Why Have Business Cycle Fluctuations Become Less Volatile?

Transcription

1 Preliminary April 22, 2005 Why Have Business Cycle Flucuaions Become Less Volaile? Andres Arias Miniserio de Hacienda y Crédio Publico, Republic of Colombia Gary D. Hansen UCLA Lee E. Ohanian UCLA and Federal Reserve Bank of Minneapolis Absrac This paper shows ha a sandard RBC model driven by produciviy shocks can successfully accoun for he 50 percen decline in cyclical volailiy of oupu and is componens, and labor supply ha has occurred since 983. 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 find ha he wo mos commonly used business cycle shocks - governmen spending shocks and preference shocks ( labor wedges ) canno accoun for he change in he volailiy of he Solow Residual. We do find some poenial ha i can be accouned for by changes in he volailiy of shocks o he ineremporal firs order condiion.

2 . Inroducion Business cycle volailiy has decreased subsanially in he las 20 years. Kim and Nelson (999), McConnell and Perez-Quiros (2000) and Sock and Wason (2002) all idenify a large and saisically significan permanen decline in U.S. GDP volailiy beginning in he firs quarer of 984. 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, in he variance of he HP derended labor inpu, and in he variance of HP derended oal facor produciviy (TFP). All of hese variances are abou percen smaller in he pos-983 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 organize he analysis using he accouning framework of Chari, Kehoe, and McGraan (2004), This framework uses he firs-order and feasibiliy condiions from a sandard business cycle model o idenify four empirical shocks: a produciviy shock, a shock o he household s saic firs order condiion, a shock o he household s dynamic firs order condiion, and a shock o he resource consrain. We calculae he volailiy of hese four shocks during he high GDP volailiy period (953:-983:4) and during he low GDP volailiy period (984: 2004:x). We hen conduc wo ses of simulaions. The firs se simulaes he model wih he shock volailiies se o heir values from he firs period. The second se is wih he shock volailiies se o heir values from he second period. To assess he relaive conribuions of each of he 4 shocks, each se of

3 simulaions includes simulaions wih each of he four shocks individually and wih muliple shocks. We hen compare he differences in he volailiies of he endogenous variables in he model over he wo periods. We find ha a reducion in he volailiy of he produciviy shocks is by far he dominan source of he reducion in he volailiy of he endogenous variables. The variabiliy of he TFP shock falls abou 50 percen beween he wo periods, which individually reduces he volailiy of all he endogenous variables by abou 50 percen. The conribuion of he hree oher shocks is very small, eiher because he volailiies do no change much beween he wo periods, and/or because he quaniaive impac of he shock is no very large wihin he model. Given he size and imporance of he TFP volailiy reducion, we nex invesigae poenial explanaions for he change in his facor. Perhaps he mos likely candidae explanaion is ha lower TFP variabiliy is due o changes in he volailiies of oher shocks operaing hrough mis-measured capial and labor services. This view follows from he perspecive ha cyclical TFP flucuaions are arifacs of capial and labor mis-measuremen responding o oher shocks (see Basu (996) and Burnside, Eichenbaum and Rebelo (995) ). We herefore assess wheher lower oupu volailiy, labor inpu volailiy and TFP volailiy can be joinly accouned for in our model, augmened wih variable capial uilizaion and labor hoarding, operaing hrough he hree remaining shocks. Our augmened model is quie similar o he Burnside and Eichenbaum (996) model. We find ha he wo mos commonly used business cycle shocks governmen spending shocks (Chrisiano and Eichenbaum (992), McGraan (994), Braun (994)) and preference shocks (Hall, Parkin, Mulligan, Chari, Kehoe, and McGraan, Bencivengna, Ingram, Kocherlakoa, and Savin,) canno do his. We do find some evidence ha changes in he volailiy of shocks o he consumer s ineremporal firs order 2

