Shocks Do SVAR Models Justify Discarding the Technology Shock-Driven Real Business Cycle Hypothesis? Abstract

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1 Shocks Do SVAR Models Jusify Discarding he Technology Shock-Driven Real Business Cycle Hypohesis? Hyeon-seung Huh School of Economics Yonsei Universiy Republic of Korea David Kim School of Economics Universiy of Sydney Ausralia Absrac Recen sudies by Gali (1999), Gali and Rabanal (2004) and Francis and Ramey (2005) raise a srong objecion o he echnology shock-driven real business cycle (RBC) hypohesis on empirical grounds. To furher invesigae he validiy of echnology shocks as a driving force of U.S. business cycle flucuaions, we revisi some of he mos commonly undersood srucural vecor auoregression (SVAR) models of he empirical business cycle: namely, Gali (1999), Shapiro and Wason (1988), and King, Plosser, Sock and Wason (1991). Unlike previous conribuions, we uilize hese models o analyze how srucural shocks are associaed wih he variaions of oupu and hours worked a business cycle frequencies. Empirical evidence indicaes ha, across he models, echnology shocks remain as an imporan source of cyclical movemens in oupu even if all oher shocks are combined and used agains he echnology shocks. Furhermore, in conras o previous sudies, our resuls show ha a posiive echnology shock does no lead o a decline in hours worked. These resuls remain robus wheher hours worked is assumed o be a difference-saionary or rendsaionary process. Our SVAR-based evidence does no suppor discarding a echnology shock-driven business cycle heory. Keywords: Srucural vecor auoregressive (SVAR) models, Technology shocks, Demand shocks, Real business cycle heory. JEL Classificaion: C32, E32. The auhors wish o hank Lance Fisher, Gary Hansen, Glenn Oo, and Adrian Pagan for helpful commens, as well as paricipans a he 2011 Economeric Sociey Asian Meeings and he 2011 Ausralasian Macroeconomics Workshop. This work was suppored by he Naional Research Foundaion of Korea Gran funded by he Korean Governmen (NRF B00098). The usual caveas apply.

2 1. Inroducion Is he ques for he dominan driver of economic flucuaions over? Furhermore, should he echnology shock-driven real business cycle (RBC) hypohesis be discarded? The RBC hypohesis posis ha echnology or produciviy shocks are he dominan source of flucuaions, propagaed hrough ineremporal subsiuions by opimizing households and firms in response o he shocks. The hypohesis implies ha governmen sabilizaion policies could be couner-producive. In conras, he New Keynesian models emphasize he role of demand shocks propagaed due o he presence of price sickiness and imperfec compeiion, hence jusifying acive demand managemen hrough shor-run sabilizaion programs. Thus, empirical invesigaion of he main source of business cycle flucuaions is imporan no only as a guide for developing a useful posiive heory bu also because policy implicaions can vary subsanially, depending on which inerpreaion is correc. Following he emergence of he New Keynesian research program, here has been a considerable debae as o wheher he RBC predicions are borne ou by daa. Many empirical sudies have relied on srucural vecor auoregression (SVAR) approaches o evaluae he empirical validiy of he RBC hypohesis. Noably, Gali (1999), Gali and Rabanal (2004), and Francis and Ramey (2005) all repored ha, in SVAR models, posiive echnology shocks lead o a decline in hours worked, casing serious doub on he usefulness of RBC heory as a quaniaive heory of economic flucuaions. Typically, hese sudies use long-run resricions o idenify shocks wih he inerpreaion of echnology shocks and compare how he congruence beween he impulse responses from an esimaed SVAR model and hose of an RBC model. A key yardsick used o evaluae he RBC hypohesis using an esimaed SVAR model is wheher echnology shocks lead o a rise in hours? in acual daa as prediced by he heory. However, McGraan (2004), Chrisiano e al. (2003), and Chari e al. (2008) all challenged his rejecion of echnology-shock driven RBC models based on such an 2

3 evaluaion sraegy. Specifically, hey argued ha he SVAR models used o refue RBCbased explanaions are eiher misspecified or no appropriaely designed o evaluae he calibraed general equilibrium business cycle heory. In a similar vein, Wang and Wen (2011) argued ha condiional impulse responses generaed by SVAR models canno serve as grounds o rejec he echnology shock-driven RBC hypohesis because he dimension of such a highly sylized model is differen from ha of an empirical characerizaion of daa. In his paper, we uilize several SVAR models and presen a se of furher resuls ha provide alernaive perspecives ino he empirical source of flucuaions. Our work is no an aemp o engage in he mehodological debae over he bes pracice o empirically evaluae he RBC heory or, more generally, calibraed macroeconomic models. While our SVAR analysis produces impulse response funcions, we do no simply follow wha Gali and ohers did in heir analyses. Insead, we focus on business cycle frequencies and esimae he conribuion of echnology vs. demand (and oher) shocks by imposing a minimal number of idenifying assumpions. Hence, our work is similar, in spiri, o Cochrane (1994a) in ha i is a ques for which empirical shocks drive business cycle flucuaions. Unlike Cochrane s bivariae seing, however, we employ exended models ha accommodae various underlying shocks o allow for differen dynamics depending on he naure of he shocks. The resuls are used o examine he robusness of empirical findings produced by he exising sream of SVAR models. The SVAR models uilized here are aken from Gali (1999), Shapiro and Wason (1988), and King e al. (1991). These hree SVAR models were selced because hey are among he bes undersood and he mos popular models in empirical business cycle research. Along wih hese SVAR models, we use he decomposiion of permanen and ransiory componens as a key analyical ool, similar o ha of Beveridge and Nelson (1981). The permanen componen deermines he long-run movemens of he variables, while he ransiory componen capures he shor-run dynamics. Boh componens can be consruced 3

