Why Have Business Cycle Fluctuations Become Less Volatile?

Transcription

1 Augus, 006 Why Have Business Cycle Flucuaions Become Less Volaile? Andres Arias Miniserio de Agriculura y Desarrollo Rural, Republic of Colombia Gary D. Hansen UCLA & NBER Lee E. Ohanian UCLA, Federal Reserve Bank of Minneapolis, & NBER Absrac This paper shows ha a sandard Real Business Cycle model driven by produciviy shocks can successfully accoun for he 50 percen decline in cyclical volailiy of oupu and is componens, and labor inpu ha has occurred since 98. The model is successful because he volailiy of produciviy shocks has also declined significanly over he same ime period. We hen invesigae wheher he decline in he volailiy of he Solow Residual is due o changes in he volailiy of some oher shock operaing hrough a channel ha is absen in he sandard model. We herefore develop a model wih variable capaciy and labor uilizaion. We invesigae wheher governmen spending shocks, shocks ha affec he household s firs order condiion for labor, and shocks ha affec he household s firs order condiion for saving can plausibly accoun for he change in TFP volailiy and in he volailiy of oupu, is componens, and labor. We find ha none of hese shocks are able o do his. This suggess ha successfully accouning for he pos-98 decline in business cycle volailiy requires a change in he volailiy of a produciviy-like shock operaing wihin a sandard growh model. * We hank Sephen Parene, Ed Presco, John Taylor, and wo anonymous referees for helpful commens and suggesions.

2 . Inroducion Kydland and Presco (98) and Presco (986) esablished ha produciviy shocks could accoun for mos pos-world War II business cycle volailiy. Business cycle volailiy was roughly consan up hrough he period sudied by Kydland and Presco, bu has changed subsanially since hen. Kim and Nelson (999), McConnell and Perez-Quiros (000) and Sock and Wason (00) all idenify a large and saisically significan permanen decline in U.S. GDP volailiy beginning in he firs quarer of 98. This paper examines his decreased volailiy hrough he lens of neoclassical business cycle heory. We focus our analysis on changes in he variance of he Hodrick-Presco cyclical componen of real GDP, is componens, labor inpu, and oal facor produciviy (TFP). All of hese variances are abou 0-50 percen smaller in he pos-98 period compared o he period. Wihin he neoclassical framework, changes in cyclical volailiy are he resul of eiher changes in he volailiy of he exogenous shocks ha are fed ino he model, and/or changes in he srucure of he model ha maps he exogenous shocks ino he endogenous variables. We focus our analysis on changes in he exogenous shock volailiy. We firs evaluae he impac of changes in he volailiy of TFP shocks. We find ha he volailiy of his shock declines abou 50 percen afer 98. We find ha his volailiy change reduces he volailiy of oupu and is componens, and labor inpu also by 50 percen in he Hansen (985) model. This finding suggess ha lower produciviy shock volailiy can be a significan facor underlying lower cyclical volailiy. Some economiss will quesion his finding, however, because hey argue ha TFP shocks are no produciviy shocks per se, bu raher he endogenous consequence of oher shocks operaing hrough unmeasured capial and

3 labor uilizaion. This mis-measuremen view of TFP would sugges ha he change in TFP volailiy is due o he change in he volailiy of some oher shock, combined wih unmeasured changes in facor uilizaion. We herefore pursue his possibiliy using he model of Burnside e al. (996) ha feaures boh variable capial and labor uilizaion. We follow Chari, Kehoe, and McGraan (00, 006) and Cole and Ohanian (00) who focus on hree oher shocks for undersanding flucuaions in he growh model: a shock o he household s saic firs order condiion, a shock o he household s dynamic firs order condiion, and an addiive shock o he resource consrain, such as governmen spending shocks. We es wheher changes in he volailiy of hese oher shocks can accoun for boh he change in TFP volailiy and he change in he volailiy of he oupu, is componens and labor. Our main finding is ha none of hese shocks do his. The volailiy of he saic preference shocks is roughly unchanged beween he wo periods. The volailiy of he shock o he resource consrain changes significanly, bu his change is quaniaively unimporan for he volailiy of TFP and he oher variables. The volailiy of he shock o he Euler equaion changes significanly, bu generaes business cycle saisics ha are grossly counerfacual. We conclude ha he mos promising candidae for undersanding lower pos-98 business cycle volailiy is a shock ha operaes like TFP in a sandard sochasic growh model. The change in he correlaion srucure beween he wo periods provides some addiional evidence on his issue. The paper is organized as follows. Secion discusses he lieraure. Secion presens changes in volailiy of macroeconomic variables and he impac of lower volailiy of echnology shocks in a sandard real business cycle model. Secion describes how we idenify muliple shocks in his model and Secion 5 sudies he change in TFP volailiy in he model

