George Stadler (1994)

7/28/2019 George Stadler (1994)

1/34

Journal of Economics L it eratuteVol. XXXI I(December 1994), pp . 17501783

Stadl er : Real Business Cycles

Real Business Cycles

ByGEORGE W. STADLERUni ver sit y of Newcastl e upon Tyne

I have received numer ous valuable comments fr om many ind i -

viduals, compr ising a list t hat i s too long to acknow ledge here,

but special thanks are due to Jeremy Greenwood and David

L aidl er . I also wi sh t o acknow ledge the excell ent comments I r e-

ceived f r om the reviewer s, wh ich also substant iall y impr oved t hi sarticle.

I . Introduction

THE 1970S saw a distinctive shift inmacroeconomic research. The tradi-

tional Keynesian research program wasconcerned with the determination ofoutput and employment at a point intime and with how to alter and stabilizethe time paths of major macroeconomicvariables. I n the 1970s this research pro-gram increasingly gave way to businesscycle theory, that is, the theory of thenature and causes of economic fluctua-tions. This paper is a summary and as-sessment of Real Business Cycle (RBC)theory.1

The development of the New Classicalmacroeconomics brought about the re-vival of business cycle theory. The NewClassical paradigm tried to account forthe existence of cycles in perfectly com-petitive economies with rational expecta-

tions. I t emphasized the role of imper-fect information, and saw nominalshocks, in the form of monetary misper-ceptions, as the cause of cycles. The NewClassical theory posed a challenge toKeynesian economics and stimulated thedevelopment of both the New Keynesianeconomics and RBC theory. The NewKeynesian economics has generally ac-cepted the idea of rational expectations,but emphasizes the importance of imper-fect competition, costly price adjustmentand externalities and considers nominalshocks as the predominant impulsemechanism.

RBC theory has developed alongside

1750

1

There have been a number of surveys of RealBusiness Cycle Theory, including Jean-PierreDanthine and John Donaldson (1993), Chan Huhand Bharat Trehan (1991), Gregory Mankiw(1989), and Bennett McCallum (1989). These sur-veys do not always consider recent developmentsand extensions, which have gone some way to-wards mitigating some of the early criticisms ofthis theory. However, even where they do considerrecent developments, they tend to focus on par-ticular aspects of RBC research. For example,Danthine and Donaldson focus on developmentsconcerning the labor market, while Huh and Tre-han focus on the role of money in these models.

Anyone interested in further reading on business

cycles is referred to Thomas Cooley (forthcom-ing), which covers a number of areas of RBC re-search, that are dealt with only briefly in this sur-vey, in greater depth, and provides an excellentintroduction to the techniques required for build-

ing RBC models.


2/34

the New Keynesian economics, but,unlike it, RBC theory views cycles asarising in frictionless, perfectly competi-tive economies with generally completemarkets subject to real shocks. RBC

models demonstrate that, even in suchenvironments, cycles can arise throughthe reactions of optimizing agents to realdisturbances, such as random changes intechnology or productivity.2 Further-more, such models are capable of mim-icking the most important empiricalregularities displayed by business cycles.Thus, RBC theory makes the notablecontribution of showing that fluctuationsin economic activity are consonant with

competitive general equilibrium environ-ments in which all agents are rationalmaximizers. Coordination failures, pricestickiness, waves of optimism or pessi-mism, monetary policy, or governmentpolicy generally are not needed to ac-count for business cycles.

The following section of the paper de-scribes the background of RBC theory,the key features of RBC models and out-

lines a simple, prototype RBC model.Section I I I considers some of the manyrecent developments that have built onthis basic RBC model. I t finds that anumber of cyclical phenomena cannot beexplained by a model driven only bytechnology shocks. Increasingly, this haslead to the development of modelswhere technology shocks are supple-mented by additional disturbances thatare analogous to taste shocks. I t also as-

sesses extensions of the basic model thatincorporate money, government policy

actions, and traded goods. Section I V ex-amines the criticisms that have been lev-eled against RBCs. The strongest criti-cisms are first, there is no independentcorroborating evidence for the large

technology shocks that are assumed todrive business cycles and second, RBCmodels have difficulty in accounting forthe dynamic properties of output be-cause the propagation mechanisms theyemploy are generally weak. Thus, whileRBC models can generate cycles, theseare, as a general rule, not like the cyclesobserved. Section V surveys the empiri-cal evidence, and finds little to mitigatethese criticisms. The final section sums

up, and considers the challenges thatRBC theory still faces. The strong aggre-gation assumptions these models makeby relying on representative agents castdoubt on their ability to assess policyquestions, and also on their claim to haveprovided a more rigorous microfounda-tion for macroeconomics than competingparadigms.

I I . The Basic Real Business Cycle ModelA. H istor ical Background and

Development

Business cycles vary considerably interms of amplitude and duration, and notwo cycles appear to be exactly alike.Nevertheless, these cycles also containqualitative features or regularities thatpersistently manifest themselves. Amongthe most prominent are that output

movements in different sectors of theeconomy exhibit a high degree of coher-ence; that investment, or production ofdurables generally, is far more volatilethan output; consumption is less variablethan output; and the capital stock muchless variable than output (Robert Lucas1977). Velocity of money is countercycli-cal in most countries, and there is con-siderable variation in the correlation be-

tween monetary aggregates and output

2An alternative way of classifying these modelsis through the location of the dominant impulsesdriving the cycle: do they arise on the demandside or the supply side of the economy? New Clas-sical and New Keynesian models are driven by de-mand-side shocks, while RBCs are driven by sup-ply-side shocks. Some writers question theusefulness of this distinction, pointing out that anysupply-side innovation causes a change in demand

and vice versa.

Stadler : Real Business Cycles 1751


3/34

(Danthine and Donaldson 1993). Long-term interest rates are less volatile thanshort-term interest rates, and the latterare nearly always positively correlatedwith output, but the correlation of longer-

term rates with output is often negativeor close to zero. Prices appear to becountercyclical, but I argue below thatthis evidence is tenuous. Employment isapproximately as variable as output,while productivity is generally less vari-able than output, although certain coun-tries show deviations from this pattern.RBC models demonstrate that at leastsome of these characteristics can be rep-licated in competitive general equilib-

rium models where all agents maximizeand have rational expectations. Further-more, this research program originatedin the U.S.A. and usually American datahave been used as the benchmark againstwhich these models are judged.

Real Business Cycle theory regardsstochastic fluctuations in factor produc-tivity as the predominant source of fluc-tuations in economic activity. These

theories follow the approach of RagnarFrisch (1933) and Eugen Slutzky (1937),which clearly distinguishes between theimpulse mechanism that initially causes avariable to deviate from its steady statevalue, and the propagation mechanism,which causes deviations from the steadystate to persist for some time. Exogenousproductivity shocks are the only impulsemechanism that these models originallyincorporated. Other impulse mecha-

nisms, such as changes in preferences,3

or tax rates, or monetary policy, havebeen generally regarded by RBC theo-rists as having at best minor influence onthe business cycle. I t is this emphasis onproductivity changes as the predominant

source of cyclical activity that distin-guishes these models from their pre-decessors and rivals. I n particular, theabsence of a role for demand-side inno-vations coupled with the assumption ofcompetitive markets marks a clear breakfrom the traditional Keynesian theorywhere changes in investment, consump-tion, or government spending are themain determinants of output in the shortrun.

The importance of exogenous produc-tivity changes in economic theory can betraced to the seminal work of RobertSolow (1956, 1957) on the neoclassicalgrowth model that appeared in the1950s. Solow postulated a one-goodeconomy, in which the capital stock ismerely the accumulation of this compos-ite commodity. The technical possibili-ties facing the economy are captured by

a constant returns to scale aggregate pro-duction function. Technical progressproceeds at an exogenous rate in thistheory, and augments the productivity oflabor. (Technical change is Harrod neu-tral, so ensuring the constancy of relativeshares and sustained steady-stategrowth.)

However, it is Solows work on esti-mating the sources of economic growththat has proved most influential in the

RBC literature. I f markets are competi-tive and there exist constant returns toscale, then the growth of output fromthe aggregate production function is:

gy=g1+(1)gk+z,

where gy, g1 and gkare the growth ratesof output, labor, and capital respectively, is the relative share of output of labor,and zmeasures the growth in output that

cannot be accounted for by growth in la-

3Taste or preference shocks, by themselves,cannot explain cycles. Olivier Jean Blanchard andStanley Fischer (1989b, p. 336) argue that, in anequilibrium framework, taste shocks lead to largefluctuations in consumption relative to output (inreality consumption is much less variable than out-put) and fail to generate the procyclical movementin inventories and investment that is observed inthe data. Furthermore, it is difficult to believe thatmost agents suffer recurrent changes in their pref-

erences that are large enough to drive cycles.

1752 Journal of Economic L it er atur e, Vol. XXXI I(December 1994)


4/34

bor and capital. Thus zrepresents multi-factor productivity growth and has beendubbed the Solow residual. Rearrang-ing the above equation one obtains:

(gyg1)=

1

(gkgy)+(1/)z.