4 afer esimaing srucural models in conjuncion wih idenifying resricions. This allows us o analyze how he underlying shocks of models are associaed wih he ransiory componen of oupu, which capures flucuaions a business cycle frequencies. Based on he condiional correlaions of shocks wih cyclical oupu, we examine how differen srucural shocks have conribued o poswar U.S. business cycle flucuaions. We also provide deailed findings on wo imporan issues. Firs, we shed ligh on wheher he imporance of echnology shocks is sensiive o wheher hours worked is specified o be difference-saionary or rend-saionary, as RBC proponens such as Chrisiano e al. (2004) have argued. The oher issue concerns he empirical findings ha a posiive echnology shock leads o a decline in hours, which Gali and ohers have used as evidence agains he RBC heory. Overall, his sudy provides furher and alernaive perspecives using he evidence ha is clearly a odds wih he earlier findings of Gali and ohers. The remainder of his paper is organized as follows. Secion 2 oulines he hree SVAR models explored in he paper, and Secion 3 presens our empirical sraegy for measuring he relaive conribuion of srucural shocks in accouning for he business cycle flucuaions of he variables. The resuls are given in Secion 4. Secion 5 offers furher discussion of he resuls, wih paricular emphasis on robusness, and revisis he issue raised by Gali concerning he relaionship beween echnology shocks and hours worked. Secion 6 summarizes he key resuls of he paper and concludes he paper. 2. SVAR models This secion reviews he hree SVAR models and explains how hey are used in our invesigaion Gali (1999) 4

5 Gali invesigaed wheher echnology shocks could explain poswar U.S. business cycles using an SVAR model, o conclude ha he echnology shocks have a limied abiliy o explain he business cycle. He adoped wo models: (i) a bivariae SVAR model comprising labor produciviy (x) (defined as oupu less hours worked) and hours worked (n), i.e. wih he vecor x, n, and (ii) a five-variable SVAR model wih he vecor of variables x, n, m p, R p, p, where, in addiion o labor produciviy and hours worked, real money balances (nominal money, m, less he price level, p), real ineres raes (nominal ineres raes, R, minus he rae of inflaion, Δp), and he inflaion rae (Δp) ener he sysem. 1 In he curren paper, we consider only he laer model as he bivariae model does no make a disincion beween non-echnology supply shocks and demand shocks. The five-variable SVAR model assumes ha here are five srucural shocks: echnology shocks ( v 1 ), labor supply shocks ( v 2 ), and hree demand-side shocks ( v 3, v 4, and v 5 ). as The srucural vecor moving average (VMA) represenaion can be compacly wrien x C11( L) C12( L) C13( L) C14( L) C15( L) v1 n C21( L) C22( L) C23( L) C24( L) C25( L) v 2 m p C( L) v C31( L) C32( L) C33( L) C34( L) C35( L) v3 R p C41( L) C42( L) C43( L) C44( L) C45( L) v4 2 p C51( L) C52( L) C53( L) C54( L) C55( L) v 5 k where is he firs difference operaor, L is he lag operaor, C ( L) C, L, C ij, k is he response of he i h variable o he j h shock a a horizon k, and he vecor of disurbances v = ij k 0 ij k [ v, v, v, v, v ] represens a se of srucural shocks driving he sysem over ime. 2 For idenificaion of he underlying shocks, i is assumed ha labor produciviy and hours are no 1 Noe ha he lowercase variables denoe ha he variables are logged, e.g. y = log Y. 2 The consan erm is suppressed for he sake of illusraion. 5

6 affeced by he hree demand shocks, v 3, v 4, and v 5, in he long run. The implied resricions can be imposed by assuming ha C 1 j(1) C 2 j(1) 0 for j = 3, 4 and 5, where C (1) C measures he long-run response of he ih variable o he j h shock. This ij k 0 ij, k disinguishes he echnology and labor supply shocks from he demand shocks. The wo supply shocks are idenified individually on he assumpion ha he labor supply shock has no long-run effec on labor produciviy by seing C (1) The hree demand shocks are no disenangled individually, and heir combined effecs are used. As oupu is obained hrough he relaionship ha y x n, i is affeced by he wo supply shocks a all horizons, while none of he demand shocks has long-run effecs Shapiro and Wason (1988) Shapiro and Wason (henceforh SW) presen a five-variable SVAR model comprising he variables, [ o, n, y, p, R p], where o is he price of oil. In he model, he oil price is assumed o be exogenous o all of he oher variables, so ha is reduced-form residuals become he oil price shocks. This allows us o reduce he original specificaion o he fourvariable model of [ n, y, p, R p ]' wih he oil price enering he equaions as an exogenous regressor. There are assumed o be four srucural shocks governing he economy: labor supply shocks ( v 1 ), echnology shocks ( v 2 ), and wo demand shocks ( v 3 and v 4 ). The SW model can be wrien as a srucural VMA: n v1 y v. 2 CL ( ) 2 p v3 R p v 4 6

7 The labor supply shock is idenified on he assumpion ha i is he only shock ha has a long-run effec on hours. This is equivalen o assuming ha C12(1) C13(1) C14(1) 0. The echnology shock is idenified using he long-run oupu neuraliy so ha he wo demand shocks do no have long-run effecs on oupu. This can be imposed by seing ha C (1) C (1) 0. Again, he demand shocks are no idenified individually, and heir combined effecs are considered insead King, Plosser, Sock and Wason (1991) King e al. (henceforh KWSW) analyze a vecor error correcion model (VECM) comprising he six-variable, [ y, p, c, i, m p, R]', where consumpion ( c ) and invesmen ( i ) are also included. They sugges ha here are hree co-inegraing relaions presen in he sysem. Two of hese are he grea raios: ha is, ( c y ) and ( i y ) are saionary (afer he adjusmen for real ineres rae effecs), while he remaining relaion is a long-run money demand relaion among real money ( m p ), oupu ( y ), and he nominal ineres rae ( R ). On he basis of hree coinegraing relaions, here are assumed o be hree srucural shocks whose effecs are permanen, and hey are idenified as balanced-growh (produciviy) shocks ( v 1 ), inflaion shocks ( v 2 ), and real ineres rae shocks ( v 3 ). The remaining hree shocks ( v 4, v 5, and v 6 ) have only ransiory effecs on he variables, and are no given specific economic inerpreaions. 3 The KPSW model may be expressed in he form of a srucural VMA as 3 See also Gonzalo and Ng (2001) and Pagan and Pesaran (2008) for he implicaions of coinegraion in he srucural idenificaion of he VECM model. 7