4 wih variable capial and labor uilizaion. Secion 6 considers he impac of a change in he volailiy of echnology shocks on business cycle correlaions and Secion 7 concludes.. Connecion wih he Lieraure The exising lieraure offers several explanaions for he fall in business cycle volailiy, hough currenly here is no generally acceped explanaion of lower cyclical volailiy. Kahn, McConnell and Perez-Quiros (00) argue ha he informaion revoluion has changed he way shocks are propagaed. In paricular, hey argue ha he volailiy reducion resuling largely from improvemens in invenory managemen echniques, using a model ha differs subsanially from he sandard neoclassical model. Their approach hus focuses on changes in a specific model s propagaion mechanism wih a focus on invenory managemen. More recenly, Campbell and Hercowiz (005) argue ha financial reforms of he early 980 s have changed he propagaion mechanism by relaxing collaeral consrains on household borrowing. Oher auhors, for example Clarida, Galí and Gerler (000), mainain ha improved moneary policy since he early 980 s has sabilized he U.S. economy. Blanchard and Simon (00) argue ha changes in invenory managemen echniques, moneary policy, and also he volailiy of governmen spending all have been significan conribuing facors o lower volailiy. In conras, Sock and Wason (00) conduc a comprehensive saisical examinaion and find ha he volailiy reducion is primarily due o good luck. Tha is, here has been a fall in he variance of he srucural shocks ha impac he economy, raher han improved moneary policy or improved invenory conrol echniques. Ahmed, Levin, and Wilson (00) also conclude ha lower volailiy is largely a maer of good luck in he pos-98 period. Finally, Gordon (005) also finds ha he reduced variance of shocks was he dominan source of

5 reduced business cycle volailiy. We accep he good luck conclusions of hese papers, ha he shocks hiing he U.S. economy since 98 have been smaller. Our paper complemens hese laer hree sudies by providing an assessmen of he conribuion of lower shock volailiy o he business cycle using a DSGE framework. Our DSGE analysis allows us o make progress on undersanding which shocks are imporan for he change in cyclical volailiy, and on undersanding he srucural mechanisms hrough which hese shocks operae. We herefore develop a simple RBC model and we evaluae how changes in he volailiy of differen shocks affec business cycle volailiy. Comin and Phillipon (005) argue ha microeconomic volailiy (among lised corporaions) has increased recenly, and Phillipon (00) argues ha increases in compeiion can joinly accoun for higher microeconomic volailiy and lower macroeconomic volailiy. The closes sudy o ours is by Leduc and Sill (005) who sudy he conribuion of TFP shocks and moneary shocks o lower volailiy. They find ha changes in moneary policy are relaively unimporan.. Volailiy in a Basic Real Business Cycle Model In Table, we presen a measure of business cycle volailiy for a variey of U.S. aggregae ime series. Here, he business cycle is defined by deviaions from a Hodrick-Presco We do no address he possible increase in firm-level volailiy, as his is beyond he scope of his paper. I is worh noing, however, ha wihin our framework, improved access o asse markes would end o increase microeconomic volailiy. There is evidence ha asse markes have become more efficien (see Krueger and Perri (006)). Oher analyses of changes in volailiy wihin a fully ariculaed model include Posch and Waelde (005), and Jusiano and Primiceri (005). Boh analyses differ considerably from his analysis. Posch and Waelde find ha changes in ax raes can be sabiliy-enhancing in a model wih endogenous cycles, while Jusiano and Primiceri find ha changes in he variance of invesmen-specific echnological change is key in a Bayesian analysis of a model wih ime-varying mark-ups, sicky prices and wages, habi formaion, invesmen-specific echnological change, and invesmen adjusmen coss. We use quarerly daa from 955: 00:. The beginning dae is he firs for which hours based on he household survey are available. Daa has been logged before applying he Hodrick-Presco filer. All Naional Income and Produc Accoun daa is in 996 dollars. Hours (HS) is oal hours worked based on daa from he