4 condiion, which previously have been a shock ha has no been considered o be imporan in business cycles (see Chari, Kehoe, and McGraan), may be able o joinly accoun for he volailiy change in boh he Solow Residaul and in oupu, is componens, and labor supply. 2. Connecion wih he Lieraure The exising lieraure offers several explanaions for he fall in business cycle volailiy. Kahn, McConnell and Perez-Quiros (2002) argue ha he informaion revoluion has changed he way shocks are propagaed. In paricular, hey make a case for he volailiy reducion resuling largely from improvemens in invenory managemen echniques, using a model ha differs from he sandard neoclassical model. Their approach hus focuses on changes in a specific model s impac propogaion mechanism. Oher auhors, for example Clarida, Galí and Gerler (2000), mainain ha improved moneary policy since he early 980 s has sabilized he U.S. economy. Sock and Wason (2002) 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. Our paper complemens Sock and Wason s work by providing a fully ariculaed assessmen of he conribuion of lower shock volailiy o he business cycle. 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, hold he propagaion mechanism in our model economy consan across he wo subperiods and hen consider how changes in he volailiy of differen shocks would affec business cycle volailiy. While our approach appears o pu us exclusively in he good luck camp, policy explanaions may be consisen wih our 3

5 approach. In paricular, he shocks we consider can have a variey of srucural inerpreaions, as argued in Chari, Kehoe and McGraan (2004). Tha is, we consider changes in shock variances wihou rying o inerpre wha migh have led o he change. Improved moneary policy is one of he possibiliies. Our findings poin us o one possible conclusion and o a direcion for fuure research. A conclusion consisen wih our findings is ha he decreased volailiy of U.S. business cycles is due o a fall in he variance of aggregae echnology shocks or shocks ha are propagaed in a manner observaionally equivalen o echnology shocks. Anoher possibiliy, of course, is ha he mechanism hrough which non-echnology shocks affec TFP is no sufficienly capured by he Burnside and Eichenbaum (996) model ha we use in his paper. 2. 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 rend. We repor he percen sandard deviaion of quarerly daa from 955:3 o 2003:2 in he firs column of he able. In he second and hird columns, he same saisic is repored for he pre-984 and pos-984 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 volailiy of all series in he laer subperiod are significanly less volaile han in he earlier subperiod. Oupu and TFP are abou half as volaile, while he labor We use quarerly daa from 955:3 2003:2. 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 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 ). 4

6 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 percen in hese variables afer

7 Table Volailiy of U.S. Daa Percen Sandard Deviaion Series 955:3-2003:2 955:3-983:4 984:-2003:2 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 now use he accouning procedure discussed by Chari, Kehoe, and McGraan (2004) and Cole and Ohanian (200) o assess how much of he volailiy reducion in oupu and is componens, and labor can be accouned for by changes in he volailiies of four shocks: () a produciviy shock, (2), a shock o he household s saic firs order condiion governing heir ime allocaion decision, (3) a shock o he housheold s ineremporal firs order condiion governing he allocaion of income beween consumpion and savings, and (4) a shock o he resource consrain. 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 ) 2 +, + 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 7

9 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 3 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. These crieria lead us o assign he following parameer values: β =.988, δ = θ log( h ) 0.08, h = 2.547, α = 0.6, and ρ =.95. Table x shows he volailiies of hese shocks Suppose here was a one-ime decrease in he variance of echnology shocks in 984. We explore he implicaions of his change by simulaing he model using 3 differen values of σ : one ha maches measured volailiy of TFP for enire period, one ha maches TFP volailiy for he subperiod, and one ha maches TFP volailiy for he subperiod. The resuls of his experimen are shown in Table 2. Table 2 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

10 Alhough his quaniaive exercise displays a larger decrease in volailiy han found in acual daa, he 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 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 TFP volailiy o be accouned for by exogenous shocks. Hence, in he nex secion, 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. In paricular, we consider he imporance of an addiive shock o he resource consrain (governmen spending shock) and a shock ha affecs he labor-leisure radeoff (preference or labor income ax shock). Chari, Kehoe, and McGraan (2004) show ha a large number of srucural shocks (moneary shocks, ec.) are equivalen o hese. 2. 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 o 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 (993) and capial uilizaion as modeled in Greenwood, Hercowiz and Huffman (988) and Taubman and Wilkinson (970). 9