8 y v 1 2 p v 2 c v3 CL ( ) i v4 m p v 5 R v 6 The produciviy (echnology) shock is idenified under he assumpion ha neiher he inflaion shock nor he real ineres rae shock has a long-run effec on oupu by seing ha C (1) C (1) 0. 4 The shocks o inflaion and he real ineres rae are individually idenified by assuming ha he real ineres rae shock does no have a long-run effec on he inflaion, which implies ha C 23 (1) 0. These hree resricions are sufficien for exac idenificaion of he permanen shocks in he model, as he presence of hree ransiory shocks implies ha all of he elemens in he las hree columns of C(1) are zero, i.e. Cij(1) 0 for i=1, 2,,6 and j=4, 5, and 6. Unlike he Gali and SW models, KPSW allow for invesmen dynamics o be expressed wihin he sysem. Cogley and Nason (1995) showed ha invesmen dynamics plays a cenral role hrough adjusmen lags or coss in accouning for he propagaion mechanism. McGraan (2004) eloquenly argued ha echnology shocks ypically influence he business cycle hrough invesmen, raher han hours. Her poin cass doub on he premise of sicky-price models of he business cycle model because such models, including he one sudied by Gali, dispense wih he role of invesmen in propagaing echnology shocks. Fama (1992) also presened evidence ha he hump-shaped response of oupu is largely due o he muliplier effec of variaions in invesmen. A recen work by Fisher (2006) furher srenghened he case for he imporance of invesmen and he role of invesmen-specific echnology shocks. 4 We use he erms produciviy and echnology inerchangeably unless saed oherwise. 8

9 3. Measuring he conribuion of srucural shocks Le Z be a (k 1) vecor of variables consising of k 1 non-saionary variables and k 2 saionary variables, i.e., expressed as Z X X. The srucural VMA represenaion can be compacly 1 2 Z ( Lv ) (1) where v represens a vecor of srucural shocks, and he lag polynomial marix ( L) racks he response of Z o he srucural shocks. For exposiional convenience, assume ha oupu in differenced form, Δy, is he firs variable in he vecor Z. This allows he following decomposiion in a manner analogous o Beveridge and Nelson (1981): where and p c y ( L) v ( L) v ( L) v (2) y yp yc p v is a vecor of shocks ha have permanen effecs on oupu, e.g., echnology shocks, c v is a vecor of shocks ha exer only ransiory effecs, e.g., IS and LM shocks. Equaion (2) can be furher decomposed as p c p p c y yp(1) yp( L) v yc( L) v yp(1) v yp( L) v yc( L) v (3) where yp( L ) = yp( L) yp(1), (1) yp capures he effecs of p v on he long-erm rend of oupu, and ( L ) measures he effecs of v p on he shor-run dynamics of oupu. For yp insance, echnology shocks affec long-run oupu, which is refleced in yp(1), and also cause business cycles hrough changes in capial invesmen and adjusmen coss or lags in labor inpu, ha is capured by ( L ). Equaion (3) can be ransformed in levels as yp p c (1) p ( ) p ( ) c yp yp yc y y y v L v L v (4) In (4), he cyclical componen of oupu corresponds o c p c yp( ) yc( ) 0 0 y L v L v. As i comprises he componens separaely driven by 9

10 permanen shocks and ransiory demand shocks, we are able o examine which shock is mainly responsible for flucuaions in oupu a business cycle frequencies. This may provide a beer way of defining deerminans underlying business cycles han he ypical ool of impulse responses and variance decomposiions. For echnology shocks, he effec on oupu is capured by ( L ), which can be decomposed ino he effec on he shor-run dynamics yp ( L ) as well as he effec on he long-erm rend (1). yp Using he decomposiion oulined above, we calculae he condiional correlaions of differen shocks wih he cyclical componen of oupu. To ake a five-variable model as an example, le v,1 be he correlaion coefficien beween cyclical oupu yp c y and he firs shock in he model, say, echnology shock v 1. Then, he coefficien v,2345 capures he correlaion of c y wih all oher shocks combined, indexed 2 o 5 combined, e.g., he composie nonechnology shocks. The condiional correlaion quanifies he exen o which each srucural shock is associaed wih oupu flucuaions a business cycle frequencies. In addiion, by squaring he correlaion coefficiens, we can analyze he conribuion of he shocks o accouning for he variance of c y. To see his, rewrie c y in (4) as Then, he condiional correlaion of c y a01v1 a02v2 a03v3 a04v4 a05v5 a11v1 1 a12v2 1 a13v3 1 a14v4 1 a15v5 1 a21v12 a22v22 a23v32 a24v42 a25v52 c y wih he i h shock v i can be obained as 2 2 c 0i i vi, Corr( y, vi) a0i i i1 a Where 2 i is he variance of he shock v i. Squaring he coefficien of he correlaion yields 10

