Technology Shocks and Aggregate Fluctuations: How Well Does the Real Business Cycle Model Fit Postwar U.S. Data?

Transcription

1 WP/04/234 Technology Shocks and Aggregae Flucuaions: How Well Does he Real Business Cycle Model Fi Poswar U.S. Daa? Jordi Galí and Pau Rabanal

2 2004 Inernaional Moneary Fund WP/04/234 IMF Working Paper Wesern Hemisphere Deparmen Technology Shocks and Aggregae Flucuaions: How Well Does he Real Business Cycle Model Fi Poswar U.S. Daa? Prepared by Jordi Galí and Pau Rabanal 1 Auhorized for disribuion by Tamim Bayoumi December 2004 Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. Our answer: No so well. We reached ha conclusion afer reviewing recen research on he role of echnology as a source of economic flucuaions. The bulk of he evidence suggess a limied role for aggregae echnology shocks, poining insead o demand facors as he main force behind he srong posiive comovemen beween oupu and labor inpu measures. JEL Classificaion Numbers: E32 Keywords: Real Business Cycles, Technology Shocks, Nominal Rigidiies, Real Fricions Auhor(s) Address: jordi.gali@upf.edu, prabanal@imf.org 1 Prepared for he 19h NBER Annual Conference on Macroeconomics. We are hankful o Susano Basu, Olivier Blanchard, Yongsung Chang, John Fernald, Alber Marce, Barbara Rossi, Julio Roemberg, Juan Rubio-Ramirez, Rober Solow, Jaume Venura, Luz Weinke, as well as he ediors, Mark Gerler and Ken Rogoff, and discussans, Ellen McGraan and Valerie Ramey, for useful commens. We have also benefied from commens by paricipans in seminars a he CREI-UPF Macro Workshop, MIT Macro Faculy Lunch, and Duke Universiy. Anon Nakov provided excellen research assisance. We are graeful o Craig Burnside, Ellen McGraan, Harald Uhlig, Jonas Fisher, and Susano Basu for help wih he daa. Galí acknowledges financial suppor from DURSI (Generalia de Caalunya), Fundación Ramón Areces, and he Miniserio de Ciencia y Tecnología (SEC ).

3 - 2 - Conens Page I. Inroducion...4 II. III. IV. Esimaing he Effecs of Technology Shocks...6 A. Revisiing he Basic Evidence on he Effecs of Technology Shocks...7 B. Relaed Empirical Work...9 C. Implicaions...11 Possible Pifalls in he Esimaion of he Effecs of Technology Shocks...12 A. Are Long-Run Resricions Useful in Idenifying Technology Shocks?...12 B. Robusness o Alernaive VAR Specificaions...16 C. Invesmen-Specific Technology Shocks...20 Explaining he Effecs of Technology Shocks...21 A. The Role of Nominal Fricions...22 B. A Simple Illusraive Model...23 V. Technology Shocks and he Business Cycle in an Esimaed DSGE Model...30 A. Parameer Esimaion...33 B. Main Findings...35 VI. VII. Conclusions...38 Addendum: A Response o Ellen McGraan...39 A. Why Does he SVAR Evidence Fail o Mach he McGraan and CKM Models' Predicions?...40 B. Why Does he CKM Accouning Framework Predic a Rise in Hours?...42 C. Some Agreemen...43 References...60 Tables 1. The Effecs of Technology Shocks on Oupu and Hours in he Nonfarm Business Secor The Effecs of Technology Shocks on GDP and Employmen Invesmen-Specific Technology Shocks: The Fisher Model Prior and Poserior Disribuions Second Momens of Esimaed DSGE Model Variance Decomposiion from Esimaed DSGE Model Technology-Driven Flucuaions in Oupu and Hours: Correlaions Implied by Alernaive Model Specificaions (BP-Filered Daa)...51

4 - 3 - Figures 1. Business Cycle Flucuaions in Oupu and Hours The Esimaed Effecs of Technology Shocks (Difference specificaion, sample period 1948: :04) Sources of Business Cycle Flucuaions, (Difference specificaion, sample period 1948: :04) Capial Income Tax Raes Technology Shocks: VAR versus BFK Hours Worked (In naural logarihms, ) Poserior Impulse Responses o a Technology Shock, Esimaed DSGE Model The Role of Technology Shocks in U.S. Poswar Flucuaions: Model-Based Esimaes...59

5 - 4 - I. INTRODUCTION Since he seminal work of Kydland and Presco (1982) and Presco (1986a) proponens of he Real Business Cycle (RBC) paradigm have claimed a cenral role for exogenous variaions in echnology as a source of economic flucuaions in indusrial economies. Those flucuaions have been inerpreed by RBC economiss as he equilibrium response o exogenous variaions in echnology, in an environmen wih perfec compeiion and ineremporally opimizing agens, and in which he role of nominal fricions and moneary policy is, a mos, secondary. Behind he claims of RBC heory lies wha mus have been one of he mos revoluionary findings in poswar macroeconomics: a calibraed version of he neoclassical growh model augmened wih a consumpion-leisure choice, and wih sochasic changes in oal facor produciviy as he only driving force, seems o accoun for he bulk of economic flucuaions in he poswar U.S. economy. In pracice, accouning for observed flucuaions has mean ha calibraed RBC models mach prey well he paerns of uncondiional second momens of a number of macroeconomic ime series, including heir relaive sandard deviaions and correlaions. Such findings led Presco o claim...ha echnology shocks accoun for more han half he flucuaions in he poswar period, wih a bes poin esimae near 75 percen. 2 Similarly, in wo recen assessmens of he road raveled and he lessons learned by RBC heory afer more han a decade, Cooley and Presco (1995) could confidenly claim ha i makes sense o hink of flucuaions as caused by shocks o produciviy, while King and Rebelo (1999) concluded ha...[he] main criicisms levied agains firs-generaion real business cycle models have been largely overcome. While mos macroeconomiss have recognized he mehodological impac of he RBC research program and have adoped is modeling ools, oher imporan, more subsanive elemens of ha program have been challenged in recen years. Firs, and in accordance wih he widely acknowledged imporance of moneary policy in indusrial economies, he bulk of he profession has gradually moved away from real models (or heir near-equivalen fricionless moneary models) when rying o undersand shor-run macroeconomic phenomena. Second, and mos imporan for he purposes of his paper, he view of echnological change as a cenral force behind cyclical flucuaions has been called ino quesion. In he presen paper we focus on he laer developmen, by providing an overview of he lieraure ha has challenged he cenral role of echnology in business cycles. A defining feaure of he lieraure reviewed here lies in is search for evidence on he role of echnology ha is more direc han jus checking wheher any given model driven by echnology shocks, and more or less plausibly calibraed, can generae he key feaures of he business cycle. In paricular, we discuss effors o idenify and esimae he empirical effecs of exogenous changes in echnology on differen macroeconomic variables, and o evaluae quaniaively he conribuion of hose changes o business cycle flucuaions. 2 Presco (1986b).

