Real Business Cycles Theory

Transcription

1 Real Business Cycles Theory Research on economic flucuaions has progressed rapidly since Rober Lucas revived he profession s ineres in business cycle heory. Business cycle heory is he heory of he naure and causes of economic flucuaions The new Classical paradigm ried o accoun for he exisence of cycles in perfecly compeiive economies wih raional expecaions. I emphasized he role of imperfec informaion, and saw nominal shocks, in he form of moneary mispercepions, as he cause of cycles. The new Classical heory posed a challenge o Keynesian economics and simulaed he developmen of boh he New Keynesian economics and RBC heory. Keynesian economics has generally acceped he idea of raional expecaions, bu emphasizes he imporance of imperfec compeiion, cosly price adjusmen and exernaliies and considers nominal shocks as predominan impulse mechanism. RBC heory views cycles as arising in fricionless, perfecly compeiive economies wih generally complee markes subjec o real shocks. RBC models demonsrae ha, even in such environmens, cycles can arise hrough he reacions of opimizing agens o real disurbances, such as random changes in echnology or produciviy. Coordinaion failures, price sickiness, waves of opimism or pessimism, moneary policy, or governmen policy generally are no needed o accoun for business cycles. Furher more, such models are capable of mimicking he mos imporan empirical regulariies displayed by business cycles. In his par of course, I will describe he background of RBC heory, he key feaures of RBC models and oulines a simple, prooype RBC model. The sronges criicisms o RBC models are firs, here is no independen corroboraing evidence for he large echnology shocks ha are assumed o drive business cycles and second, RBC models have difficuly in accouning for he dynamic properies of oupu because he propagaion mechanisms hey employ are generally weak. Thus, while RBC models can generae cycles, hese are, as a general rule, no like he cycles observed. I) Some Facs abou Economic Flucuaions Business cycles vary considerably in erms of ampliude and duraion, and no wo cycles appear o be exacly alike. Neverheless, hese cycles also conain qualiaive feaures or regulariies ha persisenly manifes hemselves. The one very regular feaure of hese flucuaions is he way variables move ogeher. Cooley and Presco repor some feaures of he business cycle based on U.S ime series: - The magniude of flucuaions in oupu and aggregae hours of work are nearly equal. Thomas F. Cooley and Edward C. Presco 995. Economic Growh and Business Cycles. Froniers of Business Cycle Research. Princeon Universiy Press.

2 - Employmen flucuaes almos as much as oupu, while overage weekly hours flucuae considerably less. - Consumpion of nondurables and services is smooh, flucuaing much less han oupu. - Invesmen, or producion of durables generally, is far more volaile ha oupu. - The capial sock much less variable han oupu and is largely uncorrelaed wih oupu. - Produciviy is slighly procyclical bu varies considerably less han oupu. - Wages vary less han produciviy. - The correlaion beween average hourly compensaion and oupu is essenially zero. - Governmen expendiures are essenially uncorrelaed wih oupu. - Impors are more srongly procyclical han expors. Oher feaures of he business cycle are: - Oupu movemens in differen secors of he economy exhibi a high degree of coherence; - Velociy of money is couner cyclical in mos counries, and here is considerable variaion in he correlaion beween moneary aggregaes and oupu. Long erm ineres are less volaile han shor-erm ineres raes, and he laer are nearly always posiively correlaed wih oupu, bu he correlaion of longer-erm raes wih oupu is ofen negaive or close o zero. - Prices appear o be couner cyclical. II) The Basic Real Business Cycles Model The neoclassical model of capial accumulaion, augmened by shocks o produciviy, is he basic framework for RBC analysis. RBC heoriss conend ha he same heory ha explains long-run growh should also explain business cycles. Thus, RBC heory can be seen as a developmen of he neoclassical growh heory of he 950s. ) The basic Feaures of Real Business Cycle Models are: They adop a represenaive agen framework, on a represenaive firm and household. Firms and households opimize explici objecive funcions, subjec o he resource and echnology consrains ha hey face. 2

