Real Business Cycles: Reality, or just Mimicking it? … Business... · Real Business Cycles:...

Real Business Cycles: Reality, or just Mimicking it? Geoffrey H. Gill Senior Sophister

The skirmishes between Keynesian and Monetarists in their various guises that have: dominated' mainstream economic thought for most of this century run the risk of being eclipsed by the emergence of the Real Business School. Geoffrey Gill traces the evolution of this literature and questions the proponents insistence on the purity of their argument and their claims of empirical confirmation.

"Economists have long been puzzled by the observation that, during peacetime, indu~trial market, economies display recurrent, large fluctuations of output and employment over relatively short time periods... These observations should not be puzzling, for they are what standard economic theory predicts!" Prescott, 1986 Following the "Lucas Critique' ofa lack of microeconomic foundations in macroeconomic modelling, a new school emerged in the 1980s. Their approach was ari intertemporal equilibrium or Walrasian approach which concentrated on the role of real productivity shocks, in the guise of technology shocks, as the driving force behind the economy. The general consensus in macroeconomics has been that large fluctuations - boom-bust cycles - are not conducive to high longterm growth and thus should be minimised. I Real Business Cycle theorists, though, posited that agents are always optimising in the economy, that fluctuations are the natural outcome of micro economic foundations, and thus to try to restrict this would be counter-productive and costly.

This essay will outline the approach of Real Business Cycle theory and set it in its context relative to other equilibrium approaches i.e. the monetary misperceptions models of Lucas and Barro. The outline will be a simplification of the Kydland and Prescott (1982) model and refinements such as Prescott (1986) and Long and Plosser (1983). We shall then consider the implications and the results of the RBC approach. Other evidence, in particular Nelson and Plosser's analysis of time series data for the US and also Sims' study on the role of monetary impulses in the economy will then be considered. This done, an extended critical appraisal will follow. The case will conclude with a rebuttal of sorts by the Real Business Cyclists. I will conclude, however, that the model does not persuade, that 'mimicking' the animal is not enough, and that the answer lies elsewhere.

An Equilibrium Approach to Real Business Cycles One of the original considerations of the existence of cyclicality in the economy was by Joseph Schumpeter (1939) who identified three different amplitudes of

I At least since Keynes anyway

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Real Business Cycles: Reality, or just Mimicking it?

cycle in the previous 150 years. It is the shortest of the three, the forty month or 'Kitchin' cycle, that economists refer to as business trade cycles. The National Bureau of Economic Research concluded that the time profile of business cycles is irregular, but what does characterise them is the remarkably common pattern of co-movement of aggregate economic series.2 The New Classical approach to explaining this phenomenon was forwarded by Lucas, and later added to by Barro, which essentially formed an equilibrium theory of the business cycle. In this 'monetary misperceptions' model, full information on nominal variables, such as the money supply or overall price index, is available to agents only after a lag. Suppliers have difficulty distinguishing overall nominal shocks from changes in their own relative prices, and thus monetary disturbances have real effects. That is, there is a single price signal, the agent does not know how much of this is temporary (which would imply working harder now) or permanent (which would imply increasing capital stock), thus the optimal response is a weighted average. The price rise thus implies increased output and increased investment. Persistence of this is due to a lag in information and the durability of goods. It is, implausible, however, that individual agents in today's world are unable to observe nominal magnitudes.

Real Business Cycle Theory The RBC theory is an application of the equilibrium approach to business cycle analysis. Essentially, it is an outgrowth of the monetary misperceptions model of Lucas (1972) and Barro (1981), but with emphasis given to propagation mechanisms and to the role of real shocks as a major source of fluctuations. In terms of propagation mechanisms it is an extension of Lucas's ideas on cyclical phenomena. A problem arises, though, in the interpretation of the term 'real shocks'. The economy is constantly affected by the introduction of new technologies, changes in tastes for specific goods, changes in government policy etc. Most of these changes are not perfectly predictable and so the shocks cause agents to constantly revise their optimal plans. It is not clear from the literature, though, of the role attributed to technology shocks, i.e. whether they are an important source of fluctuations or the only important source of fluctuations.