6 - 5 - Much of ha lieraure (and, hence, much of he presen paper) focuses on one cenral, unconroversial feaure of he business cycle in indusrial economies namely, he srong posiive comovemen beween oupu and labor inpu measures. Tha comovemen is illusraed graphically in Figure 1, which displays he quarerly ime series for hours and oupu in he U.S. nonfarm business secor over he period 1948:1-2002:4. In boh cases he original series have been ransformed using he band-pass filer developed in Baxer and King (1999), calibraed o remove flucuaions of periodiciy ouside an inerval beween 6 and 32 quarers. As in Sock and Wason (1999), we inerpre he resuling series as reflecing flucuaions associaed wih business cycles. As is well known, he basic RBC model can generae flucuaions in labor inpu and oupu of magniude, persisence, and degree of comovemen roughly similar o he series displayed in Figure 1. Furhermore, and as shown in King and Rebelo (1999), when he acual sequence of echnology shocks (proxied by he esimaed disurbances of an AR process for he Solow residual) is fed as an inpu ino he model, he resuling equilibrium pahs of oupu and labor inpu rack surprisingly well he observed hisorical paerns of hose variables; he laer exercise can be viewed as a more sringen es of he RBC model han he usual momenmaching. The lieraure reviewed in he presen paper asks, however, very differen quesions: Wha have been he effecs of echnology shocks in he poswar U.S. economy? How do hey differ from he predicions of sandard RBC models? Wha is heir conribuion o business cycle flucuaions? Wha feaures mus be incorporaed in business cycle models o accoun for he observed effecs? The remainder of his paper describes he enaive (and someimes conradicory) answers ha he effors of a growing number of researchers have yielded. Some of ha research has exploied he naural role of echnological change as a source of permanen changes in labor produciviy o idenify echnology shocks using srucural vecor auorregressions (VARs); oher auhors have insead relied on more direc measures of echnological change and examined heir comovemens wih a variey of macro variables. I is no easy o summarize in a few words he wealh of exising evidence nor o agree on some definie conclusions of a lieraure ha is sill very much ongoing. Neverheless, i is safe o sae ha he bulk of he evidence reviewed in he presen paper provides lile suppor for he iniial claims of he RBC lieraure on he cenral role of echnological change as a source of business cycles. The remainder of he paper is organized as follows. Secion II reviews some of he early papers ha quesioned he imporance of echnology shocks, and presens some of he basic evidence regarding he effecs of hose shocks. Secion III discusses a number of criicisms and possible pifalls of ha lieraure. Secion IV presens he case for he exisence of nominal fricions as an explanaion of he esimaed effecs of echnology shocks, and summarizes some of he real explanaions for he same effecs found in he lieraure. Secion V lays ou and analyzes an esimaed dynamic sochasic general equilibrium (DSGE) model ha incorporaes boh nominal and real fricions, and evaluaes heir respecive role. Secion VI concludes.

7 - 6 - II. ESTIMATING THE EFFECTS OF TECHNOLOGY SHOCKS In Galí (1999) he effecs of echnology shocks were idenified and esimaed using a srucural VAR approach. In is simples specificaion, o which we resric our analysis here, he empirical model makes use of informaion on wo variables: oupu and labor inpu, which we denoe respecively by y and n, boh expressed in logs. Those variables are used o consruc a series for (he log of) labor produciviy, x y n. In wha follows he laer is assumed o be inegraed of order one (in a way consisen wih he evidence repored below). Flucuaions in labor produciviy growh ( x ) and in some saionary ransformaion of labor inpu ( nˆ ) are assumed o be a consequence of wo ypes of shocks hiing he economy and propagaing heir effecs over ime. Formally, he following moving average (MA) represenaion is assumed: x C ( L) C nˆ = C ( L) 11 C z ( L) ε C( L) ε, d ( L) ε (1) z d where ε and ε are serially uncorrelaed, muually orhogonal srucural disurbances, whose variance is normalized o uniy. The polynomial C(z) is assumed o have all is roos ouside he uni circle. Esimaes of he disribued lag polynomials C ij (L) are obained by a suiable ransformaion of he esimaed reduced-form VAR for [ x, nˆ ] afer imposing he long-run idenifying resricion C¹²( 1 ) = 0. 3 Tha resricion effecively defines { ε z } and { ε d } as shocks wih and wihou a permanen effec on labor produciviy, respecively. On he basis of some of he seady-sae resricions shared by a broad range of macro models (and furher discussed below), Galí (1999) proposes o inerpre permanen shocks o produciviy { ε z } as echnology shocks. On he oher hand, ransiory shocks { ε d } can poenially capure a variey of driving forces behind oupu and labor inpu flucuaions ha would no be expeced o have permanen effecs on labor produciviy. The laer include shocks ha could have a permanen effec on oupu (bu no on labor produciviy), bu ha are non-echnological in naure, as would be he case for some permanen shocks o preferences or governmen purchases, among ohers. 4 As discussed below, hey could in principle capure ransiory echnology shocks as well. 3 See Blanchard and Quah (1989) and Galí (1999) for deails. 4 I is precisely ha feaure wha differeniaes he approach o idenificaion in Galí (1999) from ha in Blanchard and Quah (1989). The laer auhors used resricions on long-run effecs on oupu, as opposed o labor produciviy. In he presence of a uni roo in labor inpu, ha could lead o he mislabeling as "echnology" shocks of any disurbances ha were behind he uni roo in labor inpu.