This states that growth of output percapita depends on the growth of thecapital-output ratio and on the Solow re-sidual, z. The Solow residual has ac-counted for approximately half thegrowth in output in the U.S.A. since the1870s (Blanchard and Fisher 1989b, pp.35). This residual is not a constant, but

fluctuates significantly over time. I t iswell described as a random walk withdrift plus some serially uncorrelatedmeasurement error (Edward Prescott1986a).

The neoclassical model of capital accu-mulation, augmented by shocks to pro-ductivity, is the basic framework forRBC analysis. RBC theorists contendthat the same theory that explains long-run growth should also explain business

cycles. Once one incorporates stochas-tic fluctuations in the rate of technicalprogress into the neoclassical growthmodel, it is capable of displaying businesscycle phenomena that match reasonablyclosely those historically observed in theU.S.A. Thus, RBC theory can be seen asa development of the neoclassical growththeory of the 1950s.

B. The Basic Featu r es of Real BusinessCycle Models

The evolution of RBC theory is nota-ble for its emphasis on microfounda-tions: macroeconomic fluctuations arethe outcome of maximizing decisionsmade by many individual agents. To ob-tain aggregates, one adds up the decisionoutcomes of the individual players, andimposes a solution that makes those deci-

sions consistent.

Typically, RBC models contain the fol-lowing features:

i) They adopt a representative agentframework, focusing on a representativefirm and household, and in so doing the

models circumvent aggregation prob-lems.ii) Firms and households optimize ex-

plicit objective functions, subject to theresource and technology constraints thatthey face.

iii) The cycle is driven by exogenousshocks to technology that shift produc-tion functions up or down. The impact ofthese shocks on output is amplified byintertemporal substitution of leisurea

rise in productivity raises the cost of lei-sure, causing employment to increase.

iv) All agents have rational expecta-tions and there is continuous marketclearing. There are complete marketsand no informational asymmetries.

v) Actual cycles are generated by pro-viding a propagation mechanism for theeffects of shocks. This can take severalforms. First, agents generally seek to

smooth consumption over time, so that arise in output will manifest itself partlyas a rise in investment and in the capitalstock. Second, lags in the investmentprocess can result in a shock today af-fecting investment in the future, andthus future output. Third, individualswill tend to substitute leisure intertem-porally in response to transitory changesin wagesthey will work harder whenwages are temporarily higher and com-

pensate by taking more leisure oncewages fall to their previous level. Fourth,firms may use inventories to meet unex-pected changes in demand. I f these aredepleted, then, if firms face rising mar-ginal costs, they would tend to be re-plenished only gradually, causing outputto rise for several periods.

The first propagation mechanism islikely to be weak, while focusing on in-

ventories yields negative serial correla-



5/34

tion for outputoutput movements arestrongly positively serially correlated inreality (Fischer 1988). Most RBC modelsfocus on the second and third propaga-tion mechanisms.

The intertemporal substitution mecha-nism is also likely to be weak. Most inno-vations in technology are regarded ashighly persistent or even permanent,raising the real wage permanently. Thisis unlikely to elicit a large labor supplyresponse, because the substitution effectof the higher wage is likely to be offsetby the income effect. Only in response totemporary shocks is significant intertem-poral substitution likely to occur. How-

ever, to fit the data, RBC models assumethat most of the technology innovation ishighly persistent. This points to the gen-eral difficulty of trying to reconcile ob-served labor market data with a technol-ogy driven equilibrium theory, and isexamined in more detail in Section I I I .Abelow.

C. A Simple Pr ototype RBC Model

Consider an economy populated byidentical, infinitely lived agents that pro-duce a single good as output. There areno frictions or transactions costs, and, forsimplicity we abstract from the existenceof money and government. Each agentspreferences are

Ut=MaxEt

j=0

ju(ct+j, 1t+j)

, 0


6/34

where uiand fidenote the partial deriva-tives ofu() and f()with respect to theirith argument, and t is the Lagrangemultiplier. The first of the above equa-tions equates the marginal utility of con-

sumption to the shadow price of output,the second equates the marginal disutil-ity of labor to labors marginal productthe real wagewhile the third equatesthe marginal product of capital to its op-portunity cost in terms of foregone con-sumption. These equations determinethe time paths of the economys values oflabor, capital, consumption, and .

Given explicit forms for the utility andproduction functions, it is possible to

solve for the time paths of the threechoice variables, ct, kt, and nt. In order toobtain a specific solution, assume, for ex-ample (as in McCallum 1989) that capitaldepreciates fully within a single period( = 1), utility is log-linear in form andthe production function is Cobb-Douglas:

u()= logct+(1)log(1 nt) (9)

ztf()=ztntkt1.(10)

Under these assumptions the utilityfunction ensures that the income andsubstitution effects of a wage changecancel each other, so that labor is con-stant in the solution. Using the methodof undetermined coefficients, one cansolve for the values of consumption andthe capital stock:4

ct= [1(1)]ztntkt1 (11)

kt+1=(1)ztntkt1. (12)

These time paths satisfy the first-orderconditions and consequently representoptimal decision rules for the agents inthis model economy. The intertemporalnature of the decision rules given byequations (11) and (12) is obvious. A

temporary change in ztaround its long-run value produces not only a change incurrent consumption, but also translatesinto a change in the capital stock, whichpropagates the effects of the shock. A

rise in productivity will raise the capitalstock and consumption for several peri-ods, causing the model to exhibit cycles.Consider the case where zt follows a firstorder autoregressive (AR(1)) process. I nthis case, as illustrated by McCallum,consumption and the capital stock willfollow AR(2) processes. This is signifi-cant because the detrended quarterlytime series of various macroeconomicvariables are well described by AR(2)

processes for U.S. data.However, normally the utility and pro-

duction functions used are more compli-cated than (9) and (10), and do not admitof an analytical solution for the decisionrules. The approach followed in such acase is to take linear approximations ofthe equivalent of equations (5) to (8)around a stationary point, which is usu-ally assumed to be the steady state of the

system, that is, those values of the vari-ables when zt = 1 for all t, given someinitial value of the capital stock. This lin-ear system can then be solved for timepaths of the endogenous variables.

The next stage is to choose specificvalues for the parameters (, , etc.),usually by referring to previous econo-metric studies. One then generates a setof artificial data from the model. This in-volves specifying a stochastic process for

the technology parameter (generally arandom walk with drift or a highly per-sistent AR(1) process with positivetrend) and generating many different se-ries of values of the innovation in thetechnology parameter. One then feedsthese series of shocks into the model toyield samples of artificial time series forct,kt, etc. The model is judged by com-paring the average properties of the sam-

ples of artificial, model-generated data

4See McCallum (1989, p. 22) for further details

on this solution method.



7/34

with an actual data set. Normally theproperties of interest are the second mo-ments of output, consumption, invest-ment, etc. as well as the comovements ofthese series with output.

As an example, Table 1 reproducessome results from Finn Kydland andPrescott (1982) (hereafter KP), one of

the seminal papers on RBC theory. KPsmodel departs from the simple prototypemodel in two important ways. First, KPassume it takes four quarters to buildcapital (hence their model has becomeknown as the time-to-build model). Thisimparts greater persistence to the effectsof shocks. Second, KP assume that laborsuffers from a fatigue effect. The harderone has worked in the past, the more onevalues leisure today. This increases the

intertemporal substitution of leisure.5Table 1 shows that the model captures

the fact that consumption is less volatilethan output and investment much morevolatile than output. However, like manyRBC models, it greatly overpredicts thecorrelation between productivity andoutput. The standard deviation of outputgenerated by the model and the data areidentical, because the variance of the

productivity shock has been chosen toensure that the volatility of the model-generated output series matches that ofthe actual data set, which is fairly com-mon practice among RBC theorists.Thus, the model is constructed so that allvolatility in output is accounted for bystochastic productivity movements, andthe model must consequently be judgedby how well it mimics properties of thedata other than the variance of output.

I I I . Extensions of t he Basic RBC Model

This section is divided into five sub-sections. The first focuses on the labormarket and deals with attempts to repli-cate labor market phenomena concern-ing hours worked, productivity, and un-employment. Subsequent subsectionsexamine the introduction of new sectors,

namely money, government, and interna-

TABLE 1KYDLANDAND PRESCOTTS (1982) MODEL,

U.S. Economy1 Models Results

(a)2 (b)3 (a) (b)

Real Output 1.8 1.8 Consumption 1.3 0.74 0.63 0.94Investment 3.1 0.71 6.45 0.80Inventories 1.7 0.51 2.00 0.39Capital Stock 0.7 0.24 0.63 -0.07Hours 2.0 0.85 1.05 0.93Productivity 1.0 0.1 0.90 0.90

1Quarterly, data, 1950:11979:2, logged and detrended using the Hodrick-Prescottfilter.2Column (a) shows standard deviations, in percentages.3Column (b) shows correlations with output.