Schumpeter's influence in this field has already been noted and technological change also played a pivotal role in his analysis of the short-run instability and long-run dynamics of capitalist development.3 Since the introduction of new technology influences the long-run growth of productivity as well as causing short-run disequilibrating effects, Schumpeter, like modem real business cycle theorists, viewed cycles and growth as inseparably interrelated. In fact, RBC theorists find the use of the expression 'business cycle' unfortunate as it leads

2 Chrystal and Price, 1994 3 Snowdon et ai, 1995, Ch.6

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people to think of a 'business cycle' component separate from a growth component, and thus they refer to business cycle phenomena.4

The model forwarded is consistent with the following sorts of assumptions: rational expectations, complete information, stable preferences and no frictions or adjustment costs. As such, the model is an intertemporal Walrasian model based on the 'representative agent'. 5 Many similar households exist, each of which seeks at time t, to maximise an objective function of the following form, where c is consumption and I is leisure during period t, while E[ ] denotes the conditional expectation based on full period-t information:

Et[u(ct, It) + pu(ct+l, It+l) + P2u(ct+2, It+2) + ... ]

and where P is a discount factor (0< P<l), and u is taken to be increasing in each argument and 'well-behaved'. On the production side, each household is assumed to have a technology that is represented by a production function: yt = zt F(nt ,kt) where zt is a stochastic index of the current state of technology ( and thus fluctuations in this represent technology shocks), nt is the labour, and kt is the capital expended by the representative household during period t. All factor markets clear in the model economy so it is not necessary to consider labour demand etc. Thus the optimisation problem is to maximise the above subject to the constraint:

kt+ 1 = ztF(nt, kt) + (1-8)kt - ct

Where 8 is the depreciation of the capital stock k in period t. The above implies that any output produced and not consumed is invested. Obviously, to derive an explicit solution to the above is impossible and so we can define a special case that permits an explicit solution. By assuming constant returns to scale and that productivity is generated by a Markov process, that is zt only depends on zt-l, and in fact that technology shocks follow an autoregressive process of the form zt =

pzt-l + ct , where ct is white noise, we can find the part of the change in output that is not explained by changes in the capital stock or labour.6 This is the Solow residual. That is, after taking first differences in logs,

4 Prescott, 1986 5 The following draws on McCallum (l989) 6 Following Kydland and Prescott (1982) we assume that p is less than but near one. This is in the spirit of the permanent income model, thus shocks are permanent



ilyt = (l-a)ilkt + ailnt + A + ilct

A is that part of the change in y not explained by changes in capital or labour.

The above follows in the spirit of the seminal work of Kydland, a~d, Prescott (1982). The problem is, though, that more complex structural specifications are necessary as the above is inconsistent with the facts in the real world; ,.That is, a constant employment level and the same degree of variability.in percentage terms of consumption and investment are implied ,by the above. Thus,theyintroduce numerous assumptions, including a Cobb-Douglas utility function:: Parameter values from other studies are used, which are intended to be close to the average values for the US economy during the., period being, explained. 'These reduce dramatically the number of free parameters that are used when they search for a set that results in cyclical covariances near those observedjn the real· economy. Some of such assumptions are a steady-state capital to annual output ratio" of 2.4 and a real interest rate of 4% per annum." The methodology of 'testing' their model is to use stochastic simulations to deduce the cyclical properties of their numerically specified models.

It is worthwhile to briefly step back from the basic model to take stock before describing the results of these Real Business. Cycle models. A positive productivity shock will have the effect, through the production function, of increasing output. Thus consumption is increased but some output is held back for investment to increase the capital stock which spreads the effects of a once-off improvement over time. Thus the persistence of shocks result emerges. This will occur even if shocks are uncorrelated over time if we assume that capital stock last beyond the current period i.e. 0<1. This is because more durable capital increases the feasibility of intertemporal substitution of. goods and leisure.7 Nevertheless, there exist deficiencies in the model with purely temporary productivity shocks. Substantial serial correlation in consumption and capital will be present as a result of consumption smoothing, but there is effectively no serial correlation in output or employment.8 Thus Kydland and Prescott introduce their 'time to build' assumption - multiple period construction of capital - which implies serial correlation in productivity shocks.