8 - 7 - A. Revisiing he Basic Evidence on he Effecs of Technology Shocks Nex, we revisi and updae he basic evidence on he effecs of echnology shocks repored in Galí (1999). Our baseline empirical analysis uses quarerly U.S. daa for he period 1948:1-2002:4. Our source is he Haver USECON daabase, for which we lis he associaed mnemonics. Our series for oupu corresponds o nonfarm business secor oupu (LXNFO). Our baseline labor inpu series is hours of all persons in he nonfarm business secor (LXNFH). Below we ofen express he oupu and hours series in per capia erms, using a measure of civilian noninsiuional populaion aged 16 and over (LNN). Our baseline esimaes are based on a specificaion of hours in firs-differences -i.e., we se nˆ = n. Tha choice seems consisen wih he oucome of Augmened Dickey-Fuller (ADF) ess applied o he hours series, which do no rejec he null of a uni roo in he level of hours a a 10 percen significance level, agains he alernaive of saionariy around a linear deerminisic rend. On he oher hand, he null of a uni roo in he firs-differenced series is rejeced a a level of less han 1 percen. 5 In a way consisen wih he previous resul, a Kwiakowski e al. (1992) (KPSS) es applied o n rejecs he saionariy null wih a significance level below 1 percen, while failing o rejec he same null when applied o n. In addiion, he same baery of ADF and KPSS ess applied o our x and x series suppor he exisence of a uni roo in labor produciviy, a necessary condiion for he idenificaion sraegy based on long-run resricions employed here. Boh observaions sugges he specificaion and esimaion of a VAR for [ x, n ]. Henceforh, we refer o he laer as he difference specificaion. Figure 2 displays he esimaed effecs of a posiive echnology shock, of size normalized o one sandard deviaion. The graphs on he lef show he dynamic responses of labor produciviy, oupu, and hours, ogeher wih (±) wo sandard error bands. 6 The corresponding graphs on he righ show he simulaed disribuion of each variable s response on impac. As in Galí (1999), he esimaes poin o a significan and persisen decline in hours afer a echnology shock ha raises labor produciviy permanenly. 7 The poin esimaes sugges ha hours do evenually reurn o heir original level (or close o i), bu no unil more han a year laer. Along wih ha paern of hours, we observe a posiive bu mued iniial response of oupu in he face of a posiive echnology shock. 5 Wih four lags, he corresponding -saisics are -2.5 and for he level and he firsdifference, respecively. 6 Tha disribuion is obained by means of a Monecarlo simulaion based on 500 drawings from he disribuion of he reduced-form VAR disribuion. 7 Noice ha he disribuion of he impac effec on hours assigns a zero probabiliy o an increase in ha variable.

9 - 8 - The esimaed responses o a echnology shock displayed in Figure 2 conras sarkly wih he predicions of a sandard calibraed RBC model, which would predic a posiive comovemen among he hree variables ploed in he figure in response o ha shock. 8 No surprisingly, he previous esimaes have dramaic implicaions regarding he sources of he business cycle flucuaions in oupu and hours displayed in Figure 1. This is illusraed in Figure 3, which displays he esimaed business cycle componens of he hisorical series for oupu and hours associaed wih echnology and non-echnology shocks. In boh cases he esimaed componens of he (log) levels of produciviy and hours have been derended using he same band-pass filer underlying he series ploed in Figure 1. As in Galí (1999), he picure ha emerges is very clear: flucuaions in hours and oupu driven by echnology shocks accoun for a small fracion of he variance of hose variables a business cycle frequencies: 5 and 7 percen, respecively. Furhermore, he comovemen a business cycle frequencies beween oupu and hours resuling from echnology shocks is shown o be essenially zero (he correlaion is -0.08), in conras wih he high posiive comovemen observed in he daa (0.88). Clearly, he paern of echnology-driven flucuaions, as idenified in our srucural VAR, shows lile resemblance wih he convenional business cycle flucuaions displayed in Figure 1. The picure changes dramaically if we urn our aenion o he esimaed flucuaions of oupu and hours driven by shocks wih no permanen effecs on produciviy (displayed in he boom graph). Those shocks accoun for 95 and 93 percen of he variance of he business cycle componen of hours and oupu, respecively. In addiion, hey generae a nearly perfec correlaion (0.96) beween he same variables. In conras wih is echnologydriven counerpar, his componen of oupu and hours flucuaions displays a far more recognizable business cycle paern. A possible criicism o he above empirical framework is he assumpion of only wo driving forces underlying he flucuaions in hours and labor produciviy. As discussed in Blanchard and Quah (1989), ignoring some relevan shocks may lead o a significan disorion in he esimaed impulse responses. Galí (1999) addresses ha issue by esimaing a five-variable VAR (including ime series on real balances, ineres raes, and inflaion). Tha framework allows for as many as four shocks wih no permanen effecs on produciviy, and for which no separae idenificaion is aemped. The esimaes generaed by ha higher-dimensional model regarding he effecs of echnology shocks are very similar o he ones repored above, suggesing ha he focus on wo shocks only may no be resricive for he issue a hand. 9 8 See, e.g., King, Plosser, and Rebelo (1988a) and Campbell (1994). 9 See also Francis and Ramey (2003a), among ohers, for esimaes using higher dimensional VARs.