3 The cycle is driven by exogenous shocks o echnology ha shif producion funcion up or down. The impac of hese shocks on oupu is amplified by ineremporal subsiuion of leisure; a rise in produciviy raises he cos of leisure, causing employmen o increase. All agens have raional expecaions and here is coninuous marke clearing. There are complee markes and no informaional asymmeries. 2) The Model The economy consiss of a large number of idenical, price aking firms and a large number of idenical, price aking, households, which are infiniely lived. ) The represenaive household maximises he expeced value of U = = 0 β U(c, l U(.) is he insananeous uiliy funcion of he represenaive household, and 0<β< is he discoun facor. The insananeous uiliy has wo argumens. Consumpion per member of he household, c, and leisure per member which is he difference beween he ime endowmen per member (normalized o for simpliciy) and he amoun each member works, l. Noice ha for simpliciy i has been assumed ha he household s uiliy funcion is separable beween c and - l. This implies ha he marginal uiliy of consumpion does no depend on leisure and vice versa. For simpliciy, U (.) is log-linear in he wo argumens: U = ln c + θln( l ) θ > 0, 2) The inpus o producion are capial, (K), labour (L), and echnology (A). The producion funcion is Cobb-Douglas, and oupu in period is: α α Y = K (A L ) 0 < α < The resource consrain: oupu is divided among consumpion (C), and invesmen (I). The low of moion of capial is: + C + I = Y k = ( δ)k + i 3) Firs generaion of RBC heory regards sochasic flucuaions in facor produciviy as he predominan source of flucuaions in economic aciviy. Exogenous produciviy shocks are he only impulse mechanism ha hese models originally incorporaed. I is his emphasis on produciviy changes as he predominan source of cyclical aciviy ha disinguishes hese models from heir predecessors and rivals. In paricular, he ) 3

4 absence of a role for demand-side innovaions coupled wih he assumpion of compeiive markes marks a clear break from he radiional Keynesian heory where changes in invesmen spending are he main deerminans of oupu in he shor run. The model assumes ha he echnology evolves as a random walk wih drif : ln A ε a ln A = (0, σ 2 ) + g + ε a Where g is he rae of echnology progress, and ε a represens a echnology shock and i is whie nose disurbances. The imporance of exogenous produciviy changes in economic heory can be raced o he seminal work of Rober Solow (956,957) on he neoclassical growh model ha appeared in he 950s. However, i s Solow s work on esimaing he sources of economic growh ha has proved mos influenial in he RBC lieraure. If markes are compeiive and here exis consan reurns o scale, hen he growh of oupu from he aggregae producion funcion is: g = αg + ( α)g y l k + Where g y, g l and g k are he growh raes of oupu, labour, and capial respecively, α is he relaive share of oupu of labour, and z measures he growh in oupu ha canno be accouned for by growh in labour and capial. Thus z represens mulifacor produciviy growh and has been dubbed he Solow residual. The SR has accouned for approximaely half he growh in oupu in he USA. This residual is no consan, bu flucuaes significanly over ime. I is well described as a random walk wih drif plus some serially uncorrelaed measuremen error. 3) Compuing equilibrium: z a) Firms maximize heir profis The firm rens capial and hire labour in each period. Max K w r K,L α α [ (A L ) rk wl ] K = α A L α A L = ( α) K A α, 4

5 Firm maximises is profi, labour and capial are paid heir marginal producs. Given consan reurns o scale, in equilibrium profis will be equal o zero. b) The household maximizes is uiliy subjec o he resources consrain Household will choose consumpion, invesmen, and hours of work a each dae o maximize he expeced discouned value of uiliy, given heir expecaions over fuure prices subjec o sequences of budge consrains and he law of moion for he household s capial sock: max k c s.,l +,i = E c = 0 ( δ)k β + i U (c, l ) w l + r k + i The Lagrange is : l α α { ln c + θln( l ) + λ (k (A l ) c k + ( δ)k )} = E β + c : l : k λ + : c θ l = o Y Y - λ + E λ + k Y - c - i = 0 λ + αλ l = o ( δ) = 0 c) The consisency of individual and aggregae decisions, ha is he condiions: c = C, i = I, k = K, l = L d) The aggregae resource consrain: C + I = Y 5

