices han Balke and Wynne finds ha moneary shocks have persisen effecs on he cross-secion disribuion of prices.

6 Four papers ha come closes o he analysis in he curren paper are Boivin, Giannovi, and Mihov (9), Ahmadi and Uhlig (7), Reis and Wason (), Foerser, Sare, and Wason (). Boivin e al (9) use a large number of disaggregaed variables o esimae a moneary facor. In fac, in one of heir specificaions hey impose a sor of long-run moneary neuraliy resricion for relaive prices. However, hey do no consider implicaions of long-run neuraliy for oher real variables. Ahmadi and Uhlig (7) examine a Bayesian FAVAR and employ sign resricions o idenify moneary shocks, bu do use long-run moneary neuraliy. Neiher paper ries o idenify aggregae produciviy shocks. Reis and Wason () look a large cross secion of price indices and exrac a common pure inflaion facor in which all prices move one-o-one wih his facor (i.e., no relaive price effecs).. However, hey do no examine disaggregae real variables nor do hey examine he impac of produciviy shocks. Foerser, Sare, and Wason () esimae a srucural facor model o secoral indusrial producion and use a muli-secor growh model o capure he inpu-oupu relaionships across secors. They find ha he aggregae facor explains a subsanial porion of secoral indusrial producion flucuaions. They do no, however, examine secoral price, wage, or labor daa, nor do hey examine aggregae nominal facors. The res of his paper is organized as follows. In secion, I discuss he secoral daa used in he paper and presen some evidence abou he degree o which his secoral daa can be described by a few common facors. In secion 3, I discuss he specificaion and esimaion of he srucural dynamic common facor model. Secion conains he empirical resuls for he benchmark facor model. In secion, I examine he effecs of

7 shocks o he aggregae facor on individual secors. Secion 6 examines he robusness of he benchmark model o alernaive shor-run priors and he number of facors. Secion 7 adds oil prices o he analysis. Secion 8 concludes.. Secoral Co-movemen In his secion, I examine he degree of co-movemen in secor price growh, oupu growh, real wage growh, and labor inpu growh for he U.S economy using principal componens. The primary source of daa is an exended version of he Jorgenson KLEM daa se originally compiled by Jorgenson, Gollop and Fraumeni (987) ha consiss of annual observaions on gross oupu, as well as he price and various inpus for 3 secors of he US economy. These hiry-five secors roughly correspond o -digi SIC level for U.S. indusries. 6 Table liss he hiry five secors by secor number and he fracion of heir oupu used for consumpion, invesmen, and maerials inpu. Two daa ses, one covering he period 97 o 989 and anoher covering he more recen period from 96-, are spliced ogeher. I divide secor price of labor inpu by secor oupu price o obain secor real wage. Table displays fracion he oal secoral variance ha can be explained by he five larges principle componens of he cross-secor covariance marix. In addiion o examining variance/covariance marices of secoral price growh, oupu growh, real wage growh, and labor inpu growh separaely, he join covariance marix of all four secoral variables is also examined. From Table, one observes ha he firs five principal componens can explain a large fracion of he cross-secor variances. For secoral prices and oupu, a single principal componen can explain over fory percen of 6

8 he oal variance. Even when one examines he covariance marix for all four secoral variables joinly, he firs hree principal componens explain over 6 percen of he sum of secoral variances. 7 In fac, he Bai and Ng () IC and IC crieria for selecing he number of facors in a saic facor model boh sugges wo facors. If one looks a each secoral variable individually, he average conribuion across secors of he firs hree principal componens is close o hiry percen for all bu secoral real wages (see Table 3). If one akes unweighed averages of secor variables o consruc aggregae variables, hese same hree principle componens accoun for over eighy percen he aggregae variables variances (Table ). Ineresingly, he firs principal componen accouns for he majoriy of he variance of secoral and aggregae oupu and labor inpu while he second principal componen accouns for mos of he variance of secoral and aggregae prices and real wages. This suggess ha he aggregae facors ha affec wages and prices may be differen from hose ha affec oupu and labor inpu. 3. Common facor model wih aggregae moneary and produciviy shocks While he principal componens analysis is suggesive of srong co-movemen across secoral variables, I build a common facor model o delve more deeply ino he naure of he co-movemen and o provide an economic inerpreaion o hese comovemens. In addiion o he secoral variables examined above, I include M growh and hree monh T-bill as observaion variables in he sysem as hese have ypically 6 The sum of he hiry-five secors oupus equals GDP. 7 There are a oal of secoral variables ye only 7 observaions for hese variables. As a resul, he variance/covariance marix of all variables is singular. 7

