Real Business Cycle Theory

1 Real Business Cycle TheoryGuido AscariUniversity of Pavia ()Real Business Cycle Theory1 / 37 OutlineIntroduction: Lucas methodological proposalThe application to the analysis of Business Cycle uctuations: TheReal Business Cycle Theory1 Data: measuring the Business Cycle (Table 1)2 The model economy: a rigorous description3 The solution of DSGE models: the Blanchard-Khan method4 Table 2: matching moments5 Evaluation of the RBC approachUniversity of Pavia ()Real Business Cycle Theory2 / 37 The Lucas Methodological ProposalLucas ( 76, 77, 80, 87). Two important references:1 Lucas, , 1976, Econometric Policy Evaluation: A Critique,Carnegie-Rochester Conference Series on Public Policy, Vol.

2 1, , , 1987, Models of Business Cycles, 1985 Yrj JahnssonLectures, Basil Blackwell, Lucas critique: Macroeconomists should build so-calledstructural models, models where the agents behavior is invariantwith respect to policyMicroeconomic foundationsGeneral EquilibriumNo distinction between micro and macro: Economic theoryUniversity of Pavia ()Real Business Cycle Theory3 / dynamic modelsfrom the outset:Dynamic optimizationNeed for a Theory of expectations formation =>The RationalExpectations Revolution of the 1970s is the logical outcome of Lucas research Methodological ProposalNew analytical and computational instruments (Lucas/Stokey andPrescott, Kydland and Prescott)A new equilibrium concept.

3 Recursive equilibrium and "from a point to apath"Importance of expectations in the design of policy experimentsWelfare analysisUniversity of Pavia ()Real Business Cycle Theory4 / 37 CONCLUSIONSM odern macroeconomics should employ dynamic general equilibriummodels (DSGE), that is, a macroeconomic model should be theresults of the solution of dynamic optimization problems underuncertainty by optimizing agents populating the model a "laboratory economy": much more di cult task than oldKeynesian theorizingKydland & Prescott (1982) accepted the challenge posed by Lucas:they built the rst Real Business Cycle (RBC) of Pavia ()Real Business Cycle Theory5 / 37 The basic RBC model in a nutshellOutline of the RBC methodology:a discrete-time stochastic model of the economy populated by maximizinghouseholds and rmsMAIN SOURCE OF FLUCTUATIONS:The erratic nature of technological progressUniversity of Pavia ()Real Business Cycle Theory6 / 37 THE BASIC MODEL.

4 AS SIMPLE AS POSSIBLEThe Ramsey model of growth =>integrating growth and cycleAll prices are exibleAll markets are walrasianRational expectationsNo moneyEndogenous labourTechnology shocks (and possibly other shocks) =>stochastic steadystateUniversity of Pavia ()Real Business Cycle Theory7 / 37 MAIN RESULT AND FIRST INTUITIONT here is only one nal good in the economy which is producedaccording to a constant return to scale (CRS) production functionYt=AtF(Kt 1,Nt)where ln(At/A)=atis an exogenous process of technologicalprogress (or total factor productivity TFP), which evolves accordingto:at= aat 1+ at, at N 0, 2a positive shock to the TFP shifts rms labor demand and the AScurveMovements in employment and economic activity are seen as thee cient responses of a perfectly competitive economy to aproductivity )Stochastic path of Walrasian equilibriaUniversity of Pavia ()Real Business Cycle Theory8 / 37 POSITIVE TECHNOLOGY SHOCKU niversity of Pavia ()Real Business Cycle Theory9 / 37 THE PLANNER PROBLEMRBC models do not consider any distortion or market imperfection,therefore the welfare theorems apply to these models.

5 1) the competitive equilibrium is pareto-optimal2) a pareto-optimal allocation can be decentralized as a competitiveequilibriumThe social planner equilibrium and the competitive equilibrium areidentical and admit a unique solutionUniversity of Pavia ()Real Business Cycle Theory10 / 37 Data: Measuring the Business CycleTRADITIONAL Business Cycle Theory :output trend Ytevolves smoothly over time, Yt=a+bt. Cycles are viewed asdeviation from trends, YtRBC Theory :cycles can be explained also assuming that Ytevolves according to a random walk, , Yt=b+ Yt 1+ thiscase much of the movements inYtare due to movements in Ytrather then to trend deviationsYt Yt=>Integrating growth andbusiness Cycle theoryUniversity of Pavia ()Real Business Cycle Theory11 / 37 Data.