10 - 9 - B. Relaed Empirical Work The empirical connecion beween echnological change and business cycle flucuaions has been he focus of a rapidly expanding lieraure. Nex we briefly discuss some recen papers providing evidence on he effecs of echnology shocks, and ha reach conclusions similar o hose in Galí (1999), while using a differen daa se or empirical approach. We leave for laer a discussion of he papers whose findings relae more specifically o he conen of oher secions, including hose ha quesion he evidence repored above. An early conribuion is given by he relaively unknown paper by Blanchard, Solow and Wilson (1995). Tha paper already spells ou some of he key argumens found in he subsequen lieraure. In paricular, i sresses he need o sor ou he componen of produciviy associaed wih exogenous echnological change from he componen ha varies in response o oher shocks ha may affec he capial-labor raio. They adop a simple insrumenal variables approach, wih a number of demand-side variables assumed o be orhogonal o exogenous echnological change used as insrumens for employmen growh or he change in unemploymen in a regression ha feaures produciviy growh as a dependen variable. The fied residual in ha regression is inerpreed as a proxy for echnology-driven changes in produciviy. When hey regress he change in unemploymen on he filered produciviy growh variable hey obain a posiive coefficien i.e. an (exogenous) increase in produciviy drives he unemploymen rae up. A dynamic specificaion of ha regression implies ha such an effec lass for abou hree quarers, afer which unemploymen sars o fall and reurns rapidly o is original value. As menioned in Galí (1999, foonoe 19) and sressed by Valerie Ramey in her discussion, he finding of a decline in hours (or an increase in unemploymen) in response o a posiive echnology shock could also have been deeced by an aenive reader in a number of earlier VAR papers, hough ha finding generally goes unnoiced or is described as puzzling. Blanchard and Quah (1989) and Blanchard (1989) are excepions in ha hey provide some explici discussion of he finding, which hey inerpre as consisen wih a radiional Keynesian model in which increases in produciviy...may well increase unemploymen in he shor run if aggregae demand does no increase enough o mainain employmen. 10 The work of Basu, Fernald, and Kimball (1999; henceforh, BFK) deserves special aenion here, given is focus and he similariy of is findings o hose in Galí (1999) despie he use of an unrelaed mehodology. BFK use a sophisicaed growh accouning mehodology allowing for increasing reurns, imperfec compeiion, variable facor uilizaion and secoral composiional effecs in order o uncover a ime series for aggregae echnological change in he poswar U.S. economy. Their approach, combining elemens of earlier work by Hall (1988) and Basu and Kimball (1997) among ohers, can be viewed as an aemp o cleanse he Solow residual (Solow, 1957) of is widely acknowledged measuremen error resuling from he srong assumpions underlying is derivaion. Esimaes of he response of he economy o innovaions in heir measure of echnological change poin o a sharp shor-run 10 Blanchard (1989, p. 1158).

11 decline in he use of inpus (including labor) when echnology improves, wih oupu showing no significan change (wih poin esimaes suggesing a small decline). Afer ha shor-run impac boh variables gradually adjus upward, wih labor inpu reurning o is original level and wih oupu reaching a permanenly higher plaeau several years afer he shock. Kiley (1997) applies he srucural VAR framework in Galí (1999) o daa from wo-digi manufacuring indusries. While he does no repor impulse responses, he finds ha echnology shocks induce a negaive correlaion beween employmen and oupu growh in 12 of he 17 indusries considered. When he esimaes an analogous condiional correlaion for employmen and produciviy growh, he obains a negaive value for 15 ou of 17 indusries. Francis (2001) conducs a similar analysis, hough he aemps o idenify indusry-specific echnology shocks by including a measure of aggregae echnology, which is assumed o be exogenous o each of he indusries considered. He finds ha, for he vas majoriy of indusries, a secoral labor inpu measure declines in response o a posiive indusry-specific echnology shock. Using daa from a large panel of 458 manufacuring indusries and 35 secors, Franco and Philippon (2004) esimae a srucural VAR wih hree shocks: echnology shocks (wih permanen effecs on indusry produciviy), composiion shocks (wih permanen effecs on he indusry share in oal oupu), and ransiory shocks. They find ha echnology shocks (i) generae a negaive comovemen beween oupu and hours wihin each indusry, and (ii) are almos uncorrelaed across indusries. Accordingly, hey conclude ha echnology shocks can only accoun for a small fracion of he variance of aggregae hours and oupu (wih wo-hirds of he laer accouned for by ransiory shocks). Shea (1998) uses a srucural VAR approach o model he connecion beween changes in measures of echnological innovaion (research and developmen (R&D) and number of paen applicaions) and subsequen changes in oal facor produciviy (TFP) and hired inpus, using indusry-level daa. For mos specificaions and indusries he finds ha an innovaion in he echnology indicaor does no cause any significan change in TFP, bu ends o increase labor inpus in he shor run. While no much sressed by Shea, however, one of he findings in his paper is paricularly relevan for our purposes: in he few VAR specificaions for which a significan increase in TFP is deeced in response o a posiive innovaion in he echnology indicaor, inpus including labor are shown o respond in he direcion opposie o he movemen in TFP, a finding in line wih he evidence above. 11 Francis and Ramey (2003a) exend he analysis in Galí (1999) in several dimensions. The firs modificaion hey consider consiss in augmening he baseline VAR (specified in firs differences) wih a capial ax rae measure in order o sor ou he effecs of echnology shocks from hose of permanen changes in ax raes (more below). Second, hey idenify echnology shocks as hose wih permanen effecs on real wages (as opposed o labor produciviy) and/or no long-run effecs on hours, boh equally robus predicions of a broad class of models ha saisfy a balance growh propery. Those alernaive idenifying 11 See he commen on Shea's paper by Galí (1998) for a more deailed discussion of ha poin.