9 played a role in sudies of aggregae shocks and o some exen reflec moneary condiions in he economy. The relaionship beween he secoral variables and aggregae facors is given by: Y A (L)Y H (L)S E, () where Y is he vecor of secoral daa (plus M growh and he nominal ineres rae), S is he vecor of aggregae common facors, and E is a vecor of secor specific or idiosyncraic shocks. H(L) is he facor loading marix on curren and lagged values of he common facors; in he empirical analysis I se he number of lags in H(L) o four. As S reflecs he co-movemen of variables across secors, he A(L) marix is resriced so ha lags of variables in oher secors are zero. Similarly, he elemens of E are uncorrelaed across secors bu no necessarily wih in a secor; ha is, secor specific shocks affec variables in ha secor bu no variables in oher secors. A low order VAR describes he inra-secor relaionship of oupu, prices, real wages, and labor inpus. Individual secoral variables are assumed o have no direc effec on he aggregae money sock or ineres rae. The evoluion of he common facors is governed by S F(L)S V, () where V is a vecor of shocks o he common facors. The common facors are orhogonal o one anoher so ha F(L) consiss of saionary univariae AR() processes for he common facors while he elemens of wih he elemens of V are uncorrelaed wih each oher and E. Based in par on he principal componens analysis in he previous secion, I will specify hree common facors in he benchmark model: a 8

10 moneary facor ( s m, ), an aggregae produciviy facor ( s z, ), and a hird facor ( f, s ) ha a priori does no have a specific economic inerpreaion. 8 I assume he moneary facor shock is disribued: v ~ N (, ), while o fix he scale of he aggregae m, s m produciviy facor and he hird common facor I assume v and v ~ N (,). Finally, z, f, he facor loading in he ineres rae equaion for s is consrained o be posiive. f, 3. Idenifying Moneary and Aggregae Produciviy Shocks The moneary facor is assumed o saisfy long-run moneary neuraliy; ha is, an increase o he moneary facor is assumed o have no effec on real economic aciviy and ha all prices move proporionally o he money sock in long-run. This means ha he level of secoral oupu, real wages, and labor inpu are unaffeced in he long-run by an exogenous money shock while log secoral prices, nominal wages, and he money sock move one-for-one in he long-run in response o a moneary shock. 9 While longrun moneary neuraliy a he macro level has previously been used o idenify moneary shocks (Gali 99 and Lasrapes and Selgin (99)), I impose hose resricions on secoral prices and oupus. Why long-run neuraliy? The shor-run effecs of moneary shocks are sill of subsanial debae wihin he profession; long-run neuraliy is less conroversial (Lucas 8 While he Bai and Ng () crieria suggesed wo saic facors, I sar wih hree common facors in he benchmark dynamic facor model. I do his for wo reasons. Firs, he moneary and produciviy facors impose subsanial resricions across secors and adding anoher facor migh be useful capuring he remaining co-movemen across secors. Second, i seems plausible from economic grounds ha here could be imporan aggregae sources of secor co-movemen oher han moneary or aggregae produciviy shocks. 9 Long-run moneary neuraliy can also imply ha nominal ineres raes are unchanged in long-run so long as a moneary shock does no change he long-run inflaion rae. Lasrapes and Loo (998) examine he effec on money shocks on indusry level oupu while Lasrapes (6) examines he effec of money shock on relaive prices. Boh hese papers use he long-run idenifying assumpion ha a moneary shock has no effec on aggregae real oupu in he long-run bu no such resricion is implied for individual secor oupus or relaive prices. 9

11 996). Also, many of he New Keynesian models such as Chrisiano, Eichenbaum, and Evans (999 and ), Gali and Gerler (999), and Mankiw and Reis () and nominal mispercepions models such as Lucas (97) and Barro (976) imply long-run moneary neuraliy bu do no necessarily have he same predicions for he shor-run. In order o idenify he aggregae produciviy facor, I assume ha an aggregae produciviy shock will resul in an increase in secor oupus and real wages in he longrun. This increase need no be he same across secors, and here is no resricion on he long-run effec of he produciviy shock on secoral prices, labor inpu, and he sock of money. Unlike moneary neuraliy which implies a one-for-one change in prices and money and a zero response for oupus and real wages, he resricion on aggregae produciviy akes he form of a sign resricion on he long-run response of secor oupu and real wages o an aggregae produciviy shock. Noe ha i is no jus he long-run resricions ha maer in he idenificaion bu also he common facor resricions. These cross-secion resricions are paricularly imporan here because he cross-secion dimension is subsanially larger han he ime dimension ( variables in he observaion vecor versus 7 observaions). For hese idenificaion schemes o be valid, he (logarihms) of money sock, secoral prices, and secoral wages mus be inegraed of a leas order one (or I()). Tha is, here mus be permanen shocks o he money sock, prices and wages in order o use long-run resricions o idenify a facor. In order o use long-run resricions o idenify he aggregae produciviy facor, oupu and real wages mus be I(). For our daa, he assumpion of nonsaionary money sock, prices and wages is unconroversial. While i While an aggregae labor supply shock could also conceivably move real wages across secors in he same direcion, secoral oupu would move in he opposie direcion from real wages.