How though are the existence of procyclical employment fluctuations explained in the RBC framework? By including leisure in the utility function the labour supply decision is thus endogenised. Blanchard and Fisher describe Lucas and Rapping's (1986) use of the intertemporal substitution of leisure as an explanation of the joint behaviour of employment and wages over the business cycle. Workers

7 King, Plosser and Rebelo, 1988 8 ibid.


Geoffrey Gill

substitute leisure for labour from periods in which it is expensive to periods in which it is cheap. Thus labour will respond to temporary movements in the real wage' but may not to permanent changes. A positive shock will cause firms to increase their labour demand and thus wages increase. Thus, labour supplied will increase and in the following periods, although the technology shock is no longer present, and labour demand (which depends in part on past employment) remains relatively high. Wages return slowly to equilibrium and so does labour supplied. Thus, white noise technological shocks lead to serial correlation in wages and employment Two conditions are needed for the above:9

I. elasticity of substitution between leisure in different periods to be high 2. aggregate real wage movements must be largely transitory

It may be noted here, though, that empirical'evidence does not support either of the two conditions. Prescott attempts to show that workers willingly intertemporally substitute leisure in response to shifts in the marginal product of labou~ even without the wage shifts. This will supposedly occur if the real wages include an insurance component that causes them not to vary with the underlying MPL . As competitive equilibrium ensures that resources are allocated efficiently, the above intertemporal substitution will occur.

Results The results of the RBC models are shown below. Numerous extensions to the basic model exist in attempting to match the data closely. McCallum (1989) gives a flavour of these in two tables; shown below. As can be seen, the results are not unfavourable, at least qualitatively, and to a good extent quantitatively. The cyclicality shown in Table 1 and the comovement in Table 2 seem to be reasonably accurate.

From Table 1 an identical ordering can be seen of the model's implications for investment, consumption etc. and the US time series i.e. investment is the most volatile.

9 Blanchard and Fisher, 1989, Ch.7



Table J: Standard deviation o/percentage departures from trendlO

Variance US Basic Kydland- Hansen economy model Prescott model*

Output 1.76 1.76 1.76 1.76 Consumption 1.29 0.55 0.44 0.51 Investment 8.6 5.53 5.40 5.71 Capital Stock 0.63 0.47 0.46 0.47 Hours 1.66 0.91 1.21 1.35 Productivity 1.18 0.89 0.70 0.50 ..

* mcludes changes m labour supply declSlon makmg

Table 2: Contemporaneous correlations with output (departures from trend)1l

Variance US Basic Kydland- Hansen economy model Prescott model

Consumption 0.85 0.89 0.85 0.87 Investment 0.92 0.99 0.88 0.99 Capital stock 0.04 0.06 0.02 0.05 Hours 0.76 0.98 0.95 0.98 Productivity 0.42 0.98 0.86 0.87

Of course this is not econometrics - it is simply comparing the benchmark case to what the models predict - and as such there can be no formal tests of significance using this approach. To mimic the data is by no means a proof of the correctness of the model - but more of this later.

Extensions Backus, Kehoe and Kydland attempt to extend the basic RBC model to account for the correlation of cycles across national boundaries. In a world economy, countries experience imperfectly correlated shocks. The ability to borrow and lend internationally should lead to smoother consumption paths and as capital might be expected to be allocated to the country with the most favourable technological shock, this could lead to increased variability in domestic investment. Unfortunately, the theory does not appear to be very robust and a number of discrepancies arise between theory and data, especially in correlations of consumption and output across countries. In the data, outputs are more highly correlated than con sum pt ions (in the model we see the opposite). King and Plosser (1984) explicitly incorporate a financial or banking industry and posit a demand for real currency. They found that, under a variety of conditions, the

10 Source: McCallum, 1989 11 Source: McCallum, 1989


Geoffrey Gill

vanatlOn in the nominal quantity of outside money (either currency or the monetary base) is neutral. Inside money, though, is endogenous -it is determined by the real supply and demand for transaction services. They predict a positive correlation between money and real activity but the causation runs from real activity to money and the banking sector. 12

Evidence Nelson and Plosser's important (1982) paper utilises historical time series for the US and they find that they are unable to reject the hypothesis that the business cycle is a stochastic process of the difference stationary class. They find fluctuations in the cyclical component of aggregate output to be small in comparison with fluctuations in the trend component of that variable. If the cyclical component can be assumed to be transitory (stationary), then any underlying non-stationary in output must be attributable to the secular component. Since innovations in the non-stationary component have a larger variance than in the transitory component, this implies that real (non-monetary) disturbances are likely to be a much more important source of output fluctuations than monetary disturbances. 13 Thus if shocks to productivity growth are frequent and random then the path of output following a random walk will resemble a business cycle. Fluctuations are in the trend itself due to the permanence of the shocks.