12 resricions are no rejeced when combined ino a unified (overidenified) model. Francis and Ramey show ha boh he model augmened wih capial ax raes and he model wih alernaive idenifying resricions (considered separaely or joinly) imply impulse responses o a echnology shock similar o hose in Galí (1999) and, in paricular, a drop in hours in response o a posiive echnology shock. Francis, Owyang, and Theodorou (2003) use a varian of he sign resricion algorihm of Uhlig (1999) and show ha he finding of a negaive response of hours o a posiive echnology shock is robus o replacing he resricion on he asympoic effec of ha shock wih one imposing a posiive response of produciviy a a horizon of en years afer he shock. A number of recen papers have provided relaed evidence based on non-u.s. aggregae daa. In Galí (1999) he srucural VAR framework discussed above is also applied o he remaining G-7 counries (Canada, he Unied Kingdom, France, Germany, Ialy, and Japan). He uncovers a negaive response of employmen o a posiive echnology shock in all counries, wih he excepion of Japan. Galí (1999) also poins ou some differences in hese esimaes relaive o hose obained for he Unied Saes: in paricular, he (negaive) employmen response o a posiive echnology shocks in Germany, he Unied Kingdom, and Ialy appears o be larger and more persisen, which could be inerpreed as evidence of "hyseresis" in European labor markes. Very similar qualiaive resuls for he euro area as a whole can also be found in Galí (2004), which applies he same empirical framework o he quarerly daa se ha has recenly become available. In paricular, echnology shocks are found o accoun for only 5 percen and 9 percen of he variance of he business cycle componen of euro-area employmen and oupu, respecively, wih he corresponding correlaion beween heir echnology-driven componens being Francis and Ramey (2003b) esimae a srucural VAR wih long-run idenifying resricions using long-erm U.K. annual ime series racing back o he nineeenh cenury; hey find robus evidence of a negaive shor-run impac of echnology shocks on labor in every subsample. 12 Finally, Carlsson (2000) develops a varian of he empirical framework in BFK (1999) and Burnside, Eichenbaum, and Rebelo (1995) o consruc a ime series for echnological change, and applies i o a sample of Swedish wo-digi manufacuring indusries. Mos prominenly, he finds ha posiive shocks o echnology have, on impac, a conracionary effec on hours and a non-expansionary effec on oupu, as in BFK (1999). C. Implicaions The implicaions of he evidence discussed above for business cycle analysis and modeling are manifold. Mos significanly, hose findings rejec a key predicion of he sandard RBC paradigm namely, he posiive comovemen of oupu, labor inpu, and produciviy in response o echnology shocks. Tha posiive comovemen is he single main feaure of ha 12 The laer evidence conrass wih heir analysis of long-erm U.S. daa, in which he resuls vary significanly across samples and appear o depend on he specificaion used (more below).

13 model ha accouns for is abiliy o generae flucuaions ha resemble business cycles. Hence, aken a face value, he evidence above rejecs in an unambiguous fashion he empirical relevance of he sandard RBC model. I does so in wo dimensions. Firs, i shows ha a key feaure of he economy's response o aggregae echnology shocks prediced by calibraed RBC models canno be found in he daa. Second, and o he exen ha one akes he posiive comovemen beween measures of oupu and labor inpu as a defining characerisic of he business cycle, i follows as a corollary ha echnology shocks canno be a quaniaively imporan (and, even less, a dominan) source of observed aggregae flucuaions. While he laer implicaion is paricularly damning for RBC heory, given is radiional emphasis on aggregae echnology variaions as a source of business cycles, is relevance is independen of one's preferred macroeconomic paradigm. III. POSSIBLE PITFALLS IN THE ESTIMATION OF THE EFFECTS OF TECHNOLOGY SHOCKS This secion has wo main objecives. Firs, we ry o address a quesion ha is ofen raised regarding he empirical approach used in Galí (1999): To wha exen can we be confiden in he economic inerpreaion given o he idenified shocks and, in paricular, in he mapping beween echnology shocks and he nonsaionary componen of labor produciviy? Below we provide some evidence ha makes us feel quie comforable abou ha inerpreaion. Second, we describe and address some of he economeric issues ha Chrisiano, Eichenbaum, and Vigfusson (2003) have raised in a recen paper, and which focus on he appropriae specificaion of hours (levels or firs differences). Finally, we discuss a recen paper by Fisher (2003), which disinguishes beween wo ypes of echnology shocks, neural and invesmen-specific. A. Are Long-Run Resricions Useful in Idenifying Technology Shocks? The approach o idenificaion proposed in Galí (1999) relies on he assumpion ha only (permanen) echnology shocks can have a permanen effec on (average) labor produciviy. Tha assumpion can be argued o hold under relaively weak condiions, saisfied by he bulk of business cycle models currenly used by macroeconomiss. To review he basic argumen consider an economy whose echnology can be described by an aggregae producion funcion: 13 Y = F K, A N ), (2) ( where Y denoes oupu, K is he capial sock, N is labor inpu, and A is an index of echnology. Under he assumpion ha F is homogeneous of degree 1, we have Y = A F k ( k,1), (3) N 13 An analogous bu somewha more deailed analysis can be found in Francis and Ramey (2003a)