11 a c 2 0i i vi, Corr( y, vi, ) a0i i i1 The denominaor represens he variance of y c explained by all shocks in ime and he numeraor measures he conribuion of he i h shock v i. 4. Empirical resuls 4.1. Impulse responses and hisorical decomposiions The Gali, SW, and KPSW models in Secion 2 are esimaed using he same daa series, lag lenghs, and saring daes as hose used in he original conribuions. 5 This paper, however, exends he sample period for all models o end in 2008:Q4. 6 We firs presen he resuls from impulse responses and hisorical decomposiions. For he former, we examine how a variable responds o he srucural shocks and check wheher hese responses are consisen wih he heory. For he laer, we assess he abiliy of srucural shocks o explain he sochasic movemen in a variable over ime. A he ouse i should be remembered ha demand shocks in he Gali and SW models, and ransiory shocks in he KPSW model were no individually idenified (see Secion 2). As such, he responses of he variables o hese shocks are no repored in he impulse response analysis, while he hisorical decomposiion analysis repors heir combined conribuion o racking he sochasic movemens of he variables. I should be noed ha hours worked is assumed o be a difference-saionary process. In he nex secion, we will examine how he resuls differ when hours worked is assumed o be a rendsaionary process. (i) Gali SVAR 5 The number of lags is 4, 6, and 8, and he saring dae is 1959:Q1, 1951:Q1, and 1954:Q1 for he Gali, SW, and KPSW models, respecively. 6 This effecively excludes he full effec of he recen financial crisis as an oulier. 11

12 Figure 1.1 depics he responses of labor produciviy, oupu and hours in levels o he wo supply-side shocks idenified, ha is, echnology (TN) and labor supply (LS) shocks. Also repored around each response is he one sandard error confidence inerval generaed by 1,000 boosrap replicaions. All of he responses are no differen from hose presened by Gali. A posiive echnology shock raises labor produciviy and oupu permanenly, while hours show a significan decline a shor ime horizons. As Gali forcefully argues, his finding is apparenly evidence agains he RBC heory, which predics pro-cyclical labor hours in response o echnology shocks. A posiive labor supply shock increases hours and oupu permanenly, and he effec on labor produciviy converges o zero by he idenifying assumpion. Figure 2.1 shows he hisorical decomposiions of he key variables. Technology shocks explain mos of he variaion in labor produciviy, while he variaion of hours is mosly accouned for by labor supply shocks. Ineresingly, he resul shows ha he labor supply shock is also he main deerminan of he movemens in oupu. None of he echnology or demand shocks plays any significan role. We will discuss hese resuls subsequenly in deail. (ii) Shapiro and Wason SVAR Figure 1.2 shows he responses of he variables o echnology and labor supply shocks esimaed from he SW model. Overall, oupu and hours respond in a very similar manner o he Gali model. The level of hours falls in response o a posiive echnology shock before converging o zero by he idenifying resricion. Posiive shocks o labor supply and echnology increase oupu permanenly. The hisorical decomposiion yields similar resuls, as displayed in Figure 2.2. The labor supply shock is he main facor in explaining he sochasic movemens in hours and oupu, while echnology and demand shocks conribue lile o he movemens in oupu. 12

13 (iii) King, Plosser, Sock, and Wason SVAR Figure 1.3 shows he responses of hree real variables - oupu, consumpion, and invesmen o he hree permanen shocks: shocks o echnology (TN), inflaion (IF), and he real ineres rae (RR). A posiive echnology shock raises oupu, consumpion and invesmen permanenly, as expeced a priori. The inflaion shock has lile impac on he variables excep a some shor ime horizons. In response o a posiive real ineres rae shock, he hree variables show srong iniial increases. I is difficul o provide precise economic inerpreaions o hese impulse responses, as also acknowledged by KPSW. However, Fisher e al. (2000) suggesed ha a real spending shock, in place of he real ineres rae shock, provides a beer economic inerpreaion of he KPSW findings. Under his alernaive inerpreaion, he srong iniial increases in he variables in response o he shock are consisen wih he predicions of convenional economic heory. Figure 2.3 shows he resuls of hisorical decomposiion esimaed from he KPSW SVAR. Technology shocks accoun for mos of he variaions in oupu and consumpion. The oher wo permanen shocks as well as ransiory shocks do no appear o conribue as much. In he case of invesmen, he echnology shock is sill a major deerminan, bu he combined ransiory shocks also capure a sizable porion of he movemens paricularly for he second half of he sample period Cyclical oupu and shocks As saed previously, he crux of his paper is an examinaion of he sources of flucuaions a business cycle frequencies. While he resuls in he preceding secion provide useful insighs, hey are no complee for an ofen negleced reason ha he impulse response funcion is designed o capure he combined effecs of shocks on boh long-erm rends and shor-run dynamics. To business cycle researchers, one odd observaion concerning he Gali and SW models would be ha oupu flucuaions were mosly accouned for by labor supply shocks. 13

14 As shown before in his paper, echnology and demand shocks conribued relaively lile in heir models, which is hard o reconcile wih he RBC or even wih he Keynesian perspecive. When focusing on business cycle flucuaions, as in he curren sudy, i may be more pruden o look a he relaionships beween underlying shocks and cyclical oupu, raher han he oupu variable per se. As RBC models are ypically analyzed in erms of he seady sae deviaions in response o a shock, decomposing oupu ino permanen, defining he seady sae, and ransiory componens is legiimae, jusifying he empirical sraegy deailed in Secion 3. Assuming he ransiory componen as a measure of cyclical oupu, we examine how and o wha exen cyclical oupu is associaed wih he shocks in he model. (i) Gali SVAR Table 1.1 repors he condiional correlaions of cyclical oupu wih respec o he shocks idenified from he Gali model. The correlaion coefficien beween cyclical oupu and echnology shocks is 0.69; squaring i shows ha echnology shocks accoun for abou 48 percen of he variance in cyclical oupu. Demand shocks are almos as highly correlaed wih cyclical oupu ( v, ) as echnology shocks. In conras, he correlaion coefficien beween he labor supply shock and cyclical oupu is low, a 0.33; only 10 percen of variance in cyclical oupu is explained by he labor supply shock. To elaborae on hese resuls, Figure 3.1 repors he hisorical decomposiion of cyclical oupu, and he shaded areas represen periods beween peaks and roughs in he U.S. business cycles, daed by he Naional Bureau of Economic Research (NBER). Indeed, boh echnology and demand shocks capure he movemens in cyclical oupu equally well, while labor supply shocks perform poorly. The resuls are quie differen from hose of he impulse response and variance decomposiion analysis in he preceding secion. Tha is, he echnology and demand shocks now emerge as he main deerminan of oupu movemens a business cycle 14