6 rend. We repor he percen sandard deviaion of quarerly daa from 955: o 00: in he firs column of he able. In he second and hird columns, he same saisic is repored for he pre-98 and pos-98 subperiods. In he las column, he raio of he volailiy measure for he lae subperiod o he early subperiod is given. This able shows ha volailiies of all series in he laer subperiod are significanly smaller han in he earlier subperiod. Oupu and TFP are abou half as volaile, while he labor inpu is 70 percen as volaile. This fall in volailiy of he labor inpu is essenially idenical in boh hours worked measured using he household survey as well as hours from he esablishmen survey. A componen of GNP on which we focus paricular aenion is consumpion of services and nondurables, since his corresponds concepually o consumpion in a sochasic growh model. Similarly, consumer durables plus fixed invesmen corresponds o invesmen in our heoreical model. We find ha invesmen is 58 percen as volaile, and consumpion 65 percen, in he laer subperiod as compared wih he early subperiod. Governmen spending is 55 percen as volaile. Overall, hese saisics show ha volailiy declined 0-50 percen in hese variables afer 98. Curren Populaion Survey and available on he Bureau of Labor Saisics websie. The BLS daa has been seasonally adjused prior o compuing our volailiy saisics. Hours (ES) is based on daa from esablishmen payrolls and is also available on he BLS websie. Measured oal facor produciviy (TFP) is compued as log( TFP) = log( GNP).6log( Hours). We have ignored he sock of capial because i does no vary much over he business cycle following Presco (986). 5

7 Table Volailiy of U.S. Daa Percen Sandard Deviaion Series 955:-00: 955:-98: 98:-00: Lae/Early GNP Hours (HS) Employmen Hours per worker Hours (ES) Labor Produciviy (HS) Labor Produciviy (ES) TFP (HS) ( = GNP Hours ) TFP (ES) Consumpion Expendiures Nondurables Services Durables Nondurables + Services Invesmen Expendiures Fixed Invesmen Fixed Invesmen + Consumer Durables Governmen Expendiures

8 We firs assess he impac of lower TFP volailiy on oupu and is componens, and labor. We do his using he following real business cycle model. The equilibrium of his model economy is characerized by he soluion o a social planner s problem (where he iniial capial sock, k 0, is given): max E β log c, + θh k + h = 0 log( h ) h subjec o c k e k h k z α α + + = + ( δ ) z = ρ z + ε, ε ~ N(0, σ ) +, + In his economy, labor is indivisible (individuals work h or no a all), and he labor marke allows rade in employmen loeries conracs ha specify a probabiliy of working h hours (see Hansen (985) for deails). In his problem, z is he log of TFP, c is consumpion, and h is aggregae hours worked. The log of TFP follows a firs order auoregressive process. The model is calibraed in way ha is sandard in he real business cycle lieraure (see Cooley and Presco (995)). In paricular, he value of he discoun facor, β, is deermined so ha he average quarerly k/y raio for he model is he same as in U.S. daa. The depreciaion rae is calibraed o he average invesmen o oupu raio and he reduced form preference θ log( h) parameer,, is chosen so ha individuals spend on average percen of heir h subsiuable ime working. The parameer α is se equal o average labor s share in he U.S. naional income accouns, and ρ is se close o one in order o mach he auocorrelaion of measured TFP (addiional deails provided in he nex secion). These crieria lead us o assign 7