14 where K k = is he raio of capial o labor (expressed in efficiency unis). For a large A N class of models characerized by an underlying balanced growh pah, he marginal produc of capial F mus saisfy, along ha pah, a condiion of he form k γ ( 1 τ) F k ( k,1) = (1 + µ)(ρ + δ + ) (4) σ where µ is he price markup, τ is a ax on capial income, ρ is he ime discoun rae, δ is he depreciaion rae, σ is he ineremporal elasiciy of subsiuion, and γ is he average growh rae of (per capia) consumpion and oupu. Under he assumpion of decreasing reurns o capial, i follows from equaion (4) ha he capial labor raio k will be saionary (and will hus flucuae around a consan mean) so long as all he previous parameers are consan (or saionary). In ha case, equaion (3) implies ha only shocks ha have a permanen effec on he echnology parameer A can be a source of he uni roo in labor produciviy, hus providing he heoreical underpinning for he idenificaion scheme in Galí (1999). How plausible are he assumpions underlying ha idenificaion scheme? Preference or echnology parameers like ρ, δ, σ, and γ are generally assumed o be consan in mos examples and applicaions found in he business cycle lieraure. The price markup µ is more likely o vary over ime, possibly as a resul of some embedded price rigidiies; in he laer case, however, i is likely o remain saionary, flucuaing around is desired or opimal level. In he even ha desired markups (or he preference and echnology parameers lised above) displayed some nonsaionariy, he laer would more likely ake he form of some smooh funcion of ime, which should be refleced in he deerminisic componen of labor produciviy, bu no in is flucuaions a cyclical frequencies. 14 Finally, i is imporan o noice ha he previous approach o idenificaion of echnology shocks requires ha (i) F k be decreasing, so ha k is uniquely pinned down by equaion (4), and (ii) ha he echnology process { A } is exogenous (a leas wih respec o he business cycle). The previous assumpions have been commonly adoped by business cycle modelers. 15 Do capial income ax shocks explain permanen changes in labor produciviy? The previous argumen, however, is much less appealing when applied o he capial income ax rae. As Uhlig (2004) and ohers have poined ou, he assumpion of a saionary capial income ax rae may be unwarraned, given he behavior of measures for ha variable over 14 Of course ha was also he radiional view regarding echnological change, bu one ha was challenged by he RBC school. 15 Excepions include sochasic versions of endogenous growh models, as in King, Plosser, and Rebelo (1988b). In hose models any ransiory shock can in principle have a permanen effec on he level of capial or disembodied echnology and, as a resul, on labor produciviy.

15 he poswar period. This is illusraed graphically in Figure 4, which displays wo alernaive measures of he capial income ax rae in he Unied Saes. Figure 4.A displays a quarerly series for he average capial income ax rae consruced by Jones (2002) for he period 1958:1-1997:4. Figure 4.B shows an annual measure of he average marginal capial income ax rae consruced by Ellen McGraan for he period ha corresponds o an updaed version of he one used in McGraan (1994). 16 Henceforh, we denoe hose series by τ and J τ M, respecively. Boh series display an apparen non-saionary behavior, wih highly persisen flucuaions. This is confirmed by a baery of ADF ess, which fail o rejec he null hypohesis of a uni roo in boh series, a convenional significance levels. Furhermore, as evidenced in Figures 4.C and 4.D, which display he same series in firs differences, he presence of sizable shor-run variaions in hose measures of capial axes could hardly be capured by means of some deerminisic or smooh funcion of ime (heir sandard deviaions being 0.79 percen for he quarerly Jones series, and 2.4 percen for he annual McGraan series). In fac, in boh cases he firs-differenced series τ shows no significan auocorrelaion, suggesing ha a random walk process can approximae he paern of capial income ax raes prey well. The previous evidence, combined wih he heoreical analysis above, poins o a poenial cavea in he idenificaion approach followed in Galí (1999): he shocks wih permanen effecs on produciviy esimaed herein could be capuring he effecs of permanen changes in ax raes (as opposed o hose of genuine echnology shocks). Tha mislabeling could poenially accoun for he empirical findings repored above. Francis and Ramey (2003a) aemp o overcome ha poenial shorcoming by augmening he VAR wih a capial ax rae variable, in addiion o labor produciviy and hours. As menioned above, he inroducion of he ax variable is shown no o have any significan influence on he findings: posiive echnology shocks sill lead o shor run declines in labor. Here we revisi he hypohesis of a ax rae shock misaken for a echnology shock by z looking for evidence of some comovemen beween (i) he permanen shock ε esimaed using he srucural VAR discussed in Secion II, and (ii) each of he wo capial ax series, in J M firs-differences. Given he absence of significan auocorrelaion in τ and τ, we inerpre each of hose series as (alernaive) proxies for he shocks o he capial income ax rae. Also, when using he McGraan series, we annualize he permanen shock series obained from he quarerly VAR by averaging he shocks corresponding o each naural year. The resuling evidence can be summarized as follows. Firs, innovaions o he capial income ax rae show a near zero correlaion wih he permanen shocks from he VAR. More J z M z precisely, our esimaes of he correlaion coefficiens beween ( τ,ε ) and ( τ,ε ) are, 16 We are graeful o Craig Burnside and Ellen McGraan for providing he daa.

16 respecively, and 0.12, neiher of which is significan a convenional levels. Thus, i is highly unlikely ha he permanen VAR shocks may be capuring exogenous shocks o capial axes. J Secondly, an ordinary leas squares (OLS) regression of he Jones ax series τ on curren z and lagged values of ε yields joinly insignifican coefficien esimaes: he p-value is 0.54 when four lags are included, 0.21 when we include eigh lags. A similar resul obains when M we regress he McGraan ax series on curren and several lags of ε, wih he p-value τ for he null of zero coefficiens being 0.68 when four lags are included (0.34 when we use 8 lags). Since he sequence of hose coefficiens corresponds o he esimaed impulse response of capial axes o he permanen VAR shock, he previous evidence suggess ha he esimaed effecs of he permanen VAR shocks are unlikely o be capuring he impac of a possible endogenous response in capial axes o whaever exogenous shock underlies he esimaed permanen VAR shock. We conclude from he previous exercises ha here is no suppor for he hypohesis ha he permanen shocks o labor produciviy, inerpreed in Galí (1999) as echnology shocks, could be insead capuring changes in capial income axes. 17 Do permanen shocks o labor produciviy capure variaions in echnology? Having all bu ruled ou variaions in capial axes as a significan facor behind he uni roo in labor produciviy, we nex presen some evidence ha favors he inerpreaion of he VAR permanen shock as a shif o aggregae echnology. In addiion, we also provide some evidence agains he hypohesis ha ransiory variaions in echnology may be a significan force behind he shocks idenified as ransiory shocks, a hypohesis ha canno be ruled ou on purely heoreical grounds. Francis and Ramey (2003a) es a weak form of he hypohesis of permanen shocks as echnology shocks, by looking for evidence of Granger-causaliy beween a number of indicaors ha are viewed as independen of echnology on he one hand, and he VAR-based echnology shock on he oher. The indicaors include he Romer and Romer (1989) moneary shock dummy, he Hoover and Perez (1994) oil shock dummies, Ramey and Shapiro's miliary buildup daes (1998), and he federal funds rae. Francis and Ramey show ha none of hem have a significan predicive power for he esimaed echnology shock. Here we provide a more direc assessmen by making use of he measure of aggregae echnological change obained by BFK. 18 As discussed earlier, hose auhors consruced ha z 17 A similar conclusion is obained by Fisher (2003), using a relaed approach in he conex of he muliple echnology shock model described below. 18 In paricular, we use heir "fully correced" series from heir 1999 paper. When revising he presen paper BFK made us aware of an updaed version of heir echnology series, exending (coninued )