5The KP model adds two further features tothe prototype model: (i) I nventories are includedas a factor of production. This improves the matchof the models serial correlation properties withthe U.S. data. (ii) Agents observe a noisy signal ofthe productivity shock which contains a permanentand a transitory component. This noise is neces-sary to create a role for inventories to act as abuffer stock when expectations about productivity

are not fulfilled.



8/34

tionally traded goods. A final subsectionconsiders other extensions.

A. The Labor Market

There are a number of labor market

regularities that are inconsistent not onlywith the simple prototype RBC model ofSection II , but also with KPs model.

The first troublesome fact is the em-ployment variability puzzle. Employ-ment (or total hours worked) is almost asvariable as output, and strongly procycli-cal, while real wages are at best mildlyprocyclical. I f most shocks hitting theeconomy shift the production functionand alter the marginal product of laborthen, ceteris paribus, the shifts in labordemand should trace out an upward-sloping labor supply function in realwage-employment space. Because microstudies suggest that the wage elasticity oflabor supply is low, much of the adjust-ment to a productivity shock should beborne by wages, rather than employ-ment. Consequently, RBC models likeKPs predict that employment is less

variable than in reality.Second, in a world where cycles are

caused by productivity shocks, the corre-lation between productivity and outputshould be high. In reality the correlationis moderate for most economiesfor theU.S. estimates range from 0.4 to 0.6, de-pending on the sample period.6 In KPsmodel the correlation is 0.90, and corre-lations of similar magnitude occur in

many RBC models. As McCallum (1989)points out, the production function mostRBC models (including KP) employ isessentially Cobb-Douglas. This implies

that the marginal product of labor willmove quite closely with the averageproduct of labor, or productivity. Thus,although they generally do not generateartificial data series for real wages, these

models imply that real wages (and pro-ductivity) are much more procyclicalthan in reality.7

Third, labors share of income movescountercyclically over the cycle. How-ever, if technology is Cobb-Douglas, la-bors share is constant over the cycle.

A fourth labor market regularity thatposes problems for RBC models is theso-called productivity puzzle. If pro-ductivity shocks drive the cycle, employ-

ment and productivity would be highlycorrelated, and this is exactly what RBCmodels predictusually the correlationbetween hours and productivity in thesemodels is above 0.9. I n reality, produc-tivity and employment are negativelycorrelated for most economies. For theUnited States the correlation is roughlyzero.8

Finally, there is no unemployment in

KPs model. All variation in employmentis due to variation in hours worked bythe representative worker. Even whereRBC models do succeed in accommodat-ing unemployment, it is always voluntary,unless the Walrasian assumptions thatunderpin these models are dropped.

The remainder of this section dealswith attempts to overcome these prob-lems. The assumption that labor supplyis indivisible goes a long way toward re-

solving the employment puzzle. How-

6The correlation between productivity and out-put given by Kydland and Prescott in Table 1 isonly 0.1. I n Prescott (1986a), using data from 1954I to 1982 IV, the correlation is 0.34, and for stud-ies using more recent data it is higher still. Thissuggests that the size of some of these correlationsmay be sensitive to the sample period employed,and is not a robust feature of the postwar U.S.

economy.

7Kydland and Prescott (1993) argue that theimplicit return to labor is much more procyclicalthan the aggregate data suggest. They define realwages as total labor compensation divided by ag-gregate, qualit y adjustedlabor input derived frompanel data, and find this is significantly procycli-cal.

8See Danthine and Donaldson (1993, table 6,p. 13). For the United States (and possibly forother countries as well) the magnitude of this cor-relation also seems to vary with the sample period

and definition of employment.



9/34

ever, the productivity puzzle and the be-havior of wages cannot be reconciledwith a model driven solely by technologyshocks. These facts can only be repli-cated by models that contain shocks to

labor supply as well as labor demand.A.1 The Employment Vari abili ty Puz-zle. Under what conditions will RBCmodels display realistic real wage-em-ployment correlations? Within an equi-librium framework, large movements inemployment accompanied by only smallwage changes suggest that the labor sup-ply function is fairly flat, that is, theremust be a high degree of intertemporalsubstitution over the business cycle.

However, many critics (e.g., LawrenceSummers 1986; Mankiw 1989) regard thereliance on a high degree of intertempo-ral substitution as a weakness of thesemodels, partly because there is no con-vincing empirical evidence for this.

Generally, quarterly data are used toassess the performance of RBCs, whilemicro studies of the elasticity of laborsupply use annual data and are based on

life cycle models. John Kennan (1988)argues that life cycle models, which esti-mate low elasticities, are not designed tomeasure responses to temporary wagechanges within short periods of less thana year. He says that these models as-sume that leisure in February 1989 is aperfect substitute for leisure in October1989. He goes on to argue that

a short-run elasticity of 0.1 is not credible: a

30 percent wage increase is not needed tocall forth a 3 percent increase in hoursworked (this would mean that in order to getsomeone to stay 15 minutes longer on the jobtoday, he would have to be paid 30 percentmore for the whole day).9

However, even if one accepts that theshort-run labor elasticity is much higherthan micro studies suggest, Kennan findsthat, in an equilibrium framework,shocks to labor demand alone cannot

generate the observed time series. Be-cause innovations in real wages and em-ployment both show great persistence,two separate impulse mechanisms are re-quired to explain the data. Thus, Ken-nans analysis also suggests that produc-tivity shocks must be augmented bylabor supply shocks, although the lattercan have much smaller variance than theformer.

In reality about two thirds of the vari-

ation in total hours worked appears to bedue to movements into and out of em-ployment, while the remainder is due toadjustments in hours worked by employ-ees. This contrasts with the basic RBCmodels where all variation in hours isdue to changes in intensity of work effortby the employed.

A different case occurs when a workeris constrained to work for a fixed amount

of time or not at all, so that all changesin hours are brought about by changingemployment (Gary Hansen 1985). Be-cause the length of the working week isfixed, the marginal utility of leisure isconstant. I n this case the marginal bene-fit of working cannot be brought intoequality each period by adjusting laborsupply smoothly between periods. Underthese circumstances, a representativeagent will want to work as much as possi-

ble when the wage is high, so that theeconomy as a whole behaves like a hypo-thetical agent with infinite elasticity ofsubstitution of leisure, even though indi-vidual agents have diminishing marginalutility of leisure. Thus, this type of non-convexity in labor supply can reconcile

9Kennan (1988, pp. 19697). Kennan alsopoints out that hours worked at the individuallevel tend to be very variable, with a standard de-viation of year-to-year changes of around 20 per-cent for the U.S. In a typical downturn, the de-cline in aggregate hours is less than 3 percent. The

magnitude of individual variations is thus much

larger than is necessary to explain cyclical vari-ations, but the sources of these large variations are

not pinned down in the microdata.



10/34

the disparity in micro and macro findingswith respect to the labor supply elastic-ity, as Prescott (1986b) emphasizes in hisrebuttal of Summers (1986) criticisms,and goes a long way towards resolving theemployment puzzle. G. Hansen finds thatin the presence of this nonconvexity thevariability of hours rises considerably: in-deed, in his model hours turn out to be

far more variable relative to productivitythan in the U.S. economy.10 The resultsof Hansens model are shown in Table 2.

A.2 The Productivity Puzzle. If allshocks impinging on the economy areproductivity shocks that shift labor de-mand, hours and productivity will movetogether closely, for changes in employ-ment result only from changes in pro-

ductivity. Thus, an RBC model like KPsor G. Hansens (1985) predicts that pro-ductivity is highly positively correlatedwith both hours and output. In reality,the first correlation is zero or negative,while the second is moderate (0.5 ratherthan 0.9). One way of reducing the cor-relation between employment and pro-ductivity is to introduce factors that will

shift the labor supply function. Shifts inlabor supply may arise through nominalwage stickiness, taste shocks, shocks tohome or nonmarket production, or gov-ernment spending shocks.

A traditional way of causing shifts inlabor supply is through nominal wagestickiness and money supply shocks. I fwages are preset, a nominal innovationshifts the effective supply of labor func-tion. I f both labor demand and labor

supply are shifting, there is no a priorireason to expect a strong positive corre-lation between productivity (or wages)and hours or productivity and output.

Shifts in labor supply can also occur asa result of preference shocks that di-rectly alter the willingness of agents tosupply labor (Valerie Bencivenga 1992).However, there is no independent evi-dence that agents in aggregate suffer

from large, recurrent fluctuations in

TABLE 2HANSENS (1985) INDIVISIBLE LABOR MODEL


(a)2 (b)3 (a) (b)

Real Output 1.76 1.76 Consumption 1.29 0.85 0.51 0.87Investment 8.60 0.92 5.71 0.99Capital Stock 0.63 0.04 0.47 0.05Hours 1.66 0.76 1.35 0.98Productivity 1.18 0.42 0.50 0.87

1Quarterly data, 1955:31984:1, logged, seasonally adjusted, and detrendedusing the Hodrick-Prescott filter.2,3See Table 1 above.