9 θ log( h ) he following parameer values: β =.988, δ = 0.08, h =.57, α = 0.6, and ρ =.95. We now use he model o quanify he conribuion of changes in TFP volailiy o he volailiy of he oher variables. We firs calculae he volailiy of he endogenous variables when σ is se o is value over he enire 955: 00: period. We hen calculae he volailiies for he endogenous variables for he subperiod when σ is calibraed so ha TFP volailiy in he model is equal o acual TFP volailiy in ha subperiod, and we analogously do his for he subperiod. The TFP volailiies we calibrae o are lised in Table. The resuls of his experimen are shown in Table. Table Volailiy in a Sandard Real Business Cycle Economy Percen Sandard Deviaions Series Enire Period Early Subperiod Lae Subperiod Lae/Early Oupu Hours Capial Invesmen Consumpion Labor Produciviy TFP Calibraed σ The fall in he volailiy of GNP and oher aggregae variables is no a puzzle from perspecive of pure real business cycle heory. In addiion, because here is only one shock in We use he esablishmen survey measure of hours worked for calibraing TFP in our model. 8

10 his model and he propagaion mechanism is close o linear, he volailiy of all variables falls by he same amoun. This would no be he case if we inroduced addiional shocks o he model. Several researchers, however, [Basu (996) and Burnside, Eichenbaum and Rebelo (995)] have argued ha aggregae procyclical TFP flucuaions are due primarily o unmeasured changes in facor uilizaion. According o hese sudies, once unmeasured uilizaion is aken ino accoun, here is lile in he way of exogenous echnology shocks o be accouned for by exogenous shocks. Hence, in Secion 5, we consider he impac of changes in he volailiy of shocks oher han echnology shocks in a model wih endogenous movemens in TFP due o labor hording and capial uilizaion. Before doing ha, we describe how we idenify hese oher shock in he following secion.. Idenifying Muliple Shocks Our approach for idenifying shocks is similar o ha of Chari, Kehoe, and McGraan (00) and Cole and Ohanian (00) in ha flucuaions in he endogenous variables from heir seady sae values is due o one or more deviaions in he equaions ha characerize he soluion o he planner's problem. In boh our case, and in he case of hese oher papers, he goal is o deermine which deviaions are cenral for undersanding he flucuaions in he endogenous variables. I is worh noing ha here is a sligh difference in erminology, however, bu no in subsance. Whereas Chari e.al. refer o hese deviaions as wedges which can be mapped ino a variey of shocks, we refer o hese deviaions as shocks: a echnology shock, a governmen expendiure shock, a shock o preference for leisure, and a shock o he discoun facor. Noe ha as in he case of Chari e.al., he deviaions (shocks) ha we specify can be mapped ino differen classes of deeper shocks. For example, he shock o he preference for leisure can be modeled more deeply as a shock o home producion, or a shock o changes in union power. The key poin 9

11 is ha our invesigaion, as in he case of Chari e.al., idenifies plausible broad classes of shocks ha may or may no be imporan for he quesion of ineres. The following planner s problem incorporaes all of shocks considered in his paper: subjec o max E β log, c + θh k + h = 0 log( h ) h c k g e k h k z α α = + ( δ ) g = ge z θ = θe z z β = β β e, β = + 0 log zi, + = ρilog zi, + εi, +, εi~ N(0, σi) for i = k 0 given. There are four ypes of sochasic shocks in his economy, which we denoe by z o z. The firs is he same echnology shock as in he previous secion. The second shock is an addiive shock o he resource consrain. Following Chrisiano and Eichenbaum (99), we measure his as a governmen spending shock. The hird shock is a preference shock ha disors he labor-leisure decision. The imporance of his class of shocks for business cycles has been argued by Hall (997) and a number of ohers. The las is a shock o he subjecive discoun facor and inroduces a sochasic wedge in he ineremporal Euler equaion. Each of hese shocks is idenified from he daa as follows: z = log y α log h z = log g 0