17 series using an approach unrelaed o ours. The BFK variable measures he annual rae of echnological change in he U.S. nonfarm privae business secor. The series has an annual frequency and covers he period Our objecive here is o assess he plausibiliy of he echnology-relaed inerpreaion of he VAR shocks obained above by examining heir correlaion wih he BFK measure. Given he differences in frequencies, we annualize boh he permanen and ransiory shock series obained from he quarerly VAR by averaging he shocks corresponding o each naural year. The main resuls can be summarized as follows. Firs, he correlaion beween he VARbased permanen shock and he BFK measure of echnological change is posiive and significan a he 5 percen level, wih a poin esimae of The exisence of a posiive conemporaneous comovemen is apparen in Figure 5, which displays he esimaed VAR permanen shock ogeher wih he BFK measure (boh series have been normalized o have zero mean and uni variance, for ease of comparison). Second, he correlaion beween our esimaed VAR ransiory shock and he BFK series is slighly negaive, hough insignificanly differen from zero (he poin esimae is -0.04). The boom graph of Figure 5, which displays boh series, illusraes he absence of any obvious comovemen beween he wo. Finally, given ha he BFK series is mildly serially correlaed, we have also run a simple OLS regression of he (normalized) BFK variable on is own lag, and he conemporaneous esimaes of he permanen and ransiory shocks from he VAR. The esimaed equaion, wih -saisics in brackes, is given by: BFK = 0.29 BFK (1.85) ε (2.16) z 0.32 ε ( 1.11) d, which reinforces he findings obained from he simple conemporaneous correlaions. In summary, he resuls from he empirical analysis above sugges ha he VAR-based permanen shocks may indeed be capuring exogenous variaions in echnology, in a way consisen wih he inerpreaion made in Galí (1999). In addiion, we canno find evidence supporing he view ha he VAR ransiory shocks which were shown in Secion II o be he main source of business cycle flucuaions in hours and oupu may be relaed o changes in echnology. B. Robusness o Alernaive VAR Specificaions In a recen paper, Chrisiano, Eichenbaum, and Vigfusson (2003; henceforh, CEV) have quesioned some of he VAR-based evidence regarding he effecs of echnology shocks he sample period hrough o 1996, and incorporaing some mehodological changes. The resuls obained wih he updaed series were almos idenical o he ones repored below.

18 found in Galí (1999) and Francis and Ramey (2003a), on he basis of he lack of robusness o he ransformaion of labor inpu used. In paricular, CEV argue ha firs-differencing he (log) of per capia hours may disor he sign of he esimaed response of ha variable o a echnology shock, if ha variable is ruly saionary. Specifically, heir findings based on a bivariae VAR model in which (per capia) hours are specified in levels ( n ˆ = n ) imply ha oupu, hours, and produciviy all rise in response o a posiive echnology shock. On he oher hand, when hey use a difference specificaion hey obain resuls similar o he ones repored above i.e. a negaive comovemen beween oupu (or produciviy) and hours in response o echnology shocks. Perhaps mos ineresing, CEV discuss he exen o which he findings obained under he level specificaion can be accouned for under he assumpion ha he difference specificaion is he correc one, and vice versa. Given idenical priors over he wo specificaions, ha "encompassing" analysis leads hem o conclude ha he odds in favor of he level specificaion relaive o he difference specificaion are abou 2 o CEV obain similar resuls when incorporaing addiional variables in he VAR. Our own esimaes of he dynamic responses o a echnology shock when we specify (per capia) hours in levels do indeed poin o some qualiaive differences. In paricular, as shown in an appendix available on reques, he poin esimae of he impac response of hours worked o a posiive echnology is now posiive, hough very small. Ye, and in conras wih he findings in CEV, ha impac effec and indeed he enire dynamic response of hours is no significanly differen from zero. The sign of he poin esimaes, however, is sufficien o generae a posiive correlaion (0.88) beween oupu and hours condiional on he echnology shock. Furhermore, as repored in he second row of Table 1, under he level specificaion, echnology shocks sill accoun for a (relaively) small fracion of he variance of oupu and hours a business cycle frequencies (37 and 11 percen, respecively), hough ha fracion is larger han he one implied by he difference specificaion esimaes. 20 While we find he encompassing approach adoped by CEV enlighening, heir sraegy of pair wise comparisons wih uniform priors (which mechanically assigns a ½ prior o he level specificaion) may lead o some bias in he conclusions. In paricular, a simple look a a plo of he ime series for (he log of) per capia hours worked in he Unied Saes over he poswar period, displayed in Figure 6, is no suggesive of saionariy, a leas in he absence of any furher ransformaion. In paricular, and in agreemen wih he ADF and KPSS ess repored above, he series seems perfecly consisen wih a uni roo process, hough possibly no a pure random walk. On he basis of a cursory look a he same plo, and assuming ha one wishes o mainain he assumpion of a saionary process for he sochasic componen 19 Tha odds raio increases subsanially when an F-saisic associaed wih a covariaes ADF es is incorporaed as par of he encompassing analysis. 20 Wih he excepion of heir bivariae model under a level specificaion, CEV also find he conribuion of echnology shocks o he variance of oupu and hours a business cycles o be small (below 20 percen). In heir bivariae level specificaion ha conribuion is as high as 66 percen for oupu and 33 percen for hours.