10

G. Hansens model suggests all changes inhours are due to changes in employment, which isclearly counterfactual. Jang-Ok Cho and ThomasCooley (1988) address this problem by allowingagents to decide both on hours and whether toparticipate in the labor force at all. This extensionimproves the performance of the model in someareas. I n particular, the ratio of the standard de-viation of aggregate hours to the standard devia-tion of productivity produced by the model is vir-tually identical to that found in American data,around 1.4, whereas in Hansens model the figureis around 2.7, because hours are so volatile in hisframework. However, there is insufficient variabil-

ity in all of Cho and Cooleys artificial time series.



11/34

preferences, and Bencivenga herself rec-ognizes that such shocks might moreplausibly be interpreted as shocks to thetechnology of home production.

Home production is potentially impor-

tant because the household sector islarge: home produced output relative tomeasured GNP is estimated to range be-tween twenty and fifty percent, and in-cludes such things as preparation ofmeals, cleaning and transportation ser-vices, and some residential maintenanceactivity. Assume that households have ac-cess to a home production function thatuses time and capital to produce a non-tradeable consumption good. A rise in

market productivity leads not only to arise in hours to accumulate more capital,but also to a substitution of market forhome consumption, which also causeshours spent in the market consumptionsector to rise. In a model with home pro-duction agents do not just substitute in-tertemporally, but also substitute laborbetween home and market commoditiesat a given date. Introducing this further

margin of substitution improves themodels performance relative to modelswithout home production. Moreover, ifshocks to home productivity occur (pos-sibly as the productivity of consumerdurables changes) and these shocks arenot perfectly correlated with shocks tomarket productivity, labor supply willfluctuate as relative changes in homeproductivity change the amount peopleare willing to work in the market at a

given wage, and this reduces the correla-tion between market productivity andoutput and productivity and hours to val-ues close to those observed in reality(Jess Benhabib, Richard Rogerson, andRandall Wright 1991).

Two criticisms can be leveled againsthousehold production models. In realityinvestment in market and nonmarketcapital is positively correlated over the

cycle (Greenwood and Zvi Hercowitz

1991), but negatively correlated in homeproduction models unless the correlationbetween home and market disturbancesis very high, in which case the productiv-ity puzzle reappears. Second, these mod-

els suggests that business cycle episodeslargely represent voluntary movementsbetween home and market activities,which must be somewhat unsettling tothe traditional macro theorist.

Two further factors that can help toresolve the productivity puzzle are laborhoarding behavior by firms and shocks togovernment spending. Government con-sumption and private consumption arenot perfect substitutes in utility, so that

a rise in government consumption fi-nanced by taxes results in a negativewealth effect that shifts labor supply.

Labor hoarding enables firms tochange the effective labor supply with-out altering employment, so reducingthe correlation between productivity andmeasured labor input, because reportedhours worked are not an accurate mea-surement of true labor input under these

circumstances. Labor hoarding can beintroduced into an RBC model by assum-ing that the firm must hire workers be-fore the current state of technology anddemand are observed. Such a procedureattempts, rather crudely, to capture thefact that the firm cannot adjust the sizeof its workforce in response to every bitof new information it receives. Conse-quently, if productivity is higher than ex-pected, labor input is initially adjusted

only by varying labor effort, not by vary-ing the number of employeesemploy-ment can only be adjusted with a one-pe-riod lag. Thus labor effort will beprocyclical, rising during booms and fall-ing during recessions, so that the Solowresidual captures changes in labor effortthat are not reflected in the labor inputstatistics. Both government expenditureshocks and labor hoarding cause fluctua-

tions in the effective supply of labor



12/34

which, acting in conjunction, signifi-cantly reduce the positive productivity-hours correlation that is implied bystandard RBC models (Craig Burnside,Martin Eichenbaum, and Sergio Rebelo

1990). A model of this kind is also impor-tant because, as is discussed below, itcan account for the dynamics of output,unlike most RBC models.

This section has examined several fac-tors that can shift the effective supply oflabor: the existence of a nonmarket pro-duction sector also subject to technologyshocks, the existence of nominal wagecontracts, taste shocks, governmentspending shocks, and labor hoarding be-

havior by firms. I t is likely that in realitythese factors have acted in conjunctionin determining the pattern of employ-ment, which makes it difficult to deter-mine how significant each mechanism isempirically. For instance, it is question-able whether government spendingshocks have a significant impact on laborsupply, as opposed to labor demand (asis the case in traditional Keynesian mod-

els). I know of no empirical evidence tosupport this, and the low responsivenessof labor supply to tax changes thatemerges from micro studies suggests thatresponses to changes in the govern-ments provision of goods and serviceswill also be low. (However, as discussedabove, these micro studies are generallynot informative about labor supply be-havior over short horizons.) The fact thatintroducing government spending shocks

into an RBC model in this way appearsto have a significant effect on the model(as Lawrence Christiano and Eichen-baum 1992, find), does not prove thatthis mechanism has any relevance in re-ality. The same, unfortunately, appliesequally to the other mechanisms consid-ered and highlights the need for inde-pendent corroborating evidence, notonly for shocks to labor demand, but also

shocks to labor supply.

A.3Unemployment and L abor s Share.RBC models can readily account for vol-untary and frictional unemployment.This can be accomplished by the intro-duction of labor market search, where

matching workers to jobs depends on ag-gregate search and recruiting effort. I nsearch equilibrium, changes in employ-ment tend to respond positively to per-manent, rather than temporary, innova-tions in productivity. (By contrast,intertemporal substitution occurs in re-sponse to temporary shocks.) Further in-teresting features of this analysis are thatsearching increases the effect of a pro-ductivity shock on output and increases

the persistence displayed by the cyclicalcomponent of macroeconomic time se-ries (Dale Mortenson 1990; David An-dolfatto 1994).11

In order to account for involuntary un-employment, one must assume that thewage no longer clears the labor market,but performs a different allocative role,for example, that it determines the levelof labor effort, or is used to provide in-

surance against risk or must be set abovea legal minimum level that is perceivedto be fair. Suppose that within an RBCframework risk averse older workers arecovered by risk sharing wage contracts,but young workers must find employ-ment in the casual labor market. I f mini-mum wage legislation exists, it provides afloor to the wage in the casual labor mar-ket, allowing involuntary unemploymentto occur in unfavorable states of the

world. Results of simulations from amodel similar to this due to Danthineand Donaldson (1991) are presented inTable 3.

RBC models with real wage rigidity

11Indivisibilities in labor supply (discussedabove) also result in voluntary unemployment,with workers receiving the same income in bothgood and bad states of the world. (There is com-plete unemployment insurance in G. Hansens

model.)



13/34

have the advantage that the correlationbetween wages and employment is lowerthan in standard models. A further ad-vantage is that, like labor market search,real rigidities tend to amplify the impactof shocks on output, so that the varianceof productivity shocks required to gener-ate a certain standard deviation in outputis much lower than in, say, KPs model.

The existence of risk-sharing contracts

can also help to resolve the problem ofthe cyclical behavior of labors share ofincome. Assume two types of agents in-habit an RBC model: entrepreneurs whoprovide optimal, risk-sharing contracts,and workers who thus obtain insuranceagainst income losses due to cyclicalfluctuations. I n a bad state of the worldthe real wage rises relative to profits asthe insurance element of the wage rises.This results in a countercyclical labor

share and roughly acyclical wages, as ob-served in reality (Paul Gomme andGreenwood forthcoming).

B. Extensions: Money

The literature has explored severalways of introducing money into an RBCmodel, and RBC models can readily ac-count for the procyclical movement of

the money stock. Suppose that transac-

tions (or financial) services can be pro-duced more rapidly than goods, andthese services are used by both firms andhouseholds to save time. A positive shockto productivity that increases output willalso increase the demand for financialservices: a model with these featurespredicts that these services will covarywith output. Thus, the model explainsthe money-output correlation by means

of a reverse causation argument: finan-cial services change in response to out-put changes. I nside money is in factmuch more closely correlated with out-put than outside money, which is exactlywhat this model predicts (Robert Kingand Charles Plosser 1984).

Other studies consider whether mone-tary shocks can have a significant effecton output variability in an RBC frame-work. These papers consider (1) a trans-

actions technology, where changes in themoney supply alter the time or resourcesneeded to transact; (2) monetary shocksthat affect output through price misper-ceptions in a Lucas (1972) informationalisland framework, along with realshocks (Kydland 1989); (3) a cash-in-ad-vance constraint on the purchase of con-sumption goods, so inflation acts as a taxon consumption (Cooley and G. Hansen

1989). None of these approaches lead to

TABLE 3DANTHINEAND DONALDSONS (1991) NON-WALRASIAN MODEL


(a)2 (b)3 (a) (b)

Real Output 1.76 1.76Consumption 1.29 0.85 0.34 0.69Investment 8.60 0.92 6.08 0.99Capital Stock 0.63 0.04 0.54 0.03Hours 1.66 0.76 1.26 0.98Productivity 1.18 0.42 0.61 0.91

Unemployment rate 5%

1,2,3See Table 2 above.



14/34

monetary innovations contributing sig-nificantly to output variability.