12 is no necessary for our idenificaion scheme, we model secoral labor inpu as I() as well. The nominal ineres rae (here 3 monh T-Bill) is arguably I() and is modeled as such. This means ha he ineres rae does no have a direc effec on he idenificaion of he moneary facor. We do use he nominal ineres rae o normalize he hird common facor. To see he resricions imposed by he proposed long run resricions, wrie he common facor model implied by equaion () for a single secor, i: p q w l i, i, i, i, A i (L ) p q w l i, i, i, i, H i,m (L ) H i,z (L ) H i,f (L ) s s s m, z, f, e e e e i,p, i,q, y i,w, i,l,, (3) where p q w l is he vecor of observable variables in secor i, i, i, i, i, s s s is he vecor of unobserved common facors, A i (L ) is a x lag m, z, f, polynomial marix, (L ) H, m i, H, z (L ) i, and H i, f (L ) are x vecors ha reflec he effec of he curren value and four lags of he common facors on he secoral variables, and e e e e is he vecor of secor specific shocks. I allow hese secor specific i,p, i,q, i,w, i,l, shocks o be correlaed wihin secors bu no across secors. For M growh and ineres rae, he equaions have he form: m A (L) m H (L) H (L) H (L) s e, () m m,m m,z m,f s s m, z, f, m, For all hiry-five secors sandard augmened Dickey-Fuller ess (wih consan and ime rend) fail o rejec uni roo in log prices and log real wages while for log oupu he uni roo null is rejeced in only five secors and for log labor inpu in six secors. Noe ha aggregae oupu and labor inpu (summing up gross oupu and labor inpu across secors) also appear o conain a uni roos.

13 and r A (L)r H (L) H (L) H (L) s e. () r r,m r, z r,f s s m, z, f, r, The errors e m, and r, e are uncorrelaed wih each oher and wih secor specific shocks. Long-run neuraliy for he moneary facor implies he following resricion: (I A ()) H (), (6) i i,m for every secor. Tha is, he long-run muliplier of he moneary facor is one for all secoral prices and zero for secoral oupu, real wages, and labor inpu. For M, he long-run muliplier for moneary facor mus saisfy: ( A ()) H (). (7) m m, m Thus, he money sock and all prices and nominal wages move one-for-one in he long run wih he moneary facor. Because ineres raes are saionary, long-run neuraliy has no implicaions for ineres raes. For aggregae produciviy he long-run muliplier for secor i variables is: i,p i,q i,w ( I A ()) H i i, z (), (8) i,l where i, p, i, q,, w i, and i, l are he long-run mulipliers for secor i price, oupu, real wage, and labor inpu, respecively. I impose he sign resricions, i, q > and i, w >, o ensure ha he aggregae produciviy facor resuls in increases in secor oupu and

14 real wages in he long run. However, hese effecs can differ across secors. The longrun responses of secor i price, i, p, and labor inpu, i, l, are unresriced. Similarly, he long-run response of M (no shown) is unresriced. Oher han he long-run effec of he moneary facor and he long-run sign resricions for he aggregae produciviy facor, here are oher few resricions. Mos imporanly, no hard consrains are placed on he shor-run responses of prices, oupu, real wages, and labor inpu o a money shock nor are consrains placed on he shor-run response of secoral variables o an aggregae produciviy shock. Noe ha he specificaion does no rule ou he possibiliy ha shocks o he oher aggregae facor ( s f, ) can have permanen effecs on secoral variables. As one is primarily ineresed in idenifying he effecs of aggregae shocks, he secoral shocks, e i s, do no have clear economic inerpreaions. They do, however, allow he model o capure any secor specific co-movemen in oupu, price, real wage, and labor inpu no capured by he common (across secors) facors. 3. Bayesian Esimaion of Common Facor Model. I ake a Bayesian approach raher han he more sandard maximum likelihood approach o esimae he common facor model. By using Markov Chain Mone Carlo mehods, here he Gibbs sampler, we can break up a raher large problem ino a number of smaller, bu compuaionally racable, problems by sequenially drawing a parameer from is condiional disribuion given all he oher parameers (and unobserved saes). Furhermore, by reaing unobserved common facors like parameers, we can obain he join poserior disribuion of he parameers and unobserved saes. In fac, he linear srucure of he model and sandard conjugae priors make i very easy o wrie poserior 3