11 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 2 θ = θe z 3 z4 β = β β e, β = log zi, + = ρilog zi, + εi, +, εi~ N(0, σi) for i = 4 ( z o 4 k 0 given. This model economy is subjeced o four ypes of uncorrelaed sochasic shocks z ). The firs is he same echnology shock as in he previous secion. The second can be inerpreed as a governmen spending shock, assuming ha governmen expendiures are financed wih lump sum axes [see Chrisiano and Eichenbaum (992)]. The hird is a preference shock ha disors he labor-leisure decision. The imporance of his class of shocks for business 0

12 cycles has been argued by Hall (997). The las is a shock o he subjecive discoun facor and inroduces a sochasic wedge in he ineremporal Euler equaion. 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), boh his feaure and labor hording 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 0.3 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 ρ =.95 ; ρ 2 =.98 ; ρ 3 =.99 ρ 4 =.99., and The volailiy of governmen spending in he daa falls by almos half in he laer subperiod. To measure he impac of reducing he volailiy of governmen spending, we simulae he model as follows, seing σ 3 = σ 4 = 0 :. Se σ and σ 2 o mach he volailiy of TFP and governmen spending for he enire period shown in Table. 2. Keep σ a he same value, bu choose σ 2 o mach he volailiy of g during he early subperiod. 2 The cyclical properies of he model do no depend on he value of he parameer γ.

13 3. Keep σ a he same value, bu choose σ 2 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 3. Table 3 Volailiy in a Model wih Variable Facor Uilizaion The Role of Governmen Spending Shocks ( σ 3 = σ 4 = 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 o be drawn from Table 3 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 of he endogenous variables. 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 3. To do so, we use he firs order condiion for choosing e, which can be wrien as follows: y cnh θ e = α( ω he) 2

14 The volailiy of he lef hand side can be compued from daa, bu he righ hand side is a funcion of unobservable effor. We choose σ 3 so ha simulaions of he model imply volailiy of he lef hand side of his equaion (our hea arge ) ha is he same as ha measured in U.S. daa. More precisely, Table 4 gives resuls from he following experimen (assumeσ 2 = σ 4 = 0):. Se σ and σ 3 o mach he volailiy of TFP and he hea arge for he enire period shown in Table. 2. Keep σ a he same value, bu choose σ 3 o mach he volailiy of he arge during he early subperiod. 3. Keep σ a he same value, bu choose σ 3 o mach he volailiy of he arge during he lae subperiod. 3

15 Table 4 Volailiy in a Model wih Variable Facor Uilizaion The Role of Tase Shocks ( σ 2 = σ 4 = 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 4 shows very lile change in business cycle volailiy from he calibraed change in he variance of he ase shock. The reason his change is small is quie differen han for he case in Table 3. Here, he volailiy of our hea arge falls by only 7 percen from he early o he lae subperiod. This implies relaively lile change in he value of σ 3. If he variance of he hea arge had fallen more subsanially, we would find a bigger change in business cycle volailiy beween he early and lae subperiods. In his case, he volailiy of all endogenous variables is reduced subsanially. However, he volailiy of consumpion (nondurables and services) falls by more ha he volailiy of invesmen. The opposie is rue in he daa. Similarly, he volailiy of hours worked falls by more han he volailiy of oupu. Again, he opposie is seen in U.S. daa. Finally, a large fall in he volailiy of θ canno accoun for he subsanial fall in TFP volailiy repored Table. 4

16 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 4 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 (0.83). 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 2 = σ 3 = 0 ):. Se σ 4 o mach he volailiy of consumpion for he enire period shown in Table. 2. Choose σ 4 o mach he volailiy of consumpion during he early subperiod. 3. Choose σ 4 o mach he volailiy of consumpion during he lae subperiod. 5