Thus, the introduction of a transac-tions technology or cash-in-advance con-straint, by themselves, do little to alterthe RBC model. For money to affectoutput significantly, it appears that one

must depart from the Walrasian para-digm and allow for some nominal fric-tions in the economy. Consider a worldin which agents face a cash-in-advanceconstraint for consumption goods, andmoney wages are set in advance for oneor more periods to be equal to the ex-pected market clearing wage, but thatoutput prices are flexible. I n such aworld, any unanticipated movements inthe money supply cause relative wage

changes that have real effects over andabove inflation tax effects. Incorporatingnominal wage rigidity into an otherwisestandard RBC model can amplify the ef-fect of a monetary shock on output sev-enty-fold, and incorporating only a smallamount of nominal wage rigidity (affect-ing one third of wage settlements) im-proves the performance of such an RBCmodel once both monetary and technol-

ogy shocks are allowed for (Cho and

Cooley 1990). I n particular, as was notedabove, this model can account for theproductivity puzzle. A summary of Choand Cooleys results with respect to two-period staggered wage contracts is pre-sented in Table 4.

RBC models that incorporate some

nominal rigidity are important for tworeasons. First, their properties suggestthat nominal rigidity may well be an im-portant missing element in standardRBC models. Second, such models intro-duce important Keynesian features intoRBC analysis. They consequently bridgethe dichotomy between two very differ-ent schools of thought in macroeconom-ics, and are likely to be regarded as amore acceptable development by some

critics of RBCs. However, some aspectsof the data generated by these modelsappear to be inconsistent with the U.S.data. For instance, in Table 4 nominalprices are very slightly procyclical, whilein reality they appear to be countercycli-cal, at least if detrended by the Hodrick-Prescott filter.

This section has shown that it is quitepossible to incorporate money into an

RBC model, and to obtain the positive

TABLE 4CHOAND COOLEYS (1990) MODELWITH NOMINAL CONTRACTS

U.S. Economy1 Models Results4

(a)2 (b)3 (a) (b)

Real Output 1.74 1.80 Consumption 0.81 0.65 0.37 0.53Investment 8.49 0.91 6.54 0.95Capital Stock 0.38 0.28 0.55 0.09Hours 1.80 0.87 1.31 0.84Productivity 1.09 0.56 0.93 0.68Prices (CPI) 1.60 0.53 1.78 0.04

1Quarterly data, 1955:31984:1. Series are logged, seasonally adjusted,and detrended using the Hodrick-Prescott filter.2,3See Table 1 above.4Results for the model with 2-period staggered contracts and shocks totechnology and the monetary base.



15/34

correlations between money and outputthat are observed in reality. However, inthe absence of some nominal rigidity,changes in the inflation rate or in trans-actions costs caused by changes in the

real money supply appear to have anegligible effect on real variables. Onlythe existence of significant nominal ri-gidity results in significant non-neutral-ity of money in an RBC model, and im-proves the fit of the model in somerespects.

C. Extensions: Gover nment

RBC models containing a government

sector have been used to investigate theimpact of government expenditure onthe volatility of output. Generally, gov-ernment spending is assumed to followan exogenous stochastic process that ap-proximates the real data on expenditurereasonably well. Innovations in govern-ment spending appear to contributefairly little to output volatility (less thanten percent). Depending on the modelstructure, government spending shocks

may even reduce the variability of out-put, because they are negatively corre-lated with Solow residuals (Mary Finn,forthcoming).12

An increasing number of papers haveused RBC models to evaluate the bene-fits of alternative government policies.The long-run policy implications of thesemodels are broadly consistent with theNeoclassical growth model, because

RBC models are essentially extensions ofthe Neoclassical growth model. How-

ever, in RBC models the impact policieshave over shorter horizons is very sensi-tive to the model structure. A change inthe assumptions, such as requiring thegovernment to balance the budget over

the business cycle as opposed to leavingthe level of government debt a free vari-able, can reverse the welfare rankings ofalternative policies (V. V. Chari, Chris-tiano, and Patrick Kehoe 1994). I nterest-ingly, it has been found that the pres-ence of distortionary taxes amplifies thepersistence effects shocks have on aggre-gate time series and also increases thevariability of these series (Greenwoodand Gregory Huffman 1991).

One can conclude from this that RBCmodels can readily be used to evaluatethe welfare costs of alternative policies.However, given the absence of agentheterogeneity in these models, and theconsequent absence of any distributionsof income and wealth, the absence ofmarket power, of transactions costs, ofexternalities, and public goods, it is dif-ficult to regard these models as they

currently stand as providing plausiblevehicles to assess policy issues. In par-ticular, the reliance on a representativeagent framework is regarded by someas especially damaging to the credibil-ity of these models (see Section IV be-low).

D. Extensions: The Open Economy

One of the most active areas of busi-

ness cycle research in recent years hasbeen the development of open economyRBC models to explain patterns of tradeand correlations across countries. Openeconomy RBC models have been suc-cessful in accounting for several stylizedfacts. First, the balance of trade movescountercyclically and second, the tradebalance is positively correlated with theterms of tradethe relative price of ex-

12Solow residuals derived from a conventionalproduction function like (2) above tend to be posi-tively correlated with government spending (Burn-side, Eichenbaum, and Rebelo 1991). Finn mea-sures Solow residuals much more precisely,allowing for variable capital utilization and energyas a separate input. Her residuals are negativelycorrelated with government spending shocks,which is why they reduce output volatility undercertain circumstances.

1 LINE SHORT



16/34

ports to imports (David Backus, Kehoe,and Kydland 1994). Third, savings andinvestment are positively correlated inopen economies (F inn 1990).

However, there are two stylized facts

that these models cannot easily explain.RBC models with traded goods generallyassume that each country experiences adifferent technology shock (though pos-sibly positively correlated with the othercountrys shock). Agents can participatein international capital markets, so thatconsumption and investment are nolonger constrained to equal domesticoutput. Given the opportunities of inter-national risk sharing, one would expect

consumption to be smoother than underautarky. Furthermore, it is a property ofone-good economies with complete mar-kets and additively separable preferencesthat consumptions of agents are posi-tively correlated, even if their incomesare not. RBC models reflect this prop-erty and predict that correlations of con-sumption across countries are muchhigher than correlations of output, in

contrast to what one observes in reality.This has been referred to as the quantityanomaly, because it is extremely robustto changes in parameter values andmodel structure. The second fact is thatthe terms of trade are much more vari-able and display greater persistence thanRBC models suggest. This volatility inreal exchange rates is called the priceanomaly.

A large number of extensions to the

theory have been proposed to deal withthese two anomalies, including non-traded goods, taste shocks, energy priceshocks, incomplete asset markets, andmoney. While some of these extensionshave been able to account for the quan-tity anomaly, they are much less able toaccount for the quantity and priceanomalies in conjunction (Backus, Ke-hoe, and Kydland forthcoming).

E. Extensions: Other

RBC models have been extended in avariety of other ways but, for reasons ofspace, only two further extensions are con-

sidered hereimperfect competition,and RBCs implications for asset prices.Introducing imperfect competition

into an RBC model has important conse-quences. Under imperfect competition,productivity shocks have very little effecton employment, so that the sizeable cy-clical variation in employment one ob-serves must be due to other shocks. Fornot implausible parameter values, a risein productivity can even reduce employ-

ment slightly, because the wealth effectof a productivity shock on employment isgreater than under perfect competitionand offsets the substitution effect to agreater extent (Julio Rotemberg and Mi-chael Woodford 1994). Furthermore,with increasing returns and imperfectcompetition, the economy may exhibitmultiple equilibria, which suggests thatsuch models are closer in spirit to the

New Keynesian theory than the RBCparadigm.The asset pricing implications of a

standard RBC model are generally atvariance with the stylized facts, becauseit is more difficult to account for signifi-cant risk premiums in a production econ-omy than in an endowment economy. Inan endowment economy, the repre-sentative agent simply consumes her en-dowment, but in a production economy

the consumption decision is endogenous.As the degree of risk aversion rises, con-sumption becomes smoother and riskpremiums less variable across assets.Thus, a standard RBC model cannot ac-count for cross-sectional differences inreturns on assets (such as the equity pre-mium puzzle) nor for the time series be-havior of returns (Geert Rouwenhorst1994). I t has been conjectured that other

1 LINE SHORT



17/34

sources of shocks, or imperfect informa-tion, might be required to explain assetprices within an RBC framework.

IV. Cr it icisms of RBC Theory

Over the years a number of criticismshave been leveled against RBCs.13 Thissection discusses five major criticisms.First, there is no independent evidencefor the large, economy-wide distur-bances that drive these models. Second,the models are not subjected to formaleconometric tests: there is no objectiveyardstick to measure how well RBC mod-els account for cycles. Third, they cannot

account for the periodicity of cycles: thepattern of cycles generated by RBCmodels does not match reality at all well,because the models contain such weakmechanisms for propagating shocksthrough time. Fourth, RBCs cannot ac-count for recessions, for this would re-quire economy-wide reductions in pro-ductivity. Fifth, the utilization of arepresentative agent framework limitsthe ability of these models to addresswelfare or policy issues.