Another empirical paper supporting (or at least not denying) the RBC hypothesis is that of Sims (1980). He shows that there is very little explanatory power for output variations provided by money stock innovation in vector autoregression CV AR) systems when nominal interest rates are included as an explanatory variable. 14 According to Sims: monetary policy surprises are not important in explaining the real component of post-war business cycles".15 Taking all the evidence summarised in this paper so far, Real Business Cycle models may look attractive, but what are the implications if we accept this as the explanation of business cycle phenomena?

Implications The RBC theory implies a striking conclusion alluded to in the quote at the beginning of this paper - fluctuations are what economic theory predicts. Indeed Prescott goes on to say:16 "economic fluctuations are optimal response to uncertainty in the rate of technological change." This does not imply that the amount of technological change is optimal or invariant to policy. According to

12 Plosser, 1990 13 Nelson and Plosser, 1982 14 McCallum, 1989 15 Quoted in McCallum, 1986 16 Prescott, 1986



the RBC theorists, if, policies to stabilise the economy reduce the average rate of technological change, then stabilisation is -c·ostly.17 Observed unemployment is always voluntary as it is optimal for workers to be so. Money is 'super-neutral', in this model there is no possibility_ for' nominal variables to affect the real economy in the short or long run. Fi~cal. policy influences the economy only through incentive effects. Economic fl~ctuations are caused by supply rather than demand shocks. To many macroeconomists this denies propositions thought self evident through years offorecasting anddontrolling the economy on a day-to-day basis. '.:, To .. many laypeople, the proposition -that the economy is perpetually optimising and that unemployment is esseiltially voluntary may seem outlandish and perhaps comical. As Summers points out: "most of the work of contemporary macroeconomists is worth little more ,than ,. that of those pursuing astrological science!~' if the RBC theory is correct. ~ -Perhaps., then, it is worthwhile to consider a criticism or two... . ,,; ,:

'tf' ;, r ~' q ',L,'\',.

Critical Appraisal '; . ;r Methodological Problems lco''- ,'.:

A fundamental point can be raised about the RBC framework and 'evidence' of its existence· in' that 'mimicking' real' world' data is by no means a proof of the correctness of the underlying model.;.Indeed, Adelman and Adelman (1959) performed similar simulations using a standard Keynesian model and were able to mimic the data successfully tooY The methodology of testing is at question here as there can be no formal tests of statistical' significance using this simulation approach. The :whole process is. driven by inherently unobservable productivity shocks; :.', Thus, there is a circularity, to th'eir ~r!iument creeping in as originally the variance _ of the· shocks was chosen to generate an output variance equal to the data'. ~~ (We shall return to the productivity shock issue later in this section.) Moreover, it can be argued that, in fact" Kydland and Prescott (and other simulations) do not even mimic the data closely enough. McCallum (1989) points out hat there exists a 'sharp divergence' between the model and actuality with regard to correlations between output and subsequent productivity levels at various leads and lags. The methodology also implicitly assumes away any aggregation problems in concentrating on a stylised 'representative agent' model. In aggregation, though, problems of asymmetric information, exchange and coordination arise and become highly significant., It is difficult, in this author's view, to abstract from the real world so much that partial breakdowns in the exchange mechanism cannot exist, which surely are a significant factor in cyclical fluctuations. During the Great Depression, firms had output they wanted to sell, workers wanted to exchange their labour for it -. but the exchange did not take

17 ibid. 18 Scarth, 1988, Ch.ll.4 19 Chrystal and Price, 1994


Geoffrey Gill

place.20 Breakdowns in credit markets are a recurrent theme in events leading to recession in recent years.