12 z = log y log c log h z = Ac + Bz + B z + B z The firs equaion is he log of TFP, measured using esablishmen hours. As in Table, since we are ineresed in cyclical flucuaions, we ignore capial because i does no vary significanly over he business cycle. The second shock is compued from he log of governmen expendiures. 5 To compue he hird shock, we ake he firs order condiion for hours worked, z log( h) α y θ e =, and solve for z (ignoring consans). Finally, he fourh shock is h ch z ( α)( y ) + k+ + δ compued from he ineremporal firs order condiion, = β e E. c c+ Solving a log-linearized version of his model enables us o express he condiional expecaion on he righ hand side as a linear funcion of z i (i =,..,) and log k. Nex, his linearized firs order condiion can be solved for z, where AB,, B, and B are he resuling coefficiens. Again, as in he case of z, our empirical measure of z ignores capial (he coefficien on log k is se equal o zero). The auoregressive parameers of he firs hree shocks ( ρ, ρ, and ρ ) are esimaed by removing a linear ime rend from our measures of z, z, z and compuing an auoregression using OLS. From his, we obained ρ =.95, ρ =.98, and ρ =.99. In order o compue he empirical counerpar o he fourh shock, we needed o guess a value for ρ so ha we could solve for he condiional expecaion. Using his value, we consruced a ime series for z and esimaed ρ from his ime series. We solve for he fixed poin where he guessed value for ρ 5 As poined ou by a referee, we are ignoring ne expors in his idenificaion of he addiive shock.

13 used o compue he z ime series and he auoregressive coefficien esimaed from his ime series are idenical. This procedure led us o se ρ = Volailiy in Model wih Endogenous Facor Uilizaion In his secion, we use he model of Burnside and Eichenbaum (996) o sudy he impac of changes in he size of alernaive shocks on business cycle volailiy in a model wih unmeasured facor uilizaion. This model incorporaes wo sources of facor uilizaion in a real business cycle model similar o he one sudied in he previous secion. These include labor hording as modeled in Burnside, Eichenbaum and Rebelo (99) and capial uilizaion as modeled in Greenwood, Hercowiz and Huffman (988) and Taubman and Wilkinson (970). The equilibrium of his model is characerized by he soluion o a social planner s problem like he one in he previous secion excep wih wo addiional choice variables: labor effor, e, and he rae of capial uilizaion, u. Labor hording is inroduced by assuming ha employmen ( n ) is chosen before period shocks are observed. The remaining choices ( k,, + u and e ) are made afer he shocks are observed. The planner s problem is he following subjec o his iming resricion: max E β log c + θn log( ω he) k+, n, e, u = 0 subjec o α ( ) ( ) c k g e uk enh u k z = + ( δ ( )) δ( u ) = γu φ, φ > α g = ge z θ = θe z

14 z β = β β e, β = + 0 log zi, + = ρilog zi, + εi, +, εi~ N(0, σi) for i = k 0 given. Capial uilizaion, u, affecs boh producion and he rae of depreciaion. The higher capial is uilized in producion, he larger is he rae of depreciaion. As discussed in Burnside and Eichenbaum (996), his feaure and labor hoarding have imporan implicaion for he way shocks are propagaed. The model is calibraed in a similar manner as in he previous secion. In paricular, he value of β is chosen o arge he k/y raio, φ chosen o arge he i/y raio, and g chosen o arge he g/y raio. The parameer θ is chosen so ha he average ime devoed o marke aciviies, n ( ω + h), is equal o 0. and γ is chosen so ha he average uilizaion rae is The lengh of a work shif, h, is se so ha effor (e) is in seady sae. Labor s share is se equal o 0.6 and he fracion of ime spen commuing (ω ) is se equal o 6/98. The auoregressive coefficiens for he shock processes are no re-esimaed for his model and are he same as repored in he pervious secion: ρ =.95 ; ρ =.98 ; ρ =.99, and ρ =.99. Our goal in he following hree experimens is o deermine if changes in he volailiy of (i) he governmen spending shock, (ii), he saic preference shock, and (iii), he ineremporal preference shock, can plausibly accoun for boh he change in he volailiy of TFP and he change in he volailiy of oupu and is componens, and labor. We begin wih he governmen spending shock. The volailiy of governmen spending in he daa falls by almos half afer 6 The cyclical properies of he model do no depend on he value of he parameer γ.