6 Measuring the Business CycleH-P FilterMinfygtg t=0 t=1n(yt ygt)2+ ygt+1 ygt ygt ygt 1 2oH-P lter suppresses the really low frequency uctuations 8 yearsquarterly data =1600linear trend > original series =0 This makes the trend component a weighted average of past, present andfuture values =>and the cyclical component is de ned asyct=yt ygt=yt J j= Jajyt jUniversity of Pavia ()Real Business Cycle Theory12 / 37 University of Pavia ()Real Business Cycle Theory13 / 37 University of Pavia ()Real Business Cycle Theory14 / 37 Business cycles are all alikeUniversity of Pavia ()Real Business Cycle Theory15 / 37 University of Pavia ()Real Business Cycle Theory16 / 37 University of Pavia ()Real Business Cycle Theory17 / 37 University of Pavia ()Real Business Cycle Theory18 / 37 Some stylized facts about growthUniversity of Pavia ()Real Business Cycle Theory19 / 37 University of Pavia ()

7 Real Business Cycle Theory20 / 37 The Basic Structure of the RBC model1 Endowment, initial condition and ownership2 Preferences3 Technology4 Law of motions of endogenous/exogenous state variables5 Individual resource constraints6 Aggregate resource constraints7 Markets equilibrium condition8De nition of equilibriumUniversity of Pavia ()Real Business Cycle Theory21 / 37 HOW TO SOLVE THE MODEL - SEVEN STEPS1 Find all the rst order necessary conditions2 Calculate the economy steady state3 Log-linearize the model around the steady state4 Solve for the recursive law of motion5 Calculate the IRFs in response to di erent shocks6 Calculate the moments: correlations, and standard deviations for thedi erent variables both for the arti cial economy and for the how well the model economy matches the actual economy scharacteristicsUniversity of Pavia ()Real Business Cycle Theory22 / 37Go to of Pavia ()Real Business Cycle Theory23 / 37 THE BASIC MODEL.

8 AS SIMPLE AS POSSIBLEP rescott did not think such a simple model could be of any use =>surprising result!Main policy conclusion: uctuations of all variable (output,consumption, employment, ) are the optimal responsesto technology shocks exogenous changes in the are not always desirable. But once they occur, this is the bestpossible outcome: Business Cycle uctuations are the optimal responseto technology shocks =>no need for government interventions: itcan be only deleteriousUniversity of Pavia ()Real Business Cycle Theory24 / 37 Furious response from the "people from the Oceans" =>Rogo :"brilliant theories rst look ridiculous then they become obvious".

9 From mid 80s to mid 90s: ten years lost in useless ideological debatesbetween the Oceans and the LakesFrom mid 90s: convergence on methodology: "the RBC approach asthe new orthodoxy in macroeconomics"University of Pavia ()Real Business Cycle Theory25 / 37 CriticismEmpirical philosophy: calibration vs. estimationToo many parameters?Too much exibility in choosing parameters? "The book of Ed"No possible statistical testing against alternativesis matching moments a desirable feature? econometrician aresuspicious of correlationsUniversity of Pavia ()Real Business Cycle Theory26 / 37 CriticismSolow residual and technology shocksNeed for highly persistent technological shocks: why?

10 And above all:what are they?Solow residual is highly correlated with outputUniversity of Pavia ()Real Business Cycle Theory27 / 37 RBC View:RBC Theory argue that the strong correlation between output growthand Solow residuals is the evidence that productivity shocks are animportant source of economic :Are economic uctuations really caused by productivity shocks?Expansions arise because of increases in productivity!..What does that mean about recessions? (Summers 1986)It means that recessions are periods of technical regress! Burnside etal. estimates the probability of technological regress implied by SR tobe 37%!Less implausible if supply shock considered more broadly (OPEC,strikes etc.)