15 frequencies while he conribuion of he labor supply shock is subsanially reduced once he low frequency componen of oupu is removed. Figure 4.1 displays he cross correlaions of cyclical oupu wih he shocks a leads up o eigh quarers. The correlaions a leads can assess he predicive properies of he shocks over he business cycle. The echnology shock is found o lead cyclical oupu more srongly han demand shocks across he leads while he labor supply shock fails o lead cyclical oupu. (ii) Shapiro and Wason SVAR Table 1.2 repors he condiional correlaions beween cyclical oupu and he srucural shocks esimaed from he SW model. For echnology shocks, he correlaion coefficien is 0.58, while he coefficien for he combined demand shocks is much higher, a Similar o he Gali SVAR, he associaion beween oupu and labor supply shocks becomes significanly weaker and saisically insignifican over he business cycle. Alhough he level of correlaion beween echnology shocks and cyclical oupu is lower han in he Gali SVAR, echnology shocks sill accoun for abou 34 percen of he variance in cyclical oupu wih he remainder being explained by he demand and labor supply shocks ogeher. The hisorical decomposiion in Figure 3.2 confirms hese findings. Demand shocks closely follow he movemens in cyclical oupu over he sample period while labor supply shocks conribue very lile. The echnology shock sill reains a considerable abiliy o explain cyclical oupu, alhough no as well as demand shocks. Again, hese resuls are quie differen from hose of he hisorical decomposiion for oupu in which demand and echnology shocks played a negligible role. Figure 4.2 displays he cross correlaions of cyclical oupu wih he shocks a various leads. Demand shocks beer predic cyclical oupu han echnology shock, alhough he difference is diminished a long leads. The labor supply shock does no exhibi any discernible abiliy o lead cyclical oupu across all leads. Overall, he Shapiro and Wason SVAR produces qualiaively similar resuls o hose from he Gali 15

16 SVAR. In boh models, echnology and demand shocks are he main drivers of cyclical oupu, while he labor supply shock becomes insignifican. (iii) King, Plosser, Sock and Wason SVAR Table 1.3 repors he condiional correlaion of oupu wih respec o he srucural shocks from he KPSW model. The echnology shock is he mos significan force, wih he correlaion coefficien of The correlaion of cyclical oupu wih he wo demand shocks combined (shocks o inflaion and he real ineres rae) is 0.48, while he correlaion wih he hree (unidenified) ransiory shocks is Alhough he resuls depend somewha on how he ransiory shocks are acually idenified, hey are more likely o originae from he demand side raher han he supply side. This allows us o combine hese ransiory shocks wih he wo permanen demand shocks and inerpre hem as non-echnology shocks ha mainly reflec changes in demand. As a consequence, he non-echnology shock is more highly correlaed wih cyclical oupu ( v, ) han he echnology shock. Figure 3.3 shows he decomposiion of cyclical oupu aribuable o he srucural shocks. The echnology and ransiory shocks appear o rack he movemens in cyclical oupu equally well. When he demand and ransiory shocks are combined, he resuling non-echnology shock shows a beer fi wih cyclical oupu hroughou he enire sample period. Figure 4.3 adds an ineresing observaion concerning he abiliy of he shocks o predic cyclical oupu. The non-echnology shock ouperforms he echnology shock for up o hree quarers of leads, while he reverse is rue hereafer. As he forecasing horizon increases beyond hree quarers, he echnology shock exhibis beer predicive abiliies for cyclical oupu. 5. Issues surrounding hours worked 16

17 In he New Keynesian-RBC debae over he imporance of echnology shocks, here are wo imporan issues concerning he empirical characerizaion of hours worked. The firs issue is he sensiiviy of he resuls o he assumpion of wheher hours worked is differencesaionary or rend-saionary. The second issue, relaed o he firs one, is wheher a posiive echnology shock does, in fac, lead o a decline in hours worked, as argued by Gali (1999). This secion addresses each of hese issues wih respec o our resuls from he Gali and SW models Saionary vs. non-saionary hours worked Theoreically speaking, hours worked is a bounded series, and convenional RBC models predic ha in he presence of echnology shocks, he subsiuion and income effecs cancel each oher ou wih no clear impac on he seady sae level of hours. In finie samples, however, i is debaable wheher such heoreical consrains are borne ou by he daa. Some RBC proponens such as Chrisiano e al. (2004) argue ha he findings of Gali (1999) depend criically on wheher he level of hours is assumed o be saionary. This was also noed earlier by Shapiro and Wason (1988) as hey observed ha he oupu effecs of echnology and labor supply shocks may vary depending on wheher hours worked is assumed o be difference-saionary or rend-saionary. In he preceding secion, he Gali and SW models adoped he assumpion of difference-saionary hours. Figures 5.1 and 5.2 display he impulse responses and hisorical decomposiions esimaed from he Gali and SW models when hours worked is assumed o be a rend-saionary process. For boh models, he impulse responses remain largely unchanged wih wo obvious excepions; he ransiory effecs of he labor supply shock and he responses of hours converging o zero in he long run, reflecing he assumpion of he rend saionary hours. Again, a posiive echnology shock leads o a decline in hours, analogous o he finding under he assumpion of difference-saionary hours. However, he hisorical 17