A. The Natu r e of the Shocks

Perhaps most frequently heard objec-tion is that there is no independent evi-dence for the impulse mechanism thatRBCs rely on. There is, says Summers(1986, p. 24) no discussion of the sourceor nature of these shocks,. . . nor anymicroeconomic evidence of their impor-

tance. Furthermore, the way the shockis introduced into the models placesstrong implicit restrictions on the pro-cess of technological change. Technologyshocks are assumed (a) to affect all sec-tors of the economy equally, and (b) toaffect the productivity of all factors ofproduction (or of all labor inputs in some

formulations) equally, regardless of thevintages of capital or the ages and skilllevels of labor. Not surprisingly, manypeople regard such pervasive, economy-wide changes in technology as implausi-

ble. Normally, a technological or scien-tific innovation affects only a fewproducts. This section considers alterna-tive characterizations of technicalchange, by examining a multisectoralRBC model and a model where technol-ogy shocks only affect new capital goods.I t also assesses the importance of therole of energy price shocks in accountingfor cycles.

I f productivity innovations primarily

affect only a particular sector, one mustconsider a multisectoral economy thatproduces many heterogeneous goods.Suppose these goods can be either con-sumed or used as inputs into next pe-riods production process. I f the differ-ent sectors are subject to independentshocks to productivity that follow aMarkov process, aggregate output willdisplay damped oscillations about its

steady state that are similar to the busi-ness cycles observed in U.S. data (J ohnLong and Plosser 1983). The problemwith this approach is that much of thevariation of individual sectors is averagedout: the variance of output aggregatedacross n sectors is much lower than thevariance within each sector.14 Using adisaggregated approach therefore hasthe drawback that the technology shockshitting each sector have to be even larger

than in a one-good model to result in thesame variance of aggregate output.15

13Papers critical of RBC theory include Sum-mers (1986), Mankiw (1989), McCallum (1989),

and Eichenbaum (1991).

14 In general, the variability of aggregate outputtends to decrease as the number of sectors rises.For a discussion, see Per Bak et al. (1992). Theyargue that small, independent sectoral shocks canhave significant aggregate effects only if costs arenon-convex and there exist nonlinear, strongly lo-calized interactions between different parts of theeconomy.

15Long and Plossers model also appears to be

at odds with several empirical facts. Horst Entorf



18/34

Furthermore, multisectoral modelssuffer from the same problems that af-flict multicountry RBC models, becausethe basic structure of multisectoral andmulticountry models is the same. Hence

the theory will predict that consumptionacross sectors is more highly correlatedthan output across sectors, and produc-tivity more highly correlated than out-put, while in reality the reverse is muchmore likely to be true (the absence ofsectoral data on consumption makes thisdifficult to test). This suggests that disag-gregating RBC models across sectors willprove challenging.

An alternative interpretation of tech-

nology shocks is that they are shocks tothe marginal efficiency of investment. I tis natural to think of such shocks as af-fecting the productivity of only new capi-tal, not existing capital. This is a moreplausible characterization of technologyshocks, and provides a more Keynesianview of the causes of cycles, becauseshocks to the future marginal efficiencyof capital can be interpreted as demand

shocks.How successful is such a charac-terization of technology shocks in ac-counting for cycles? Consider an RBCmodel with vintage capital subject to two

shocks, a conventional RBC shock to to-tal factor productivity and a shock that isspecific to the productivity of new capi-tal equipment, so the production of capi-tal goods becomes increasingly efficient

with the passage of time. In such aframework, about twenty percent of thecyclical volatility of output is due to in-vestment-specific shocks, even thoughinvestment in new capital equipment isonly about seven percent of GNP on av-erage (Greenwood, Hercowitz, and PerKrussel 1992). This suggests that invest-ment-specific technical change is impor-tant even at cyclical frequencies.

The interpretation of real shocks as

impinging primarily on new capital goodsis much more appealing than as a shockto total factor productivity, so it is re-grettable that this formulation has notbeen adopted more widely. One reasonmay be that models with vintage capitalare computationally more difficult to an-alyse than models with a single capitalgood. A second reason may be that, atleast within this framework, most of the

cyclical volatility of output is still due tothe conventional RBC shock that im-pinges on total factor productivity. I twould therefore be interesting to see theeffects of introducing other shocks (gov-ernment spending or nominal shocks, forexample) into this model.

When asked for evidence of realshocks, RBC theorists often point to thelarge oil price shocks of the 1970s andthe recessions that followed. Indeed, all

but one of the postwar U.S. recessionshave been preceded by a sharp rise inthe price of crude petroleum (JamesHamilton 1983). This raises the questionwhether the driving force behind RBCsis really energy price shocks. I f so, theseshocks are unlike those RBC theory as-sumes: the shocks RBCs contain shift theentire production function up or down,while a change in the relative price of an

input would move one along the surface

(1991) argues that Long and Plossers model leadsto an inherent sectoral ordering, activity in somesectors leading that in others, with nonconsumersectors as exogenous. He tests this using vectorautoregressions and cross-spectral analysis, and

finds that, contrary to the theorys predictions,consumer sectors tend to precede nonconsumersectors. He concludes that this is consistent with aprominent role for demand disturbances. KevinMurphy, Andrei Shleifer, and Robert Vishny(1989) argue that the variability of relative pricesprovides evidence against a multisectoral RBC.They find that raw materials prices are more pro-cyclical than intermediate goods prices, which inturn are more procyclical than finished goodspricesthe prices of outputs relative to inputs arecountercyclical. I f cycles result from shocks tocommon inputs (as in Long and Plosser) onewould expect intermediate goods prices to decline

relative to final goods over the cycle.



19/34

of an existing production function, with-out any change in the state of technol-ogy. Because RBCs consider only oneshock to productivity, this has to absorbthe role of both changes in productivity

and any omitted factors, such as changesin availability of factor inputs, that mayhave played a role in reality but are notreally productivity shocks. I t is conse-quently of interest to introduce energyprice shocks separately into an RBC.

A number of RBC models have explic-itly incorporated energy price shocks(In-Moo Kim and Prakash Loungani1992; F inn, forthcoming). Generally, therelative price of energy is modeled as an

exogenous, stochastic ARMA processthat fits the time series on energy priceshocks quite well. These models lead tothe conclusion that energy shocks seemto account for between eight and eigh-teen percent of output variation, which,while significant, suggests that, despiteHamiltons findings, these shocks havenot been the dominant factor contribut-ing to business cycles in the U.S.

Another omitted factor that the Solowresidual might be capturing in closed-economy RBC models is changes in acountrys terms of trade. I t is possible tointroduce the terms of trade as an exoge-nous process into an RBC model insteadof endogenously determined by themodel. Allowing the terms of trade pro-cess to approximate real data for indus-trialized countries, one finds that innova-tions in the terms of trade account for

just over half of output variabilitytheyare even more important than productiv-ity shocks (Enrique Mendoza 1992). Thissuggests that changes in the terms oftrade may be an important omittedsource of output fluctuations in a closed-economy model. But, as noted above,models driven by productivity shocksalone cannot explain the volatility interms of trade when these are endo-

genously determined in a multicountry

framework. This again suggests that ad-ditional shocks are essential to replicatecycles adequately.

B. Testi ng RBC Models and the Problemof Filteri ng

Tests of RBC models are very infor-mal. Generally authors just present twosets of statistics: second moments de-rived from the model-generated data andmoments from a real data set. Casual in-spection determines how closely the twosets of moments correspond to eachother, and this decides whether themodel is a good approximation of reality.No formal test statistics are presented.

Furthermore, RBC models are nottested against alternative hypotheses. Itis not clear what the value of testing ahighly abstract, but fully articulated,model against a much less restrictive,less comprehensively articulated alterna-tive would be. In terms of predictivepower, one would expect a time seriesmodel that places few restrictions on thedata to reject an RBC model. The real

issue here is how one should judge therelative performance of alternative, fullyarticulated business cycle models. Thecurrent informal method of testing RBCmodels cannot resolve this issue and isanyway subject to two pitfalls: first, thedata filtering procedure can result inspurious inferences being made, and sec-ond, the method is purely subjective.

RBC models almost universally use theHodrick-Prescott (HP) filter to decom-

pose time series into long-run and busi-ness cycle components.16 This filter hastwo problems. F irst, it removes impor-tant time series components that havetraditionally been regarded as repre-senting business cycle phenomena(King and Rebelo 1993, p. 208). Thus

16Kydland and Prescott (1990) provide a de-scription of this filter. Essentially, the filter ampli-fies growth cycles at business cycle frequencies

and dampens short- and long-run fluctuations.



20/34

this filter removes potentially valuableinformation from time series. Second,the HP filter can impart spurious cyclicalpatterns to the data. I f one passes a ran-dom walk through the HP filter, the fil-

tered data will display cycles, eventhough none was present in the raw data.Similarly, HP filtering can induce spuri-ous correlation patterns among two dataseries that were not present in the prefil-tered data (Timothy Cogley and JamesNason, forthcoming). Application of theHP filter to real and model-generateddata sets causes them to display similarcyclical properties that were not neces-sarily present in prefiltered data. This is

illustrated by the fact that the raw datagenerated by a typical RBC are almostwhite noise, but display cycles oncepassed through the HP filter (Cogley andNason, forthcoming). Consequently, cor-respondence between real and artificialdata may simply reflect common proper-ties induced by the HP filter.