15 98. To measure he impac of reducing he volailiy of governmen spending, we simulae he model as follows, seing σ = σ = 0 ( θ = θ and β = β ):. Se σ and σ o mach he volailiy of TFP and governmen spending for he enire period shown in Table.. Keep σ a he same value, bu choose σ o mach he volailiy of g during he early subperiod.. Keep σ a he same value, bu choose σ o mach he volailiy of g during he lae subperiod. The percen sandard deviaions associaed wih each of hese parameerizaions are given in he firs hree columns of Table. Table Volailiy in a Model wih Variable Facor Uilizaion The Role of Governmen Spending Shocks ( σ = σ = 0 ) Series Percen Sandard Deviaions Early Lae Enire Period Subperiod Subperiod Lae/Early Oupu Hours Capial Invesmen Consumpion Labor Produciviy TFP Governmen Expendiure Calibraed σ Calibraed σ The key finding from Table is ha, alhough governmen spending is 55 percen as volaile in he second subperiod as he firs, his has relaively lile effec on he volailiy of any

16 of he endogenous variables. Thus he impac of an addiive resource consrain shock is quaniaively much oo small o accoun for changes in he volailiy of he oher variables in he model. Perhaps a reducion in he variance of he preference shock will have a more imporan quaniaive effec on business cycle volailiy. In order o conduc an empirically relevan experimen, we need o calibrae σ. To do so, we use he firs order condiion for choosing e (labor effor), which can be wrien as follows: y cnh θ e = α( ω he) () The volailiy of he lef hand side can be compued from daa, bu he righ hand side is a funcion of unobservable effor. This is no a problem, because we can choose σ so ha simulaions of he model imply volailiy of he lef hand side of his equaion ha is he same as ha measured in U.S. daa. More precisely, Table gives resuls from he following experimen (assumeσ = σ = 0):. Se σ and σ o mach he volailiy of TFP and he hea arge for he enire period shown in Table.. Keep σ a he same value, bu choose σ o mach he volailiy of he arge during he early subperiod.. Keep σ a he same value, bu choose σ o mach he volailiy of he arge during he lae subperiod. 5

17 Table Volailiy in a Model wih Variable Facor Uilizaion The Role of Tase Shocks ( σ = σ = 0) Series Percen Sandard Deviaions Early Lae Enire Period Subperiod Subperiod Lae/Early Oupu Hours Capial Invesmen Consumpion Labor Produciviy TFP Thea arge Calibraed σ Calibraed σ Table shows very lile change in business cycle volailiy from he calibraed change in he variance of he ase shock. The volailiy in he model variables falls beween and 7 percen, compared o he 0-50 percen declines in he daa. This finding ha he change in he shock volailiy canno accoun for he volailiy changes in he oher variables is similar o he firs case of he resource consrain shock in able, bu for a very differen reason. Here, he volailiy of he lef hand side of () falls by only 7 percen from he early o he lae subperiod. This implies relaively lile change in he value of σ. If he variance of he lef hand side of () had fallen more subsanially, we would find a bigger change in business cycle volailiy beween he early and lae subperiods. Thus, he ase shock is no a useful candidae facor for 6