18 decomposiion produces quie a differen picure; across he models, he echnology shock is now he main source of movemens in oupu, and he conribuion of he labor supply shock shrinks considerably, paricularly since he mid-1970s. Similar changes are also observed for explaining he variabiliy of hours. Now, he echnology shock emerges as he main deerminan while he labor supply shock conribues far less han before. To furher illusrae, we re-compue he condiional correlaions of he srucural shocks wih cyclical oupu under he assumpion ha hours worked is a rend-saionary process. The resuls are repored in Tables 2.1 and 2.2. Several changes are worh discussion. Examining he Gali model firs, he echnology shock is he mos highly correlaed wih cyclical oupu as documened by he correlaion coefficien of The correlaion beween demand shocks and cyclical oupu is only abou 0.2, which is quie low compared wih he correlaion coefficien of 0.68 when hours was assumed o be difference-saionary. Even when all non-echnology shocks are combined, he correlaion coefficien is jus 0.33, far less han he correlaion beween he echnology shock and cyclical oupu. The SW model produces he same implicaions. The correlaion of cyclical oupu wih he echnology shock rises considerably o 0.84, while he corresponding figure for demand shocks is diminished o 0.37, in comparison o he resul when hours was assumed o be difference-saionary. The hisorical decomposiion of cyclical oupu repored in Figure 5.3 consolidaes he resuls. The echnology shock accouns for mos of he movemens in cyclical oupu, while boh labor supply and demand shocks conribue lile. Figure 5.4 shows ha he predicive power of echnology shocks is also srenghened under he assumpion of saionary hours. For boh he Gali and SW models, he echnology shock leads cyclical oupu far beer han labor supply and demand shocks across all leads, showing paricularly srong effecs a shor leads. Even over longer leads, such as eigh quarers, he coefficien remains higher han 0.5. For he SW model, demand shocks exhibi some 18

19 predicabiliy a shor leads bu only marginally, while he labor supply shock fails o lead cyclical oupu. In summary, our resuls are sensiive o wheher hours worked is assumed o be a difference-saionary or rend-saionary process. The RBC hypohesis is more preferred under he rend-saionariy assumpion. In addiion, he evidence is more pronounced when we decompose he variables ino permanen and ransiory componens and focus only on he laer componens, which reflec movemens a business cycle frequencies. When hours worked is assumed o be difference-saionary, echnology and demand shocks are almos equally imporan in accouning for cyclical oupu. Under he assumpion of rend-saionary hours, he echnology shock becomes he major deerminan of cyclical oupu, ouperforming all oher shocks, including demand shocks. This finding provides raher srong suppor for he RBC hypohesis. The resuls are robus for boh Gali and SW models, despie he fac ha hese models have differen srucures and idenifying assumpions. 7 Therefore, wheher hours worked is a difference-saionary or rend-saionary process may be a useful yardsick for discriminaing beween RBC and New Keynesian models. Policy implicaions would differ depending on which model is a beer descripion of he real economy. While more comprehensive research is warraned, i could be difficul o draw an empirical disincion concerning he ime-series properies of hours, given he well-known low power problem of many uni roo ess coupled wih he ypical sample size of macroeconomic daa. Because his issue is beyond he scope of he curren paper, we leave i for fuure research and move on o anoher relaed issue Technology shocks and hours worked 7 For example, he Gali model assumes ha echnology shocks can affec all of he variables in he long run, bu labor supply shocks are no allowed o have a long-run effec on labor produciviy. The converse is assumed in he SW model: labor supply shocks can have a long-run impac on all of he variables while echnology shocks canno have permanen effecs on labor supply. 19

20 Gali (1999) argued ha echnology shocks lead o a decline in hours worked, wheher hours is difference-saionary or rend-saionary, using his as evidence agains he RBC hypohesis. In he impulse response analysis, we find resuls similar o hose of Gali, as displayed in Figures 1.1, 1.2, and 5.1. The figures also indicae ha he decline in hours is presen only in he shor ime horizon, afer which he responses of hours o a posiive echnology shock are saisically insignifican (Figure 1.1) or converge o zero (Figures 1.2 and 5.1) by he idenifying assumpions. As saed earlier, he impulse response analysis reflecs he composie effecs on boh long-erm movemens and shor-erm dynamics. To isolae he shor-erm from he long-erm movemens, he decomposiion oulined in Secion 3 was applied o hours worked. In his way, we sough o deermine wheher Gali s argumen would sill hold once confined o movemens a business cycle frequencies. Figure 5.5 displays he condiional correlaions beween echnology shocks and cyclical hours over he leads of one o eigh quarers. The echnology shock appears o be posiively correlaed wih cyclical hours conemporaneously across he Gali and SW models. This is robus wheher hours worked is assumed o be a difference-saionary or rendsaionary process. The correlaions range beween 0.59 and 0.88 and are paricularly srong under he rend-saionariy assumpion. I is also noable ha he Gali and SW models produce coefficiens of a very similar magniude, validaing he robusness of he resuls. Furhermore, he echnology shock is found o lead cyclical hours considerably, displaying posiive and saisically significan correlaions a mos of he leads. Thus, our evidence does no suppor Gali s finding ha a posiive echnology shock leads o a decline in hours, when examined over business cycle frequencies. Raher, our finding ha a echnology shock has a srongly posiive associaion wih cyclical variaion in hours is quie well explained by he RBC models. 8 8 In RBC models, a posiive shock o echnology leads o a rise in hours worked hrough an increase in he marginal produc of labor and he consequen adjusmens in he marginal rae of subsiuion. 20