15 condiional disribuions. Even he resricions implied by equaions (6) and (7) can be handled fairly easily. If he common facors were known, i is sraighforward o rewrie equaions (3) and (), imposing he resricions given by (6) and (7), so ha he resuling equaions are linear equaions wih no resricions on parameers (see appendix A). The inequaliy resricions for he long-run response of real wages and oupu o a produciviy shock are also easy o implemen in his conex as parameer draws ha do no saisfy he sign resricions are rejeced. The empirical esimae of he poserior disribuion is consruced by aking every fifh draw from he Gibbs sample,, imes, afer running he sampler for a burn-in period of, draws. See appendix A for a deailed discussion of he Gibbs sampler. 3.3 Prior disribuions For mos of he parameers of he model, relaively economically neural and diffuse priors are employed (see appendix A3 for deails). Seing priors over he parameers does have implicaions for he shor-run response of variables o moneary shocks. In our benchmark model, he prior disribuion is cenered around shor-run money neuraliy wih a relaively large spread of oucomes for he prior disribuion. The mean and inerior 8% of he implied prior disribuion for he impulse responses o a money shock are ploed in Figure a. 3 While he prior disribuions of he shor-run responses are cenered around moneary neuraliy, one can see ha he prior disribuions suppor a wide range of non-neural oucomes. This is paricularly rue for individual secoral responses. For aggregaed responses, here jus he unweighed average of 3 As he responses in Figure a represen he response o a uni shock in he moneary facor v ) hese responses do no reflec uncerainy abou he size of a ypical moneary shock, below and heir perceniles do reflec his uncerainy abou he value of. m m ( m,,. The responses

16 secoral responses, he prior disribuion is igher around moneary neuraliy bu sill suggess reasonable likelihood of non-neural behavior in he shor run. In secion 6, we discuss an alernaive se of priors for which he prior disribuion of impulse responses o a moneary shock implies shor-run money non-neuraliy and coincides wih responses ypically found in he radiional VAR lieraure. Figure b displays he implied prior disribuion for he response of secor and aggregae variables o an aggregae produciviy shock. The mean of he prior disribuion is posiive for he response of oupu and real wages, alhough he individual secor prior is much more diffuse han ha for he aggregae prior. For he response of prices, labor inpu, M growh, and ineres raes o a produciviy shock, he prior disribuions are cenered around zero bu wih subsanial dispersion. Wih he excepion of he nominal ineres in he curren period, he prior disribuions for he response of individual secor and aggregae variables o a hird aggregae facor shock (no shown) are all cenered abou zero. This reflecs he lack of an a priori inerpreaion for he hird aggregae facor.. Empirical Resuls: Implicaions for Aggregae Variables Figure displays he mean of he poserior disribuion along wih he h and 9 h perceniles for he moneary facor, he aggregae produciviy facor, and he hird aggregae facor which I will argue below looks like an aggregae demand facor. From he figure, he moneary facor displays subsanially more persisence han eiher he produciviy or he hird facor. The moneary facor shows a long swing upward in he mid 97s and early 98s and a decline in he lae 98s and hrough 99s. These

17 movemens mirror he general movemens in inflaion over he sample. The aggregae produciviy and demand facors feaure movemens ha ofen, bu no always, coincide wih aggregae business cycles. For example, he produciviy facor displays declines in he mid 97s and early 98s ha coincide wih recessions while hird aggregae facor displays declines in he early 99s and s. Before urning o he secoral deails, i will be insrucive o examine he aggregae implicaions of he esimaed model. Doing so will help evaluae wheher he esimaed aggregae facors make sense in ligh of more aggregaed daa. Wih ha in mind, I examine impulse responses and hisorical decomposiions for unweighed averages (across secors) of secor price, oupu, real wage, and labor.. Aggregae impulse response analysis Figure 3 displays he mean, h, and 9 h perceniles of poserior disribuion for he impulse responses of aggregae variables o a shock in he moneary facor. The mean of he cross-secion disribuion of price growh (inflaion) rises in response o an expansionary moneary shock, hence, here is no price puzzle. Perhaps his is no oo surprising given he idenifying assumpions, bu recall hese assumpions did no preclude finding a price puzzle in he shor-run. On he oher hand, mean oupu, real wage, and labor growh across secors do no appear o respond significanly even in he shor-run. Again, even hough he shor-run prior implied moneary neuraliy, i was diffuse enough o allow non-neural responses. Boh M growh and he nominal ineres rae increase in response o a moneary facor shock bu do so wih some delay. Figure displays he response of aggregae variables o an aggregae produciviy shock. Oupu, real wage, and labor inpu growh all increase in response o 6