The Nature of the Technology Shock' It is impossible to observe technology shocks directly. If they are truly technological disturbances, then it is difficult to imagine how there can be so much variability in the aggregate level.21 The economy is composed of many different goods which are produced by different technological processes and most scientific or engineering advances pertain to only a few of them. Shocks in different sectors should presumably be nearly independent, McCallum points out, and so economy-wide variability should be small in comparison to anyone industry, by the law of large numbers. New technologies are usually introduced only slowly and smoothly through time.22 Thus, are shocks in aggregate productivity sufficiently large enough to explain short-run fluctuations in output? The assumptions in calculating the Solow residual are questionable too. That is, the economy is on the production possibilities frontier, there exist constant returns to scale and there are no domestic distortions. Although the residual can be modified to include domestic distortions (i.e. how much the economy is off the PPF), then we may question whether technological shocks are driving the cyclicality or is it the domestic distortions?

Summers points out that the changes in total factor productivity could be the result of labour hoarding and other behaviour not allowed into the model. According to Summers, a sizeable proportion is the result of firms' decisions to hold labour in excess of regular production requirements. 'Shocks' may possibly be more like terms-of-trade disturbances e.g. price of imported oil or even fiscal policy changes. That is all very well, but this requires a different type of evaluation of the RBC approach - as changes are no longer unobservable.

Intertemporal Substitution of Labour To many, the elasticity of labour supply is simply not large enough for business cycles to be explained by shifts of a labour demand curve along a given labour supply function. The evidence relating to the intertemporal elasticity of substitution of labour indicates a weak response to transitory wage changes 23 - it is difficult to envisage intertemporal substitution by individuals as accounting for variations in employment. Summers asserts that Prescott in his (1986) model does not cite any direct macroeconomic evidence or any aggregate evidence on this parameter. The associated implication that unemployment is always voluntary is

20 Summers, 1986 21 McCallum, 1989 22 Blanchard and Fisher, 1989, Ch.7 23 Snowdon et al ,1995



hard to swallow. Presumably, the Great Depression in the 1930s was the result of agents anticipating WW2 and deciding to withhold labour services for a decade until a high labour demand period arrived. The European experience of high long-term unemployment rates accord to the fact that when employment falls, it is layoffs, not quits, that are rising and consumption falls (instead of rising as it should ifIeisure and consumption are complements?4·., '. ",,~,

.' '. t. .• RBC Implication: Technological Regress Implies Recession ',,; :, It is very unlikely that RBC theory can explain the three most recent recessions in the US, beginning in 1974, 1979 and 1989. Two of these were affected by supply shocks, "but these were not the stochastic draws of the Real Business Cyclists, rather they were massive blows from exogenous c1ubs".25 A related point is that of the neutrality of money and irrelevance of monetary policy for real outc'Omes, as argued by the RBC theorists, but the monetary disinflations initiated by. Vol~ker and Thatcher were followed by deep recession in both the US and UK in the, early 1980s. So we may question whether recessions can be construed as periods of technological regress. Declines in the available technology is not a widespread phenomenon. r'<~ ':' ..

Model Parameters ',;1: " ,::

Prescott (1986) identifies the share of household time devoted to market activities as important in the model and claims it is approximately one third. Data, though, indicates its average value as one sixth in the past thirty years.26 Another example is that Prescott takes the average real interest rate to be 4%, but over the thirty year period he studies, it has in fact averaged at 1 %. Are the real business cyclists picking values to suit the model's outcomes and then rationalising them ex post? ';

'-' ~

Prices Prescott does price free economic analysis. He does not look at data for7real wages and interest rates, except for his misconstrual of the average real interest rate in the post-war period. Summers' challenge is that if one confronts models like Prescott's to data on prices it produces dismal results. _ ..

Empirical Support 'l~;

McCallum (1986) criticises Nelson and Plosser's argument that nearly all major economic time series are consistent with a random walk. He shows that N~P's results are also consistent with the behaviour of a trend stationary autoregn!ssive series with a root close to one. In his 1989 paper he argues that in fact Sims;

I

demonstration that money stock innovations have little explanatory power wnen

24 h Scarth, 1988, C .11.4 25 Chrystal and Price, 1994 26 See Summers, 1986

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the nominal 'interest rate is included in the system may in fact suggest that monetary policy does affect output. This is because the Fed implements its policy bymaniptilating'nominal interest rates and so interest rate innovation will reflect the monetary policy surprises.

'".,' ~- ..