21 6. Conclusion This paper examined he empirical sources of business cycle flucuaions in he poswar U.S. economy using hree popular varians of SVAR models; hose sudied by Gali (1999), Shapiro and Wason (1988), and King, Plosser, Sock and Wason (1991). In adoping hese models, a minimum se of heoreical resricions were imposed a priori o avoid favoring a paricular heory, especially beween New Keynesian and RBC paradigms. The curren sudy wen significanly furher han he original SVAR conribuions by making exensive use of he saisical properies of he daa and resuls. In paricular, he variables were decomposed ino permanen and ransiory componens; using he laer, we invesigaed he relaionships beween underlying srucural shocks and movemens of he variables a business cycle frequencies. This sraegy appeared o pay economically ineresing dividends. Technology and demand shocks were boh shown o be he mos imporan sources of variaion in cyclical oupu. This finding is differen from ha suggesed by he convenional impulse response and hisorical decomposiion analysis. This paper also examined wo imporan issues sill being debaed in he lieraure: wheher he assumpion of saionariy of hours worked maers; and wheher a posiive echnology shock leads o a decline in hours, as claimed by Gali (1999). As o he firs issue, our resuls showed considerable changes under he assumpion of rend-saionary hours. Of paricular ineres, we found ha a echnology shock was he mos imporan deerminan of cyclical oupu, while all oher shocks, including demand shocks, showed only marginal conribuions. This sudy provided an equally ineresing resul wih respec o he second issue. While we, like oher auhors, found a decline in hours in response o a posiive echnology shock, a very differen picure emerged when focused on he movemens over he business cycle. The echnology shock was posiively correlaed wih he conemporaneous and fuure values of cyclical hours, invalidaing Gali s claim. The effecs were more 21

22 pronounced when hours was assumed o be rend-saionary. Our evidence is robus across he models under consideraion. Considering all hese resuls ogeher, we conclude ha echnology shocks should no be discarded as an imporan driver of business cycle flucuaions, nor should he RBC be hrown ou simply because of is emphasis on echnology shocks. Alhough we may forever remain ignoran of he fundamenal causes of economic flucuaions as remarked by Cochrane (1994b), echnology shocks are never likely o be dropped as an imporan source of macroeconomic flucuaions. The echnology-driven real business cycle hypohesis should be sill alive. 22

23 References Beveridge, Sephen. and Nelson, Charles R. (1981) A new approach o decomposiion of economic ime series ino permanen and ransiory componens wih paricular aenion o measuremen of he business cycle, Journal of Moneary Economics 7(2), Chari, V.V., Kehoe, Parick J. and McGraan, Ellen R. (2008) Are srucural VARs wih long-run resricions useful in developing business cycle heory?, Journal of Moneary Economics 55(8), Chari, V.V., Kehoe, Parick J. and McGraan, Ellen R. (2009) New Keynesian models: No ye useful for policy analysis, American Economic Journal: Macroeconomics 1(1), Chrisiano, Lawrence J., Eichenbaum, Marin and Vigfusson, Rober. (2003) Wha happens afer a echnology shock?, Inernaional Finance Discussion Papers 768, Board of Governors of he Federal Reserve Sysem. Chrisiano, Lawrence J., Eichenbaum, Marin and Vigfusson, Rober (2004) The response of hours o a echnology shock: Evidence based on direc measures of echnology, Journal of he European Economic Associaion 2(2-3), Cochrane, John. (1994a) Permanen and ransiory componens of GNP and sock prices, Quarerly Journal of Economics 109, Cochrane, John. (1994b) Shocks, Carnegie-Rocheser Conference Series on Public Policy 41, Cogley, Timohy and Nason, James M. (1995) Oupu dynamics in real-business-cycle models, American Economic Review 85(3), Fama, Eugene F. (1992) Transiory variaion in invesmen and oupu, Journal of Moneary Economics 30(3), Fisher, J. D. (2006), The dynamic effecs of neural and invesmen specific echnology shocks, Journal of Poliical Economy 114(3), Fisher Lance A., Huh, Hyeon-Seung and Summers, Peer M. (2000), Srucural Idenificaion of Permanen Shocks in VEC Models: A Generalizaion, Journal of Macroeconomics 22(1), Francis, Neville and Ramey, Valerie A. (2005) Is he echnology-driven real business cycle hypohesis dead?: Shocks and aggregae flucuaions revisied, Journal of Moneary Economics 52(8), Gali, Jordi. (1999) Technology, employmen, and he business cycle: do echnology shocks explain aggregae flucuaions?, American Economic Review 89(1), Gali, Jordi. (2004) On he role of echnology shock as a source of business cycles: Some new evidence, Journal of he European Economic Associaion 2(2-3),

24 Gali, Jordi and Rabanal, Paul. (2004) Technology shocks and aggregae flucuaions: How well does he RBC model fi poswar U.S. daa?, in M. Gerler and K. Rogoff (eds): NBER Macroeconomics Annual 2004, MIT Press, Gonzalo, Jesus and Ng, Serena. (2001) A sysemaic framework for analyzing he dynamic effecs of permanen and ransiory shocks, Journal of Economic Dynamics and Conrol 25(10), King, Rober G., Plosser, Charles I., Sock, James H. and Wason, Mark W. (1991) Sochasic Trends and Economic Flucuaions, American Economic Review 81(4), Kydland, Finn. and Presco Edward C. (1982) Time o build and aggregae flucuaions, Economerica, 50(6), McGraan, Ellen (2004) Commen on Gali and Rabanal s echnology shocks and aggregae flucuaions: How well does he RBC model fi poswar U.S. daa?, in M. Gerler and K. Rogoff (eds): NBER Macroeconomics Annual 2004, MIT Press, Pagan, Adrian R. and Pesaran, M. Hashem (2008) Economeric analysis of srucural sysems wih permanen and ransiory shocks, Journal of Economic Dynamics and Conrol 32(10), Shapiro, Mahew and Wason, Mark. (1988) Sources of business cycles flucuaions, in S. Fischer (ed.): NBER Macroeconomics Annual 1988, MIT Press, Wang, Pengfei and Wen, Yi. (2011) Undersanding he effecs of echnology shocks, Review of Economic Dynamics 14(4),

25 Table 1.1: Correlaions of Shocks wih Cyclical Oupu from Gali SVAR Technology shock ( v,1 ) Labor supply shock ( v,2 ) Demand shocks combined ( v,345 ) Non-echnology shocks ( v,2345) (0.31) (0.32) (0.26) (0.23) Table 1.2: Correlaions of Shocks wih Cyclical Oupu from Shapiro and Wason SVAR Technology shock ( v,2 ) Labor supply shock ( v,1 ) Demand shocks combined ( v, 34 ) Non-echnology shocks ( v, 234 ) (0.29) (0.30) (0.25) (0.13) Table 1.3: Correlaions of Shocks wih Cyclical Oupu from KPSW SVAR Technology shock ( ) v,1 Demand shocks combined ( v, 23 ) All ransiory shocks combined ( v, 456 ) Non-echnology shocks ( v, ) (0.28) (0.25) (0.19) (0.17) Noe: Figures in parenheses are one-sandard errors of he esimaes generaed by 1,000 boosrap replicaions.