18 a produciviy shock. Furhermore, heir responses display srong humped shapes. Ineres raes also end o rise afer a produciviy shock. Inflaion, on he oher hand, falls in response o a produciviy shock. This decline while no as quaniaively large as he oupu response is long lasing. The srong, procyclical response of labor o a produciviy shock conrass wih he resuls of Gali (999) and Francis and Ramey () who found a negaive response of labor o an idenified echnology shock My resuls are, however, consisen wih resuls of Peersman and Sraub (9) whose sign resricion idenificaion yielded a posiive response of labor o a echnology shock. Figure displays he aggregae responses o he hird common facor. Here he mean price, oupu, and labor inpu growh raes across secors increase as does he nominal ineres rae. On he oher, hand real wage growh falls. These aggregae responses, a leas in he shor-run, would be consisen wih an increase in aggregae demand. In fac, he response of inflaion, oupu, labor, and real wages are reminiscen of a shif in he IS curve in a radiional IS/LM/AS model wih sicky nominal wages. The slighly negaive response of M growh and posiive response of ineres raes migh also reflec a lean agains he wind sance for moneary policy in response o posiive aggregae demand shocks.. Hisorical decomposiions of aggregaed secoral variables Figures 6-9 presen poserior disribuion for he hisorical decomposiions of he unweighed average (across secors) of secor price, oupu, real wage, labor inpu growh as well as M growh and hree-monh T-Bill rae. In addiion o he mean conribuion, he figures display he h and 9 h perceniles of he poserior disribuion. Figure 6 displays he conribuion of he moneary facor o movemens in hese aggregae 7

19 variables. From Figure 6, one can observe ha he moneary facor conribues very lile o movemen in aggregae oupu, real wage, and employmen growh, bu i does conribue subsanially o he long swings in secoral price growh, M growh, and he nominal ineres rae. Clearly, he moneary facor reflecs lower frequency movemens in nominal variables prices, money sock, ineres raes (and implicily nominal wages as well) over he sample. In his respec, he moneary facor is quie similar o he pure inflaion facor in Reis and Wason (). However, unlike Reis and Wason, he moneary facor does no imply a one-o-one movemen in prices in every period, only in he long run. Recall ha he common facor model did no impose he resricions implied by long-run money neuraliy on nominal ineres raes, ye, noneheless he moneary facor explains he run up in nominal ineres raes in he 97s and early 98s and he run down of nominal raes in he lae 98s and 99s. Figure 7 displays he conribuions of he aggregae produciviy facor o flucuaions in he aggregaed secoral variables. Here, he produciviy facor explains a subsanial fracion of he movemens in he average oupu growh across secors. In fac, declines in he aggregae produciviy facor conribue o declines in oupu growh in nearly every single recession, paricularly in 97 and 98. The produciviy facor also conribues subsanially o flucuaions in real wage growh, alhough perhaps no o he exen of is conribuion o oupu growh. The effec of aggregae produciviy on labor inpu growh, on he oher hand, is much more modes han is conribuion o oupu growh wih perhaps only he decline in labor growh in 97-7 largely he resul of aggregae produciviy. Here he resuls are more in line wih hose of Gali (999) in which echnology shocks do no conribue much o employmen flucuaions. While he 8

20 produciviy facor is no nearly so imporan in flucuaions of he nominal variables (prices, M growh, and ineres rae), i does help conribue o he jump up in aggregae price growh in 97-7 and Figure 8 displays he conribuion of he hird aggregae facor, which I will inerpre as represening an aggregae demand facor. This demand facor conribues o a subsanial amoun of he flucuaions in oupu growh and mos of he flucuaions in labor inpu. In fac, wih he excepion of 97-7 and periods, his facor plays a key role in conribuing o declines in oupu and labor inpu during recessions. On he oher hand, he demand facor s conribuions o real wage growh and shor-run flucuaions in inflaion are more modes han he conribuions of he aggregae produciviy facor. While he demand facor conribues lile o he flucuaions in M growh, i does conribue o shor-run swings in he nominal ineres rae. Figure 9 shows he poserior disribuion of he oal conribuion of he aggregae facors. The resuling unexplained flucuaions are he resul of idiosyncraic facors for he secors. Togeher he hree aggregae facors conribue o a large porion of he flucuaions in he unweighed average of secor price, oupu, real wage, and labor inpu growh. Of course, aking he average of he secoral variables ends o average away he conribuion of he secoral idiosyncraic facors for prices, oupu, real wages, and labor inpu end leaving he bulk of aggregae flucuaions o be explained by he common facors. This does, however, sugges ha he hree common facors are sufficien o capure nearly all of he cross-secoral co-movemen. For M growh and ineres raes, he idiosyncraic facors are more eviden leaving a subsanial amoun of heir flucuaions unexplained by he hree aggregae facors. 9

21 .3 Inerpreaion of aggregae facors. The esimaed moneary facor appears o capure he long swings in nominal variables over he sample. As such, shocks o his moneary facor probably do no reflec so-called moneary policy shocks as ypically discussed in he VAR lieraure. These moneary policy shocks ypically idenified in he VAR lieraure can hough of surprises or misakes in he moneary auhoriy s reacion funcion. In his paper, shocks o he moneary facor migh be beer hough of as shocks o he long-run inflaion arge in somehing like a Taylor rule. Shocks in his long-run arge will over ime change inflaion, ineres raes, and he money growh rae by similar proporions. In he shorrun, however, hese variables may respond differenly o change in he long-run inflaion arge. The aggregae produciviy facor was idenified by assuming ha a posiive shock o his facor increased all secor real wages and oupus in he long run. Could his aggregae facor jus be picking up business cycles driven by oher phenomenon raher han aggregae produciviy shocks? To ge a sense wheher he produciviy facor is ruly capuring produciviy, we examine he acual unweighed average across secors of he logarihm of labor produciviy, log( Q / L ). Economic heory suggess ha shocks o produciviy should move secor (log) real wages and secor (log) average producs of labor by similar amouns. In fac, if echnology is Cobb-Douglas, he i, i, response of log real wages and log average producs should be equal. While nominal fricions and adjusmen coss may preven real wages and average producs from moving Recall, I am deflaing nominal wages by is produc price and no price of households consumpion goods.