18 undersanding changing cyclical volailiy in he indivisible labor model because is volailiy is similar beween he wo periods. 7 Our nex experimen considers he poenial of he ineremporal shock o accoun for he change in volailiy. This shock eners he ineremporal firs order condiion, which can be wrien as follows: ( α)( y / k ) + γ u =. c+ φ z β e E c A naural way o calibrae he sandard deviaion of his shock is o arge he volailiy of consumpion. If we employ his crierion, he value of σ we obain using daa for he enire period, urns ou o be While his is a considerably smaller value han our esimaes of he oher shock volailiies, i urns ou o imply considerable volailiy in he endogenous variables. In paricular, he percen volailiy of TFP implied by our model urns ou o be This is acually larger han TFP volailiy compued from U.S. daa for his same period (0.8). Because of he considerable volailiy generaed by his shock, we repor resuls for an experimen where he oher shock volailiies are se equal o zero. Tha is, Table 6 gives resuls from he following experimen (assumeσ = σ = σ = 0 ):. Se σ o mach he volailiy of consumpion for he enire period shown in Table.. Choose σ o mach he volailiy of consumpion during he early subperiod.. Choose σ o mach he volailiy of consumpion during he lae subperiod. 7 We sress ha his finding is for he indivisible labor model, and may be sensiive o alernaive formulaions. This is because he household saic firs order condiion which we used o idenify he variance of he shock depends on he preference specificaion ha is used. 7

19 Table 6 Volailiy in a Model wih Variable Facor Uilizaion The Role of Ineremporal Shocks ( σ = σ = σ = 0) Series Percen Sandard Deviaions Early Lae Enire Period Subperiod Subperiod Lae/Early Oupu Hours Capial Invesmen Consumpion Labor Produciviy TFP Calibraed σ We find ha considerable volailiy reducion can be accouned for by he ineremporal shock. In paricular, unlike he governmen spending or preference shock, his shock appears o be able o accoun for he reducion in volailiy of TFP and oher endogenous variables once endogenous facor uilizaion is aken ino accoun. While his ineremporal shock may be capable of poenially accouning for much of he change in he volailiy of TFP and he oher variables, is conribuion in his one-shock model is flawed, because wih only his one shock he model is seriously deficien as a posiive business cycle model. Specifically, i generaes several business cycle saisics ha are grossly counerfacual. For example, as shown in Table 6, he flucuaions in hours worked are significanly larger han he oupu flucuaions, and invesmen is much oo volaile. An even more sriking shorcoming of his model is he fac ha consumpion in his model economy is couner-cyclical, while i is highly pro-cyclical in he U.S. economy. These findings indicae ha his one-shock model is no a reasonable specificaion for evaluaing he poenial conribuion of 8

20 he change in he volailiy of he ineremporal shock. Doing his requires adding produciviy shocks, as i is well known ha models wih produciviy shocks end o produce reasonable volailiy and co-movemen paerns compared o acual daa. We now consider he conribuion of he change in he volailiy of he ineremporal shock in an economy where echnology shocks are imporan. Specifically, o generae a model wih poenially reasonable business cycle properies, we maximize he possible conribuion of echnology shocks as follows. The value of σ is chosen so ha i compleely accouns for TFP volailiy in he second (low volailiy) subperiod. The same value of σ is used in he firs (high volailiy) subperiod, and we choose σ in he firs subperiod o accoun for he change in he volailiy of σ beween he wo subperiods. Specifically, he experimen is conduced as follows:. Se σ = 0 and choose σ o mach he volailiy of TFP in laer subperiod (resuls are shown in he second column of Table 7).. For he early subperiod, mainain he same value of σ as in sep. Choose σ o mach he much higher volailiy of TFP during he early subperiod. Hence, in his experimen, we are allowing for a significan role for echnology shocks in boh subperiods, bu we are allowing a change in he volailiy of he ineremporal shock ( σ ) o accoun for one hundred percen of he change in he TFP volailiy beween he wo subperiods. 9