19 of (he log of) per capia hours, a quadraic funcion of ime would appear o be a more plausible characerizaion of he rend han jus he consan implici in CEV's analysis. In fac, an OLS regression of ha variable on a consan, ime and ime squared yields a highly significan coefficien associaed wih boh ime variables. Furhermore, a es of a uni roo on he residual from ha regression fails o rejec ha hypohesis, while he KPSS does no rejec he null of saionariy, a a 5 percen significance level in boh cases. 21 Figure 6 displays he fied quadraic rend and he associaed residual, illusraing graphically ha poin. When we re-esimae he dynamic responses o a echnology shock using he derended (log of) per capia hours we find again a decline in hours in response o posiive echnology shock, and a slighly negaive (-0.11) condiional correlaion beween he business cycle componens of oupu and hours. In addiion, he esimaed conribuion of echnology shocks o he variance of oupu and hours is very small (7 and 5 percen, essenially he same as under difference specificaion; see Table 1). 22 To furher assess he robusness of he above resuls, we have also conduced he same analysis using a specificaion of he VAR using an alernaive measure of labor inpu namely, (he log of) oal hours, wihou a normalizaion by working-age populaion. As i should be clear from he discussion in Secion III.A, he idenificaion sraegy proposed in Galí (1999) and implemened here should be valid independenly of wheher labor inpu is measured in per capia erms or no, since labor produciviy is invarian o ha normalizaion. 23 The second panel in Table 1 summarizes he resuls corresponding o hree alernaive ransformaions considered (firs differences, levels, and quadraic derending). In he hree cases, a posiive echnology shock is esimaed o have a srong and saisically significan negaive impac on hours worked, a leas in he shor run. Ineresingly, under he level and derended ransformaions ha negaive response of hours is sufficienly srong o pull down oupu in he shor run, despie he increase in produciviy. Noe, however, ha he esimaed decline in oupu is no significan in eiher case. 24 Furhermore, he esimaed conribuion of echnology shocks o he variance of he business cycle componen of oupu and hours is small in all cases, wih he larges share being 36 percen of he variance of hours, obained under he level and derended specificaions. 21 Given he previous observaions one wonders how an idenical prior for boh specificaions could be assumed, as CEV do when compuing he odds raio. 22 Unforunaely, CEV do no include any saisic associaed wih he null of no rend in hours in heir encompassing analysis. While i is cerainly possible ha one can ge a - saisic as high as 8.13 on he ime-squared erm wih a 13 percen frequency when he rue model conains no rend (as heir Mone Carlo analysis suggess), i mus surely be he case ha such a frequency is much higher when he rue model conains he quadraic rend as esimaed in he daa! 23 In fac, oal hours was he series used originally in Galí (1999). 24 The finding of a sligh shor-run decline in oupu was obained in BFK (1999).

20 As an addiional check on he robusness of our findings, we have also esimaed all he model specificaions discussed above using employmen as he labor inpu measure (insead of hours), and real GDP as an oupu measure. A summary of our resuls for he six specificaions considered using employmen and GDP can be seen in Table 2. The resuls under his specificaion are much more uniform: independenly of he ransformaion of employmen used, our esimaes poin o a decline in ha variable in he shor run in response o a posiive echnology shock, as well as a very limied conribuion of echnology shocks o he variance of GDP and employmen. We should sress ha hose findings obain even when we specify employmen rae in levels, even hough he shor-run decline in employmen is no saisically significan in ha case. In summary, he previous robusness exercise based on poswar U.S. daa has shown ha, for all bu one of he ransformaions of hours used, we uncover a decline in labor inpu in response o a posiive echnology shock, in a way consisen wih he lieraure reviewed in Secion II. The excepion corresponds o he level specificaion of per capia hours, bu even in ha case he esimaed posiive response of hours does no appear o be significan. In mos cases he conribuion of echnology shocks o he variance of he cyclical componen of oupu and hours is very small, and always below 40 percen. Finally, and possibly wih he excepion menioned above, he paern of comovemen of oupu and hours a business cycle frequencies resuling from echnology shocks, fails o resemble he one associaed wih poswar U.S. business cycles. As furher discussed in Valerie Ramey's discussion o his paper, Fernald (2004) makes an imporan conribuion o he debae, by uncovering he mos likely source of he discrepancy of he esimaes when hours are inroduced in levels. In paricular, he shows he exisence of a low frequency correlaion beween labor produciviy growh and per capia hours. As illusraed hrough a number of simulaions, he presence of such a correlaion, while unrelaed o he higher frequency phenomena of ineres, can significanly disor he esimaed shor-run responses. Fernald illusraes ha poin mos forcefully by re-esimaing he srucural VAR in is levels specificaion (as in CEV), hough allowing for wo (saisically significan) rend breaks in labor produciviy (in 1973:1 and 1997:2): he implied impulse responses poin o a significan decline in hours in response o a echnology shock, a resul ha also obains when he difference specificaion is used. Addiional evidence on he implicaions of alernaive ransformaions of hours using annual ime series spanning more han a cenury is provided by Francis and Ramey (2003b). Their findings based on U.S. daa poin o considerable sensiiviy of he esimaes across subsample periods and he choice of ransformaion for hours. To assess he validiy of he differen specificaions, hey look a he implicaions for he persisence of he produciviy response o a non-echnology shock, he plausibiliy of he paerns of esimaed echnology shocks, as well as he predicabiliy of he laer (he Hall-Evans es). On he basis of ha analysis hey concluded ha firs-differenced and, o a lesser exen, quadraically derended hours yield he mos plausible specificaion. Francis and Ramey show ha in heir daa hose wo preferred specificaions generae a shor-run negaive comovemen beween hours and oupu in response o a shock ha has a permanen effec on echnology in he poswar period. In he pre-world War II period, however, he difference specificaion yields an increase in hours in response o a shock ha raises produciviy permanenly. On he oher hand, when hey repea he exercise using U.K. daa (and a difference specificaion) hey find