6 4) Resoluion of he model The seady sae raes of growh of consumpion, oupu, invesmen and capial per capia are all equal o he growh rae of labour augmening echnical progress. Since ime devoed o work is bounded by he endowmen, i canno grow in he seady sae. In order o solve his problem, four seps are necessary: - Transform he problem so ha he soluion is saionary over ime. The following change of variables achieves his purpose: C Y Ĉ =, Ŷ =, Î =, and = A A A I Kˆ K A - - Compue he seady sae values: chocks are equal o zero and we eliminae he ine index. K = K + = = K C = C + = = C - A linear approximaion of he F.O.C of he choice problem abou he seady sae. This yields a se of linear difference equaions. f (x') = f (x) + f '(x)(x' x) Resoluion of he dynamic linear problem. 5) Calibraion The basic idea in he RBC lieraure is o use long-run evidence and microeconomic esimaes o calibrae he parameers of he model. Typical esimaes for he share of labour in oupu are α = 2/3, for he quarerly rae of physical depreciaion are δ = and for he discoun facor across one quarer, β = The growh rae g =.004. Based of he average division of ime beween work and leisure, θ = 2. Given a value for α and ime series daa on Y, K, and L i is possible o back-ou he Solow residual: lny = ( α)lnk + α lnl + α lna α lna = Y lnk lnl α α Using his residual ime series, one can esimae he echnology shock process described above. Given his calibraion and a compuer program which solves he model, we can compue he impulse response funcion of various aggregaes, and he correlaions and relaive comovemens of he aggregae variables implies by he model and compare hem wih hose in he real economy. 6

7 III) Implicaions RBC models replicae he relaive volailiies of consumpion, invesmen and oupu observed in he daa. One labor marke regulariy ha poses problems for RBC models is he so-called produciviy puzzle. If produciviy shocks drive he cycle, employmen and produciviy would be highly correlaed, and his is exacly wha RBC models predic, usually he correlaion beween hours and produciviy in heses models is above 0.9. In realiy, produciviy and employmen are negaively correlaed for mos economies. For he U.S he correlaion is roughly zero. They predic very srong procyclicaliy of wage and no enough procyclicaliy of employmen. In realiy, employmen (or oal hour worked) is almos as variable as oupu, and srongly procyclical, while real wages are a bes mildly procyclical. If mos shocks hiing he economy shif he producion funcion and aler he marginal produc of labour hen, ceeris paribus, he shifs in labour demand should race ou an upward-sloping labour supply funcion in real wage-employmen space. Because micro sudies sugges ha he wage elasiciy of labour supply is low, much of he adjusmen o a produciviy shock should be borne by wages, raher han employmen. To undersand his recalls ha he improvemen in echnology has wo effecs in he labour marke: - i increases he marginal produc of labour, hereby shifing he labour demand curve ou - i raises curren consumpion (if he wealh effec dominaes), causing he labour supply curve o shif in. - The ne resul depends on he relaive shifs in hese wo curves w S 0 D 0 L 7