A Rebuttle? Prescot( in' 'Response to a Sceptic' responds to some of these criticisms. He claims that it is small shocks, every period, that cause economic fluctuations, not large infrequeritshocKs'. He does not claim that public finance disturbances, changes in terms of trade etc. had no effect on fluctuations in the post-war period, rather thcittechnologyshocks account for more than half of these fluctuations. Competitive ~ equilibria are,' he ,argues, expressed in relative prices. Nonconvexities inthis framework can' imply that commodities traded are complex contractual arrangements. Forthe neoclassical growth model it is not the return on T-Bills;' but rather the return on tangible capital that represent the real interest rate. An increase in this reduces the discounted value of future wages and makes it more attractive to work today. Thus employment fluctuations could arise from variations, in the interest rate." This process, though, should imply a negative covariatiein of"rconsumption'\~and employment which is a counterfactual implicati~n.27,,This isapart from the general implausibility of the hypothesis.

I', ~,;::: '<:1 ::::<' ,0

Conclus!on "':; . ". I;' "-:>'

The attraction of real business cycle theories is obvious. In these post-Lucas days of macroeconomic' theorising,' its firm basis in microeconomic principles, and given the Jact, that, it, seems to produce cyclical variations in, major economic variables,'and'covariances between them, which are comparable to the real world, the theory is on the surface appealing. , Market imperfections arise, though, and so it is, difficult to' rationalise a macro-model as an exact aggregation of a micromodel. Many theories can approximately mimic a given set of facts, and the comparison witli the belief in Ptolemeic astronomy - that the earth is at the centre - which yielded accurate predictions, but was wrong, is useful,28 McCallum (1986) proposes a model with price and wage stickiness in which people insure against nominal risk .. His sticky price theory can also produce the same outcomes. It is appropriate to conclude with the thoughts of Lucas - the founder of the equilibrium approach to the business cycle. In his view Kydland and Prescott have,taken macroeconomic modelling into new territory, but exclusive focus on real factors alone is a mistake. He suggests a 'hybrid' model as a fruitful way forward. 29

27 Blanchard and Fisher, Ch.7 28 Summers, 1986 29 Snowdon et aI, 1995



Bibliography

Backus, D., Kehoe, P. and Kydland, F. (1992) "International Real Business Cycles", Journal of Political Economy.d,,,,

Blanchard, O. J. and Fisher, S. (1989) Lectures on Macroeconomics, MIT Press, London. . _.

Chrystal, K and Price, S. (1994) Controversies. in Macroeconomics; 3rd edn., " Harvester· Wheatsheaf. " .. : ."., f!; f

Hahn, . F; and Solow, R. ;, (1995) A.Critical, Essay' on Modern Macroeconomic Theory, Blackwell, Oxford.. ,~., , .... , 1. .

King, R., Plosser, C. and Rebelo, S. (1988) "Production,· Growth and Business Cycles 1 ", Journal of Monetary Economics .. :. :.' ':.--:

Kydland, F.E. andPrescott, E. C.,(1982) '.'Time to .Build and Aggregate '" Fluctuations", Econometrica, Vo1.50, No.6. '. '. :1':. :.>< .....

Long, J. andPlosser, c.., (1983) "Real Business Cycles~', Journal of Political ',': . Economy, Vo1.91, No. I. , , ;"; .. '

McCaIlum, B.(1986),"On 'Real' and ';Sticky-Price'. Theories 'of the Business Cycle", Journal of Money, Credit and Banking, Vo1.l8, NoA."

Nelson, C and Plosser, C. (1982) '~Trends :and Random lWalks in Macroeconomic Time Series"; Journal of Monetary Economics. '

Plosser, C. I. (1990) "Money and Business Cycles: A·Real Business Cycle Interpretation" , in Phelps, Recent Developments 'in Macroeconomics VoU. " ,

Prescott; E.,C. (1986) "Theory ahead of. Business Cycle ,Measurement", in ;<'':' Hoover The New Classical Macroeconomics, VoU. ::::.: Scarth; W.M. (1988) Macroeconomics: An Introduction to AdvancedMethods,

Harcourt Brace Jovanovich.·,· '; " .. ' , Snowdon;,B., Vane, H. and Wynarczyk,,·P. (1995) A Modern Guide to

;. . Macroeconomics, Edward Elgar, Aldershot..·. ,', '.; __ '.:. :. Summers, L. H. (1986) "Some Sceptical Observations on Real Business Cycle

't, • Theory", in Hoover, The New Classical Macroeconomics, Vo!. 3.

i \ ..... .: ~.


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