22 ogeher in he shor run, here is srong a priori reasons o believe hey are likely o move ogeher in he long-run in response o shocks in produciviy. The op panel of Figure displays he average growh rae across secors of real wages and oupu per labor. While over he sample here are periods in which he wo series move ogeher, here is also a subsanial porion of he sample in which o wo series do no move in he same direcion. The boom panel of Figure plos he longrun conribuion of he aggregae produciviy facor o real wage growh, N i s / N, i,w z, and oupu per labor growh, N i ( )s / N i,q i,l z,, where i, w,, q i, and i, l are he long-run mulipliers for secor i of a produciviy shock for real wage, oupu, and labor given in equaion (8). Unlike acual real wages and average producs, he long-run conribuion of he produciviy facor o real wages and average producs move ogeher quie closely. Furhermore, he correlaion of he produciviy facor and he unweighed average of secor KLEM Solow residual growh is.63. Taken ogeher, i appears ha he esimaed produciviy facor generaes movemens in real wages and average producs consisen wih aggregae produciviy shocks.. Empirical resuls: secoral variables.. Secoral impulse responses Turning o wha happens a he secoral level, Figure displays he mean of he poserior disribuion of he response o a moneary shock for every secor a various Noe ha while i, w and i, q were resriced o be posiive, here was no resricions on i, l nor on he relaive sizes of hese long-run mulipliers in he esimaion.

23 horizons. The horizonal axis displays he secor numbers referenced in Table. Unlike previous impulse response diagrams, hese figures display he (log) level of secor variables so ha one can beer discern he effec of shocks on relaive secoral behavior. Looking a log level of secor prices firs, one observes ha a moneary shock affecs secor prices broadly all secor prices rise; here is no evidence of a price puzzle a he secoral level. All prices, however, do no move one-for-one, suggesing ha moneary shocks have relaive price effecs, a leas in he shor run. These relaive price effecs are small iniially, rise as he horizon lenghs, and hen fall again as he horizon ges large (horizon = ). Among he secors wih he larges price increases are: coal mining, crude oil and naural gas, gas uiliy services, and peroleum refining. Among he secors wih he smalles price increases are: communicaions, personal and business services, and prining. Moneary facor shocks have differen real effecs across secors in he shor-run as well, as some secors increase while ohers decrease. Again he secoral differences are modes a firs, rise as he horizon lenghens, and hen fall again as he horizon ges large. The secors wih he larges posiive oupu response include: primary meals in he iniial period, gas uiliy service, insrumens, and communicaion in laer periods. The secors wih he larges negaive responses are apparel and fooware iniially and elecrical machinery, ransporaion equipmen, and meallic ore mining a longer horizons. Ineresingly he secors wih he larges real wage declines are ypically hose wih he larges labor inpu increases (crude oil and naural gas, coal mining, gas uiliies).

24 Figure displays he secoral responses o an aggregae produciviy shock. By consrucion, aggregae produciviy shocks have a posiive effec on all secors oupus and real wages in he long-run. Noneheless, here are subsanial differences across secors. Secors like ransporaion equipmen, fabricaed meal, machinery, elecrical machinery, and rubber show large increases in heir oupus while agriculure, FIRE, and food show only small increases. Prices in mos secors decline wih agriculure, lumber and wood producs, and FIRE being noable excepions. Labor inpu generally increases across secors bu falls in five secors, he larges declines occurring in personal and business services, agriculure, crude oil and naural gas, and prining secors. Figure 3 displays he secoral responses o a shock in he hird aggregae facor. Recall his facor s aggregae impulse responses were reminiscen of an increase in goods demand in an IS/LM model. Again he effec of a shock o his aggregae demand facor varies subsanially across secors. Among he secors wih he larges price responses are: primary meals and peroleum refining a shor horizons and peroleum refining, chemicals, and nonmeallic minerals a longer horizons. The secors wih he larges oupu response include: machinery, elecrical machinery, fabricaed meals and primary meals while agriculure, FIRE, lumber and wood producs, and consrucion display he smalles responses. The secors wih he larges labor responses include many of he secors wih large oupu responses plus he apparel and prining secors. To ge a sense of wheher secor responses vary according o how he secors goods are used, I classified secors according o wheher hey are used primarily as a consumpion good, an invesmen good, or an inermediae good (see Table ). Figures -6 display he average secoral responses (across good ype) o he hree ypes of 3