8 If he demand curve shif dominae, hen equilibrium employmen and hence oupu end o rise. If he supply curve shif dominaes hen employmen will end o fall, offseing he increase in oupu caused by A. Obviously, o fi he facs on procyclicaliy of employmen one would like he demand curve shif o dominae. However, noe ha in eiher case wage are going o be srongly procyclical, since boh shifs cause wage o rise. In a world where cycles are caused by produciviy shocks, he correlaion beween produciviy and oupu should be high. In realiy he correlaion is moderae for mos economies, for he U.S. esimaes range from depending on he sample period. In many RBC models, he correlaion is 0.9 Labour s share of income moves counracyclically over he cycle. However, if echnology is Cobb-Douglas, labor s share is consan over he cycle. Finally, here is no unemploymen in RBC models. Even where RBC models do succeed in accommodaing unemploymen, i is always volunary. IV) Exensions In RBC models, echnology shocks are assumed o a) affec all secors of he economy equally, and b) o affec he produciviy of all facors of producion equally, regardless of he vinage of capial or he age and skill levels of labor. If produciviy innovaions primarily affec only a paricular secor, one mus consider a mulisecoral economy ha produces many heerogeneous goods. RBC assumpion is produciviy shocks are exogenous and uninfluenced by oher economic facors. Charles L.Evans 2 (992), demonsraes ha money, ineres raes, and governmen spending Granger cause Solow residual, and beween one quarer and one half of he variance of he produciviy impulse can be aribued o aggregae demand shocks. Hence he measured aggregae produciviy impulses do no behave as a sricly exogenous sochasic process. These findings indicae he role of produciviy shocks in generaing economic flucuaions has been oversaed in he RBC lieraure. In he sandard compeiive model, labor effor is implicily assumed o be consan level, and herefore, independen of he wage level. The wage is se in he marke. A crucial feaure of preferences is he non-ime separable uiliy funcion ha admis greaer ineremporal subsiuion of leisure. Gary Hansen (985): worker is consrained o work for a fixed amoun of ime or no a all, so ha all changes in hours are brough abou a by changing employmen. Because he lengh of he 2 Charles L.Evans 2 Produciviy shocks and real business cycles Journal of moneary Economics 29 (992): 8

9 working is fixed, he marginal uiliy of leisure is consan. In his case he marginal benefi of working canno be brough ino equaliy each period by adjusing labor supply smoohly beween periods. Under hese circumsances, a represenaive agen will wan o work as much as possible when he wage is high, so ha he economy as a hole behaves like a hypoheical agen wih infinie elasiciy of subsiuion of leisure, even hough individual agens have diminishing marginal uiliy of leisure. In presence of his non-convexiy in labor supply, he variabiliy of hours rises considerably: indeed, in his model hours urn ou o be far more variable relaive o produciviy han in he U.S. economy. Jang-Ok cho and homas Cooley (988) address his problem by allowing agens o decide boh on hours and wheher o paricipae in he labor force a all. This exension improves he performance of he model in some areas. In paricular, he raio of he sandard deviaion of aggregae hours o he sandard deviaion of produciviy produced by he model is virually idenical o ha found in American daa, around.4, whereas in Hansen s model he figure is around 2.7, because hours are so volaile in his framework. Cogley and Nason(995) 3 found ha many RBC models have weak endogenous propagaion mechanisms and do no generae observed oupu dynamic via heir inernal srucure. The oupu dynamics are: - GNP growh is posiively auocorrelaed over shor horizons and has weak and insignifican negaive auocorrelaions over longer horizons. - In response o a permanen shock, oupu rises gradually and reaches a plaeau afer abou six years. - In response o a ransiory shock, oupu rises for a few quarers and hen reurns o is sochasic rend. This means ha a subsanial porion of he variaion in oupu growh is due o ransiory flucuaions. This has lead o he developmen of models where nominal rigidiy is assumed and echnology shocks are supplemened by addiional disurbances like moneary and governmen policy acions. These papers consider () moneary shocks ha affec oupu hrough price mispercepion in a Lucas (972) informaional island framework; (2) a cash-inadvance consrain on he purchase of consumpion goods, so inflaion acs as a ax on consumpion RBC models ha incorporae some nominal rigidiy are imporan for wo reasons. Firs, heir properies sugges ha nominal rigidiy may well be an imporan missing elemen in sandard RBC models. Second, such models inroduce imporan Keynesian feaures ino RBC model analysis. They consequenly bridge he dichoomy beween wo very differen schools of hough in macroeconomics. 3 Timohy Cogley and James M.Nason (995), oupu Dynamics in real Business Cycle Models, The American Economic Review, Vol.85 N0.3 9