26 Table 2.1: Correlaions of Shocks wih Cyclical Oupu from Gali SVAR (rend-saionary hours) Technology shock ( v,1 ) Labor supply shock ( v,2 ) Demand shocks combined ( v,345 ) Non-echnology shocks ( v,2345) (0.16) (0.19) (0.14) (0.19) Table 2.2: Correlaions of Shocks wih Cyclical Oupu from Shapiro and Wason SVAR (rend-saionary hours) Technology shock ( v,2 ) Labor supply shock ( v,1 ) Demand shocks combined ( v, 34 ) Non-echnology shocks ( v, 234 ) (0.17) (0.22) (0.20) (0.21) Noe: Figures in parenheses are one-sandard errors of he esimaes generaed by 1,000 boosrap replicaions. 26

27 Figure 1.1: Impulse Responses from Gali SVAR Labor produciviy Oupu Hours TN LS Noes: TN and LS denoe echnology and labor supply shocks, respecively. Shown around each response (in blue) is he one sandard error confidence inerval generaed by 1,000 boosrap replicaions.

28 Figure 1.2: Impulse Responses from Shapiro and Wason SVAR Hours Oupu Inflaion Real Ineres LS TN Noes: LS and TN denoe labor supply and echnology shocks, respecively. Shown around each response (in blue) is he one sandard error confidence inerval generaed by 1,000 boosrap replicaions. 28

29 Figure 1.3: Impulse Responses from KPSW SVAR Oupu Consumpion Invesmen TN IF RR Noes: TN, IF, and RR denoe shocks o echnology, inflaion, and real ineres rae, respecively. Shown around each response (in blue) is he one sandard error confidence inerval generaed by 1,000 boosrap replicaions. 29

30 Figure 2.1: Hisorical Decomposiions from Gali SVAR Noes: In each graph, he solid line is he sochasic movemen in a variable. The doed lines show he conribuion of he srucural shocks where TN, LS, and DM denoe shocks o echnology, labor supply, and demand, respecively. 30

31 Figure 2.2: Hisorical Decomposiions from Shapiro and Wason SVAR Noes: In each graph, he solid line is he sochasic movemen in a variable. The doed lines show he conribuion of he srucural shocks where LS, TN, and DM denoe shocks o labor supply, echnology, and demand, respecively. 31

32 Figure 2.3: Hisorical Decomposiions from KPSW SVAR Noes: In each graph, he solid line is he sochasic movemen in a variable. The doed lines show he conribuion of he srucural shocks where TN, IF, RR, and TR denoe echnology shock, inflaion shock, real ineres rae shock, and ransiory shocks, respecively. 32

33 Figure 3.1: Cyclical Oupu and Shocks from Gali SVAR ALL TN ALL DM ALL LS ALL Non-TN Noes: In each graph, he solid line is he sochasic movemen of cyclical oupu, while he doed lines show he conribuion of respecive shocks. The shaded areas are periods beween peaks and roughs of U.S. business cycles daed by he Naional Bureau of Economic Research (NBER). 33

34 Figure 3.2: Cyclical Oupu and Shocks from Shapiro and Wason SVAR 0.06 ALL LS 0.06 ALL DM ALL TN 0.06 ALL Non-TN Noes: In each graph, he solid line is he sochasic movemen of cyclical oupu, while he doed lines show he conribuion of respecive shocks. The shaded areas are periods beween peaks and roughs of U.S. business cycles daed by he Naional Bureau of Economic Research (NBER). 34

35 Figure 3.3: Cyclical Oupu and Shocks from KPSW SVAR ALL TN ALL TR ALL DM ALL Non-TN Noes: In each graph, he solid line is he sochasic movemen of cyclical oupu, while he doed lines show he conribuion of respecive shocks. The shaded areas are periods beween peaks and roughs of U.S. business cycles daed by he Naional Bureau of Economic Research (NBER). 35

36 Figure 4.1: Predicive Properies of Shocks from Gali SVAR 1 Gali TN 0.4 LS DM Non TN Leads Noe: The solid pronounced markers indicae saisically significan poin esimaes a he 10 percen level. 36

37 Figure 4.2: Predicive Properies of Shocks from Shapiro and Wason SVAR 1 SW TN LS DM Non TN Leads Noe: The solid pronounced markers indicae saisically significan poin esimaes a he 10 percen level. 37

38 Figure 4.3: Predicive Properies of Shocks from KPSW SVAR 1 KPSW TN 0.4 DM TR Non TN Leads Noe: The solid pronounced markers indicae saisically significan poin esimaes a he 10 percen level. 38

39 Figure 5.1: Impulse Responses wih Trend-saionary Hours (a) Gali SVAR Labor produciviy Oupu Hours TN LS

40 (b) Shapiro and Wason SVAR Hours Oupu Inflaion Real Ineres LS TN Noes: TN and LS denoe echnology and labor supply shocks, respecively. Shown around each response (in blue) is he one sandard error confidence inerval generaed by 1,000 boosrap replicaions. 40

41 Figure 5.2: Hisorical Decomposiion of Oupu and Hours wih Trend-saionary Hours (a) Gali SVAR Labor produciviy Oupu Hours TN LS DM