25 aggregae shocks. From Figure, i appears ha he response o moneary shocks does no differ subsanially across ypes of goods. Of he hree ypes of goods, he invesmen good secor s oupu and labor inpu respond he mos o a shock in he produciviy facor (see Figure ). While he responses of oupu, real wages, and labor inpu do no vary much across good ype for a demand shock (see Figure 6), prices of inermediae goods appear o respond more han do he prices of consumpion or invesmen goods. 6. Robusness 6. Alernaive shor-run priors. While he idenificaion of moneary shocks imposes long-run neuraliy, one may wan o examine he sensiiviy of he resuls o alernaive priors abou he shor-run responses of moneary shocks. In paricular, I consider a prior disribuion in which he responses of oupu, price, labor inpu, and ineres raes o a moneary shock correspond, a leas in he shor-run, o hose ypically employed in he VAR lieraure. In his lieraure, oupu responds posiively and ineres raes negaively o an expansionary moneary shock. There is much less consensus abou he iniial response of prices o a moneary shock, winess he discussion in he lieraure of he price puzzle. Here, I se he mean of he prior disribuion for prices so ha hey do no respond in he iniial period o a moneary shock as suggesed by he VAR analysis of Chrisiano, Eichenbaum, and Evans (999). Unlike he benchmark model in which he prior responses are fairly diffuse, I assume ha he prior disribuion around he so-called radiional VAR prior is relaively igh. For he response of real wages o a moneary shock, I coninue o assume he prior disribuion is cenered around zero and is fairly diffuse.

26 Figure 7 presens he means and h and 9 h perceniles for he radiional VAR prior disribuion. From Figure 7, he mean of he prior disribuion for he iniial response of secoral and aggregae oupu and labor inpu are posiive while he mean of he prior disribuion for he nominal ineres rae response is negaive. For individual secors, prior disribuion is se so ha a wide range of secoral responses is sill possible for example, i is quie possible for an individual secoral oupu o fall in response o an expansionary moneary shock. The aggregae (or unweighed mean response across secors) responses, however, sugges he radiional VAR responses o a moneary shock iniially aggregae oupu (and labor inpu) rise and he nominal ineres rae falls while he aggregae price level remains unchanged. Noe ha he prior disribuion implies a zig-zag shape for he oupu and labor responses. The reason for his shape is ha long-run neuraliy implies ha posiive oupu and labor growh responses iniially mus be offse by subsequen negaive responses. Figure 8 displays he poserior disribuion of he impulse responses of aggregae variables o a moneary facor shock. Unlike he benchmark model, seing fairly igh priors resuls in boh oupu and labor inpu growh rising in response o a moneary facor shock. This posiive response is shor-lived as long-run neuraliy requires his iniial posiive response in growh o be followed by negaive responses. Given ha he resuls for he shor-run moneary priors are quie differen, his suggess ha he daa alone are no oo informaive abou he shor-run response of oupu o a long-run neural moneary shock. On he oher hand, despie he relaively igh prior ha he inflaion response is zero, he poserior disribuion implies a srong posiive response of inflaion o a moneary facor shock. Clearly, he daa sugges a srong iniial price response o a

27 shock in he moneary facor. Similarly, despie a relaively igh prior around a negaive ineres rae response, he poserior disribuion for nominal ineres rae response is close o zero for he iniial response and posiive shorly hereafer. Finally, for he iniial response of real wage growh, he mean of he poserior disribuion is negaive, alhough he inerior 8 perceniles of he poserior disribuion includes zero. The general endency for real wages o fall is in line wih wha radiional models of wage sickiness would predic for a moneary shock. Perhaps no surprisingly, he alernaive prior disribuion does no subsanially change he impulse responses o a produciviy shock (no shown). Similarly, he radiional VAR prior has only a small effec on he means of he poserior disribuion for he responses o a shock o he hird aggregae facor (demand). However, under he radiional VAR prior, he poserior disribuions of responses o he demand facor are more diffuse. Figure 9 displays he conribuion of he moneary facor o he hisorical decomposiion of he aggregaed secoral variables when he radiional VAR prior is used. Comparison of hese decomposiions wih hose of he moneary neural prior (Figure 6 above) suggess ha assuming non-neural shor run priors does no change he inerpreaion of he main sources of flucuaions over our sample. Regardless of wheher shor-run priors imply moneary non-neuraliy or neuraliy, mos of he long swings in prices, money sock, and ineres raes are due o he moneary facor. On he oher hand, he moneary facor does no conribue much o flucuaions in real oupu, real wage, or labor growh over he sample regardless of he shor-run moneary prior. Likewise, assuming non-neural priors does no appreciably change he conribuions of he oher 6