21 Series Table 7 Volailiy in a Model wih Variable Facor Uilizaion The Role of Ineremporal Shocks ( σ = σ = 0 ) Percen Sandard Deviaions Early Lae Subperiod Subperiod Lae/Early Oupu Hours Capial Invesmen Consumpion Labor Produciviy TFP Calibraed σ Calibraed σ The resuls of his experimen ell basically he same sory as Table 6. A change in he variance of he ineremporal shock can accoun for he reduced variance of TFP, bu he implied business cycle properies when he ineremporal shock is acive (he early subperiod in Table 7) are subsanially a variance wih he business cycle properies of he U.S. economy. Specifically, hours worked flucuaes more han oupu, and consumpion is highly counercyclical (he correlaion of oupu and consumpion is -0.7). This experimen indicaes ha a change in he volailiy of an ineremporal shock ha shifs he Euler equaion is a very unlikely candidae for undersanding changing cyclical volailiy because he business cycle properies in his model are significanly a variance wih he daa. This suggess ha invesigaing his shock seems o require a model which deviaes considerably from he growh model. 0

22 6. Changes in Correlaions In he experimens carried ou in his paper, we have focused on changes in volailiy of macroeconomic variables before and afer 98. We now examine changes in he correlaions beween hese variables over hese periods. The ables below show he correlaions beween he Hodrick-Presco filered ime series from Table for he early and lae subperiods. These daa sugges ha he size of echnology shocks fell in he laer subperiod. Table 8 Business Cycle Correlaions for U.S. Daa Fixed Consumpion Invesmen+ Early Subperiod (955:-98:) GNP of Services + Consumer Nondurables Durables Hours (ES) Prod (ES) TFP (ES) GNP Services + Nondurables Fixed Invesmen + Durables Hours (ES) Prod (ES) TFP (ES).00 Fixed Consumpion Invesmen+ Lae Subperiod (98:-00:) GNP of Services + Consumer Nondurables Durables Hours (ES) Prod (ES) TFP (ES) GNP Services + Nondurables Fixed Invesmen + Durables Hours (ES) Prod (ES) TFP (ES).00 The able shows ha labor produciviy becomes counercyclical, and ha he correlaion beween TFP and he oher variables declines considerably, in he second sub-period. To assess he exen ha declining TFP volailiy can shed ligh on hese correlaion changes, we performed he following experimen. We absrac from he governmen spending shock (since is volailiy change doesn have much of an impac) and he ineremporal shock (since i generaes counerfacual business cycle properies in our model).

23 . Se σ = σ = 0 and σ = The laer is he value of σ required o mach he volailiy of he hea arge for he enire sample (see Table ). Se σ o mach he volailiy of TFP for he early subperiod.. Hold σ, σ,and σ consan and se σ o mach he volailiy of TFP for he laer subperiod. The following able shows he correlaion marix corresponding o each of he wo cases described above: Table 9 Correlaions in a Model wih Variable Facor Uilizaion The Role of Technology Shocks ( σ = σ = 0 ) Early Subperiod Oupu Consumpion Invesmen Hours Labor Produciviy TFP Oupu Consumpion Invesmen Hours Labor Produciviy TFP.00 Lae Subperiod Oupu Consumpion Invesmen Hours Labor Produciviy TFP Oupu Consumpion Invesmen Hours Labor Produciviy TFP.00 We see ha our model wih he change in TFP volailiy, and he volailiy of he ase shock held consan, indeed generaes counercyclical labor produciviy in he laer subperiod. I does no, however, predic he large changes in he correlaions wih TFP seen in Table 8.

24 7. Conclusion We find ha he approximaely 50 percen decline in business cycle volailiy ha has occurred since 98 can be accouned for by he observed decline in he volailiy of produciviy shocks. This finding is robus o allowing for endogenous TFP volailiy operaing in a model wih variable capial and labor uilizaion. In paricular, we found ha neiher changes in he volailiy of an addiive resource consrain shock, changes in he volailiy of a saic ase shock, nor changes in he volailiy of a dynamic ase shock can plausibly accoun for he change in TFP volailiy, he change in he volailiy of oupu and is componens, and labor. We see wo avenues for fuure research in his area. One is o develop heories for why he TFP shock volailiy had declined so much. Anoher is o es wheher oher plausible modificaions o he model generae very differen resuls.

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