This suggests that the properties ofreal and artificial data sets should be ex-

amined to see how sensitive they are tothe filter employed. Second, goodness offit statistics invariant to the HP filter, asused by Cogley and Nason (forthcom-ing), should begin to be more widely em-ployed. Such formal test statistics wouldalso facilitate objective comparison be-tween different RBC models.

C. Output Dynamics and the Pr oblem ofPropagation Mechani sms

Can RBC models generally account forthe output dynamics displayed by U.S.GNP? The answer is no, because thepropagation mechanisms they incorpo-rate are so weak.

In RBC models, cycles in output aredriven by cycles in the exogenous tech-nology disturbance. A purely temporaryshock to productivity does not result incyclical activity in output or employ-

ment: a temporary shock only causes

temporary deviations in output and em-ployment from their long-run paths, i.e.,detrended output and employment dis-play no serial correlation (King, Plosser,and Rebelo 1988a). In order to generate

cycles, it is necessary to incorporate sub-stantial first-order autocorrelation inproductivity shocks, causing the shocksthemselves to exhibit cycles, and this iswhat all RBC models do.

The ability of KPs widely used time-to-build construct to propagate shockshas been studied by Rouwenhorst(1991), who finds that in the KP model

the main determinant of these model dynam-

ics is the stochastic process for the shocksthat hit the economy. Time-to-build, by itselfcontains only relatively weak material propa-gation mechanisms for transferring realshocks in terms of effects on output, laborinput and consumption. For persistent devia-tions in output and investment to occur in theneoclassical model i t is requir ed that th e ti meseri es of shocks that h i t t he economy behave

very much like the fluctuations which the

model seeks to expl ain. This conclusion is ro-bust to allowing for nonseparabilities in pref-erences . . . time to build does not seem to

be central to the explanation of business cy-cles. (1991, p. 242, my emphasis)

The ability of KPs fatigue effect topropagate shocks is also barely signifi-cant: Labor input responds slightlymore elastic[ally] than in the model withtime separability, but the differences ap-pear quantitatively small (Rouwenhorst1991, p. 252). Thus, despite being widelyused, neither time-to-build nor fatigue

effects contain strong propagationmechanisms for translating uncorrelatedshocks into serial correlation in outputand investment. I nstead, the artificialtime series generated by the modellargely reflect the properties of the ex-ogenous shocks that are meant to initiatethe cycle.

This is a serious problem, for it is notconfined to the KP model. Even if one

accepts that exogenous technological in-



21/34

novations are highly autocorrelated,RBC models generally cannot replicatethe dynamics of the U.S. GNP growth.

The extensive literature on the timeseries properties of U.S. output docu-

ments two sylized facts. F irst, outputgrowth displays significant positive auto-correlations at short horizons, and weaknegative autocorrelations at longer hori-zons (Charles Nelson and Plosser 1982).Second, if one decomposes output intopermanent and transitory components,output displays a hump-shaped responseto a transitory innovation, and thus ap-pears to have an important trend-revert-ing component (Blanchard and Danny

Quah 1989).In order to account for these features,

RBC models must propagate shocks overtime in a particular way. Cogley and Na-son (1993) examine the properties ofeight different models: (i) A baselineRBC model (King, Plosser, and Rebelo1988b); (ii) A time-to-build model; (iii)Christiano and Eichenbaums (1992)model with government expenditure

shocks; (iv) A variant of Christiano andEichenbaums model that also incorpo-rates quadratic costs of adjusting thecapital stock; (v) A further variant ofChristiano and Eichenbaums model thatincorporates distortionary taxes on laborand capital; (vi) Greenwood, Hercowitz,and Huffmans (1988) model with vari-able capacity utilization and shocks onlyaffecting the productivity of new capitalgoods; (vii) Benhabib, Rogerson, and

Wrights (1991) model with home pro-duction; and (viii) Burnside, E ichen-baum, and Rebelos (1993) model withlabor hoarding.

They find that only the labor hoardingand home production models generateserial correlation in output endo-genously, but that in the latter case it isnegative, instead of positive, at short ho-rizons. Furthermore, the labor hoarding

model is also partially successful in ac-

counting for the impulse response func-tion of transitory shocks. In all the othermodels, output dynamics are nearly thesame as impulse dynamics (just as Rou-wenhorst found for the KP model).

Why, then, do RBC models appear toconform fairly well to real data? Theanswer is contained in the aforegoingsubsection: both the real and model-generated data are HP filtered, and maycontain some common cyclical propertiesinduced by this filter. One is led to con-clude that the great majority of RBCmodels studied in this survey cannot rep-licate the periodicity of output: they dogenerate cycles, but these are quite un-

like the business cycles experienced bythe postwar United States. This inabilityto account for the dynamics of outputgrowth remains a major challenge toRBC theory.

D. Recessions in RBC Models

Many critics also express skepticismabout the ability of RBCs to account for

recessions. Why should there be aggre-gate declines in productivity that causeoutput to fall? Most people do not findthe interpretation of recessions as peri-ods of technological regress convincing.

RBC theorists tend to interpret tech-nology shocks fairly broadly as changesin the production functions, or, moregenerally, the production possibilitysets of the profit centers (G. Hansenand Prescott 1993, p. 280). However,

changes in the stock of public technicaland scientific knowledge alone cannotaccount for business cycles, becauseeven though the rate of inventions mayvary, the stock of knowledge should notdecrease. Instead, RBC theorists havedrawn attention to the legal and institu-tional framework which, in part, deter-mines the incentives to adopt particulartechnologies. Changes in this framework,

for instance tighter pollution laws, can, it



22/34

is argued, be interpreted as a negativetechnology shock.17

The improvements in health, safety,and environmental standards that manyWestern economies have experienced in

recent decades may well be one explana-tion why these economies have grownslowly over the past twenty years. How-ever, some RBC theorists claim that thecyclicalcomponent of output can also beexplained by such changes: taken liter-ally, they suggest that recessions are in-duced by rashes of bureaucratic inter-vention in the market process, and arelikely to occur when the stock of knowl-edge is growing only slowly. Thus, they

see recessions as periods when there areno large technological innovations to off-set regulatory changes that depress prof-its.18

An alternative explanation of reces-sions is due to Louis Corriveau (1994),who has examined the conditions underwhich an economy driven solely by tech-nological advances will exhibit reces-sions. He assumes technical change is

endogenous and occurs through innova-tion races. Each period resources are al-located between production and innova-tion. A potential innovator cannot knowin advance whether he will succeed, butchances of success increase with factorsdevoted to innovation. He shows that

downturns in output do not requirenegative technology shocks. Downturnsare caused by increased allocation of re-sources to innovation in the face of in-creased opportunity ex ante that fails to

materialize ex post, leaving fewer re-sources for production with last periods(unchanged) technology.

E. The Repr esentati ve Agent and t heProblem of Aggregation

All macroeconomic models face aggre-gation problems. RBC models overcomethese by using representative agents.The entire economy is collapsed into asingle utility specification and a single

production specification. This solution isradical, and consequently leaves evensome economists working within themainstream neoclassical tradition un-easy.

Alan Kirman (1992) has launched astrong attack on the representative agentconstruct. His case rests on a number ofwell known results. The Debreu-Mantel-Sonnenschein result demonstrates that

individual maximization imposes only theweakest restrictions on the properties ofaggregate functions.19

Even introducing a small amount ofagent heterogeneity can have destructiveconsequences. I f agents have identicalpreferences, and differ only in terms ofthe income they receive, the repre-sentative agent for such an economyneed not be well behaved and the econ-omy can manifest a large number of un-

stable equilibria. Optimization at the

17This is stated quite explicitly by G. Hansenand Prescott: It would not be surprising then,that changes in the legal and regulatory system

within a country often induce negative as well aspositive changes in technology (1993, p. 281).18This hypothesis has some testable implica-

tions. Economies with relatively static institutionaland regulatory frameworks should, in principle,experience less cyclical activity than those econo-mies where these frameworks are more subject tochange. Furthermore, because different countrieshave very different regulatory frameworks, andlegislation to change them is seldom introduced atthe same time, and because G. Hansen andPrescott argue the stock of technical knowledge isbroadly similar across countries, a priori onewould not expect the incidence of recessions to be

significantly correlated across countries.

19More specifically, consider a pure exchangeeconomy where each individual has a well-be-haved textbook excess demand function. Summingover the finite number of individuals provides theaggregate excess demand function. Generally onlythree properties carry over from the individuals tothe aggregate excess demand function: it must becontinuous, it must satisfy Walras Law (aggregateexcess demand must equal zero at positive prices)and it is homogeneous of degree zero in absoluteprices. This is not sufficient to obtain uniqueness

and stability of equilibrium.