28 facors. This suggess ha i is he long-run idenifying assumpions and he daa raher han he shor-run priors ha are primarily responsible for he hisorical decomposiion resuls. Figure displays he mean of he poserior disribuion for all he individual secor variables responses o a moneary facor shock when non-neural priors are assumed. As in he benchmark model, here are subsanial quaniaive differences in he secoral responses o a moneary shock when he alernaive, non-neural moneary priors are used. Unlike he benchmark model, he alernaive priors resul in widespread increases in oupu and labor inpu across secors during he iniial period afer a moneary facor shock. Much like he benchmark model, he secors wih greaes oupu growh increases were primary meal manufacuring and ransporaion iniially and gas uiliy service and chemicals laer. While prior disribuions for he iniial secoral price responses are cenered around zero, he poserior mean for nearly all he secors is posiive. Thus, he daa (and no he priors) suggess ha he inflaionary effec of he moneary facor is widespread across secors. The secoral effecs of produciviy facor shocks and he demand facor shocks for he alernaive shor-run moneary prior is similar o he benchmark model. 6. Adding addiional aggregae facors. To es he sensiiviy of he iniial assumpion of hree aggregae facors, I added an addiional aggregae facor o he common facor model. This facor was normalized so ha i resuled in an increase in M growh in he iniial period, bu was oherwise unresriced. Like he demand facor in he hree facor model, he priors of he oher parameers were cenered around zero and relaively diffuse. I urns ou adding his 7

29 facor does no aler he previous resuls for he moneary and produciviy facors. I does seem o reduce he effec of wha was ermed he demand facor in he previous model. Figure displays he conribuion of his fourh facor o flucuaions in he aggregaed secoral variables over he sample. As one can see from he figure, his facor adds only a lile o explaining flucuaions in he aggregaed secoral variables. 7. Oil prices, secoral and aggregae flucuaions. The previous resuls suggesed ha he aggregae produciviy facor had imporan conribuions o boh secoral and aggregae oupu flucuaions. In paricular, he decline in oupu during he recessions of 97-7 and 98 show up largely as due o flucuaions in he aggregae produciviy facor. I is possible ha his resul migh acually reflec he effec of oil price changes ha also occurred during hese ime periods. Indeed, oil prices have been considered o be an imporan source of flucuaions in heir own righ. 6 To deermine wheher he esimaed aggregae produciviy facor was in fac picking up he effec of oil prices on secoral economic aciviy, I add oil prices o he observaion vecor and add an addiional facor o he benchmark model. To be consisen wih he oher secoral daa, I include he growh rae in nominal oil prices o he vecor of observables. Idenificaion of he moneary and produciviy facors is he same as he benchmark model above. Like he oher nominal variables, I assume ha he moneary facor affecs he (log) level of nominal oil prices one-for-one in he long run so ha he real oil price is unaffeced in he long-run by he moneary 6 Many sudies including Hamilon (983), Mork (989), and Hamilon (9) have emphasized he imporance of oil prices for aggregae flucuaions. Oher papers have quesioned he imporance of oil price shocks on economic aciviy. These include Hooker (996), Bernanke, Gerler, and Wason (997), and Barsky and Killian () among ohers. Mos of hese papers examined he effec of oil prices on aggregae economic aciviy. Davis and Haliwanger () Lee and Ni (), and Herrera (9), among ohers, examine he effec of oil prices on secoral level daa. 8

30 facor. Also like he oher nominal prices, I place no resricions on he long-run effec of he aggregae produciviy facor on nominal oil prices. In addiion o moneary and produciviy facors, I include wo addiional common facors. One facor is normalized so ha i has a posiive effec on he ineres rae in he curren period; his will urn ou o be similar o he so-called demand facor in he benchmark model. The oher is normalized so ha i has a posiive effec on nominal oil prices in he curren period; I will inerpre his facor as an oil facor. As in he benchmark model, here are no addiional resricions on he facor loadings aside from hese normalizaions. I presen he resuls from model wih radiional VAR priors abou he impac effecs of he moneary facor; hese resuls are largely unaffeced if shor-run money neuraliy priors were used insead. Firs, how are he resuls for moneary and produciviy facors affeced by including oil prices and anoher facor ino he benchmark model? Figures and 3 display he conribuion of he moneary and produciviy facors o he hisorical decomposiions of aggregae inflaion, oupu, real wage, and labor growh for he model wih oil prices. Adding oil prices and an oil facor o he model, does no appreciably change he relaive conribuions of he moneary and produciviy facors. Moneary facor sill conribues o he long swings in nominal variables over he sample and he produciviy facor is an imporan conribuor o oupu and real wage flucuaions. Even in he 97 and 98 recessions, he aggregae produciviy facor is sill an imporan source oupu declines. Thus, adding oil prices and an oil facor do no appreciably affec he previous resuls for he moneary and produciviy facors. 7 Figure 7 Adding oil prices and an oil facor also do no subsanively change he impulse response funcions for moneary, produciviy, and demand facor shocks. 9