17 Table 6 Volailiy in a Model wih Variable Facor Uilizaion The Role of Ineremporal Shocks ( σ = σ2 = σ3 = 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. 6

18 3. Conclusion (Preliminary) A decline in he variance of echnology shocks can accoun for he change in U.S. business cycle volailiy since 984. If no echnology shocks, need o consider shocks ha operaes hrough he efficiency wedge as defined in Chari, Kehoe and McGraan (2004). Examples are given in Chari, Kehoe and McGraan (2004), Comin and Gerler (2003), and Philippon (2002). Neiher governmen spending shocks nor preference shocks are successful in a model rigged o generae large endogenous changes in he Solow Residual. Shocks o he consumer s ineremporal firs order condiion, however, may be successful. 7

19 References Ahmed, S., A. Levin and B. A. Wilson Recen U.S. macroeconomic sabiliy: good policies, good pracices, or good luck? Inernaional Financial Discussion Paper No Board of Governors of he Federal Reserve Sysem. Basu, S Procyclical Produciviy: Increasing Reurns or Cyclical Uilizaion? The Quarerly Journal of Economics Vol., No. 3, Blanchard, O. and J. Simon The long and large decline in U.S. oupu volailiy. Brookings Papers on Economic Aciviy,, Burnside C. and M. Eichenbaum Facor-hoarding and he propagaion of business-cycle shocks. American Economic Review 86, Burnside, Craig, Marin Eichenbaum and Sergio Rebelo Labor Hoarding and he Business Cycle. Journal of Poliical Economy, Vol. 0, No Burnside, Craig, Marin Eichenbaum, and Sergio Rebelo, Capial Uilizaion and Reurns o Scale, in NBER Macroeconomics Annual 995, pages Chari, V.V., P.J. Kehoe and E.R. McGraan Business Cycle Accouning. Federal Reserve Bank of Minneapolis Saff Repor 328. Chrisiano, L.J. and M. Eichenbaum. 992, Curren Real Business Cycle Theories and Aggregae Labor Marke Flucuaions, American Economic Review. Clarida, R., J. Galí and M. Gerler Moneary Policy Rules and Macroeconomic Sabiliy: Evidence and Some Theory. Quarerly Journal of Economics, February, Cooley, T. F. and E. C. Presco Economic growh and business cycles. In T. F. Cooley, ed., Froniers of Business Cycle Research. Princeon Universiy Press, -38. Greenwood, Jeremy, Zvi Hercowiz and Gregory W. Huffman Invesmen, Capaciy Uilizaion, and he Real Business Cycle American Economic Review, Vol. 78, No. 3, Hansen, G. D Indivisible labor and he business cycle. Journal of Moneary Economics 6, Hall, R.E Macroeconomic Flucuaions and he Allocaion of Time. Journal of Labor Economics 5 No. P. 2, S223-S250. Kahn, J. A., M. M. McConnell and G. Perez-Quiros On he causes of he increased sabiliy of he U.S. economy. Federal Reserve Bank of New York Economic Policy Review, May, Kim, C.-J. and C. Nelson Has he US Economy Become More Sable? A Bayesian Approach Based on a Markov Swiching Model of he Business Cycle. Review of Economics and Saisics 8,

20 McConnell, M. M. and G. Perez-Quiros Oupu flucuaions in he Unied Saes: wha has changed since he early 980 s? American Economic Review 90, No. 5, Philippon, T Corporae Governance and Aggregae Volailiy. MIT Working Paper. Rogerson, R Indivisible labor, loeries and equilibrium. Journal of Moneary Economics 2, 3-6. Sock, J.H. and M.W. Wason Has he Business Cycle Changed and Why? NBER Macroeconomics Annual Taubman, Paul and Maurice Wilkinson User Cos, Capial Uilizaion and Invesmen Theory. Inernaional Economic Review, Vol., No