23/34

level of (very similar) individuals cannotensure that the economy as a whole willbehave like an optimizing individual.There is not necessarily a clear corre-spondence between the preferences and

reactions to policy changes of the indi-vidual agents and the preferences andreactions of the hypothetical averageor representative agent. This can lead toparadoxical situations where every indi-vidual in the economy may prefer situ-ation a to situation b, but the repre-sentative agent prefers situation bto a.Consequently, changes in the welfare ofthe representative agent need not corre-spond to changes in societys welfare.

Secondly, many writers (e.g., Lucas1987) regard one of the strengths of theRBC paradigm as being that it provides arigorous microfoundation for macro-economic behavior. Aggregate outcomesare explained as resulting from optimiz-ing actions at the individual level. Butthe aforementioned arguments implythat the reliance on a representativeagent deprives these models of much of

their explanatory power: aggregate fluc-tuations result from the responses of theaverage agent to stochastic change inproductivity; one cannot say that they re-sult from the responses of maximizing in-dividuals to productivity shocks.20

To take the argument further, it is wellknown that constrained maximization byall individuals is not sufficient to gener-ate a well-behaved representative. In-deed, it is not even a necessary condi-

tion: one can obtain a well-behavedaggregate excess demand function pro-vided agents have no money illusion andcomply with their budget constraints

(Jean-Michel Grandmont 1992). Well-behaved aggregate relationships do notrequire individual optimization: eveneconomies whose agents have boundedrationality or follow simple rules of

thumb can display well-behaved aggre-gate functions, a result that appears de-structive of the claim of RBC theorists tohave provided a more rigorous micro-economic foundation for macroeconom-ics than competing paradigms.21

V. The Empi r ical Evidence

The previous section showed that RBCmodels as a rule are not subjected to for-

mal statistical tests against competing al-ternatives, and that there is no micro-economic evidence for the large realshocks that drive these models. How-ever, a number of studies and empiricalfacts, to which we now turn, act as indi-rect tests of these models.

A. The Empi r ics of Business Cycles

Philip Cagan (1991) argues that the

traditional view of the sources of busi-ness cycles has tended to focus on nomi-nal demand. In this view, sluggish priceadjustment causes output to react tochanges in nominal demand broughtabout by changes in private sector confi-dence, government spending, or mone-tary policy. This view has several impli-cations for the behavior of certain timeseries over the business cycle. First, itimplies prices and output will covary

positively over the cycle. Second, onewould expect real wages to be countercy-clical since the rise in output depressesthe marginal product of labor. Third, un-der perfect competition the more inten-sive use of capital and labor duringbooms suggests, ceteris paribus, that

20An illustration of this lack of correspondencewithin the RBC paradigm is provided by G. Han-sen (1985) who shows that a small change, likefixing the hours an agent may work at some num-ber x or zero, causes the representative to ex-hibit infinite intertemporal substitution of leisure,even though the individual agents are assumed to

have conventional labor supply functions.

21RBC models are also subject to the criticismsthat can be leveled against the use of aggregateproduction functions. For an overview of this is-

sue, see Geoffrey Harcourt (1969).



24/34

productivity should be countercyclical.Fourth, the traditional view is that theclassical dichotomy holds in the long run:one would not expect nominal changes toalter the long-run time profile of out-

putnominal shocks should only causetransitory deviations from this long-runpath.

RBCs predict different patterns forprices, wages, productivity, and output.I f cycles are driven by real shocks, thenin the absence of a consistently procycli-cal monetary policy, prices will be coun-tercyclicalfor a given money stock,prices should fall as productivity andoutput rise. Furthermore, because ex-

pansions are induced by positive innova-tions in productivity, real wages and pro-ductivity will be procyclical. F inally,some real shocks are permanent and willalter the long-run path of output.

The models different time series pre-dictions have led a number of writers toconclude that the stylized facts aboutthese series can be used to discriminatebetween RBCs and competing theories. I

examine the evidence for the pattern ofoutput, wages, prices, and productivitybelow, and consider the implications thishas for RBCs.

A.1 Nonstationarity. Before the influ-ential work of Nelson and Plosser (1982),it had been common practice to treatmacro time series as stationary move-ments around a deterministic lineartrend. Nelson and Plosser found thetrends of most series to be nonstationary

stochastic processes, often well de-scribed as a random walk with trend.Their findings also led them to concludethat most output movements appear toresult from changes in the secular, orpermanent component of output, ratherthan the transitory cyclical component.

Many writers (including Nelson andPlosser) argued that these time seriesproperties are most easily explained by a

predominance of real shocks in the econ-

omy. RBC theorists typically regard thetechnology parameter as having a unit ornear unit root. Because output inheritsthe trend properties of technology, RBCmodels can readily account for nonsta-

tionarity, with transitory (though possi-bly long lasting) deviations from thistrend determining the cycle. Nominalshocks, by contrast, seem unable to ac-count for the nonstationary trend.

This argument is weakened by threepoints. First, in finite samples it is notpossible to discriminate between the hy-pothesis that a series is nonstationary (ordifference stationary) and has a unitroot, and the hypothesis that it is station-

ary but has a root that is less than, butclose to unity.22 Second, David DeJongand Charles Whiteman (1991) have ar-gued from a Bayesian perspective thatmost economic time series are in factmore likely to be trend stationary thandifference stationarygiven reasonablepriors, the relative support the data giveto a trend stationary representation isstronger than that given to a nonstation-

ary representation. Third, if technologyis endogenous to the economic system, amonetary theory of the business cyclecan account for nonstationarity just aswell as an RBC model can (Stadler1990). Despite the original claims ofNelson and Plosser, their work does notprovide unequivocal support for RBCs.23

22The widely used Augmented Dickey-Fullertest of nonstationarity will actually reject the hy-

pothesis of stationarity in series that are stationarybut have an autoregressive component close tounity (J ohn Campbell and Pierre Perron 1991).

23A further factor that creates problems forRBCs is that macroeconomic time series may con-tain non-linearities. For instance, Hamilton (1989)finds that the growth rate of output is better de-scribed by a regime-switching model than a linearmodel. Hamiltons findings can be replicatedwithin an RBC model if the productivity shocksfollow a Markov process with asymmetric transi-tion probabilities. However, this implies that theSolow residuals should exhibit heteroscedasticity,for which there is no evidence in the data (Rou-

wenhorst 1994, fn. 5).



25/34

A.2 Real Wages. Are real wages pro-cyclical? Until the mid-1980s, empiricalwork on this issue was inconclusive, andsometimes contradictory. For instance,Patrick Geary and Kennan (1982) found

wages and employment to be statisticallyindependent. Subsequent papers, usingmicro data on individuals, found a sig-nificant but mild procyclical movement(Michael Keane, Robert Moffit, andDavid Runkle 1988). However, discrep-ancies between the findings of these andother studies actually result fromchanges in the sample period, ratherthan the data set, employed. Periodsdominated by demand disturbances ex-

hibit countercyclical real wages, whileperiods dominated by supply distur-bances manifest procyclical movementsin real wages, which accounts for the lowcorrelation between wages and employ-ment (Scott Sumner and Stephen Silver1989). This finding is hardly unexpected,but does not lend strong support to RBCtheory.

A.3Prices. Are prices procyclical? The

actual pattern prices follow is difficult todetermine. When variables have beendetrended using the HP filter, regressionanalysis invariably yields a negative cor-relation between prices and output, asstressed by Kydland and Prescott (1990).However, there is some evidence thatthe sign of this correlation is sensitive tothe filter employed to detrend the data(Keith Blackburn and Morten Ravn1991). Cagan (1991) eschews detrending

and visually inspects the time profile ofthe logarithm of prices over postwarbusiness cycles. He concludes that mostof the movement is procyclical.

However, the price-output correlationis not necessarily informative about thecyclical behavior of prices. Even modelsdriven solely by demand shocks can ex-hibit a negative correlation. A change inaggregate demand initially causes prices

and output to move in the same direc-tion, but in opposite directions sub-sequently. The correlation coefficientdepends both on the initial and latermovements, and may consequently be

negative (John Judd and Trehan, forth-coming). Thus, there need be no system-atic relationship between the price-out-put correlation and the cyclical patternprices actually follow. Because similarreasoning applies to other variables aswell, it suggests that correlation coeffi-cients may not be very informative aboutcyclical comovements.

A.4 Productivity. A further feature ofthe cycle that has arguably lent support

to RBC theory is that productivity is pro-cyclical. The conventional neoclassicaltheory of the firm suggests that as outputrises and firms move down their demandfor labor functions, productivity andwages should fall, ceteris paribus (thereare short-run decreasing returns to la-bor). However, Robert Hall (1988) ar-gues that productivity is procyclical be-cause firms in imperfectly competitive

markets operate on the downward-slop-ing portion of their average cost curves.In an interesting paper, Ben Bernankeand Martin Parkinson (1991) find thatprocyclical productivity was as markedduring the Great Depression and its af-termath (19291939) as in the postwarperiod. Because the Great Depressionhardly can have been caused by technicalregress, they argue that these resultsshow that procyclical productivity can

George Stadler (1994)

Documents

Transcript of George Stadler (1994)