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Describe the stylised facts of BC behaviour. Can the RBC explain these?

It was noticed long ago that economic activity, together with some other indicators experiences cyclic movements along its trend. This essay is about the cycles that occur with roughly 4-10 year period. They are very uneven, some economists argue that the series are even stationary with drift. There are numerous features about the cycle, like the fact that long periods of slow growth are followed by short and intensive downturns. However, in this essay I am going to consider the fact that several economic measures move together and how the RBC theory can predict the co-movement of these variables.

First there is the real economy. It is quite clear that the level of national income exhibits cycles. However, different sectors of the economy tend to have similar output movements. The investment and production of durables is positively correlated with the output movement, however, its amplitude is a lot larger. Consumption and capital stock are also moving with GDP. However, they have less variance.

Secondly there is the monetary economy. Monetary variation is not that much correlated with the level of output than the real economy and the correlation differs across economies. The velocity of money (the time it takes for the stock of money to turn over) is counter-cyclical. Short-term interest is positively correlated with GDP. However, long-term interest is stationary. Prices (more the change in prices or inflation) tend to be counter – cyclical. The inflation tends to fall in recession.

Thirdly there is the labour market. Employment tends to move together with output, with unemployment rising in the recessions and wages remaining relatively stable. Productivity also moves with the cycle. It has less variability than output.

There are some other facts that move together with output, which I am not going to go into at present. Most notably, the balance of payments and terms of trade are counter-cyclical.

RBC model is set out to explain these cycles by saying that they are caused by technology shocks (initiation), followed by propagation stage that lasts a couple of years, making the variables look cyclical.

RBC model based on a neo-classical general equilibrium model of the economy. It has grown out of the Solow-Swan model of economic growth which analyses economy in the general equilibrium model. It depicts economy where people have rational expectations and they maximise utility. Unlike in New Keynesian theory of cycles where search costs, monetary shocks and imperfect competition causes cycles, in the RBC theory all the cycles are happening in perfect competition. All the shocks that create cycles are real and caused by three main things: technological change, productivity shocks and government activities.

Thus the theory talks about supply side factors (unlike Keynes with its Aggregate demand being affected by investment). The models use a representative agent that optimise subject to technology and resource costs. Thus technology is taken as exogenous and when the technology changes, the production function will shift. This will create an effect on national income that is amplified by intertemporal substitution between leisure and work. Thus when technology increases productivity, then workers will be paid more, they want to work more and they will produce even more.

This shock impact is translated to economy by propagation mechanisms that spread its impact and explain many of the stylised features of the business cycle.

Firstly there is the permanent lifetime income hypotheses whereby people like to smooth out their consumption. An increase in income (caused by the shock) will lead to more savings (thus investment) and relatively smaller increase in consumption.

There are also lags involved in investment. This will mean that firms will initially deplete their inventories and then start investing heavily to restock.

Thirdly there is the leisure substitution. However, in order to fit the empirical data, RBC model has to assume that all the technological shocks are permanent. And when the shocks are permanent there is no intertemporal substitution.

These show clearly why the investment is more variable than the income. However, in order to explain the other stylised features I will have to construct a simple RBC model.

As the model is simply an aggregation of representative agents, following Stadler, the model world will consist of identical infinitely lived agents that I assume produce just one good. There are no frictions, no money or government. Each agent’s preferences are

where b, ct and lt are a discount factor, consumption and leisure. E is expectations operator. Technology is described by constant returns to scale:


where y is output, k is capital left over from the previous period, n is labour and z is a strictly positive stochastic parameter that follows  a stationary Markov process. The capital stock evolves according to:


where d is the depreciation rate and i the gross investment. In a one good model everything not consumed is the capital stock next period. Agents face two constraint – time and income constraint:


h is total endowment of time.

Solution is the agents’ optimisation. If everyone is rational, one makes decisions only by looking at the probability distribution functions. Everyone knows current z and all markets clear. Maximising (1) s.t. 2-4 gives:

subscripts denote partial derivatives. The first equation equates the marginal utility of consumption to the shadow price of output, the second the marginal disutility of labour to labours marginal product – the real wage and the third the marginal product of capital to its oportunity cost in terms of consumption foregone. It is now possible to solve for the time paths of c k and n. For specific solution assume that capital depreciates fully in one period and we have log linear utility and cobb douglas production.

Solving that gives

These equations are intertemporal in nature. A temporary change in z produces not only a change in current consumption, but also in capital stock, which propagates the effects of the shock. A rise in productivity will raise the capital stock and consumption for several periods causing the model to exhibit cycles. These RBC models capture the fact that consumption is more volatile than output, and investment is even more volatile. However, they over-predict the correlation between productivity and output. This is called the productivity puzzle. If shocks are due to productivity changing, then the output and productivity should be correlated. However, empirically they are not. Thus RBC models have to include number of measures to reduce this correlation. It is mainly done by introducing labour supply shifting factors (productivity is labour demand side). They are nominal wage stickiness, taste changes, government spending causing negative wealth effect, home production changes due to productivity changes, and hoarding labour during recessions.

Second main puzzle is the employment variability one. While real wages remain constant, the employment changes over the cycle. This would mean a very “flat” labour supply function, however, there is no empirical evidence for that. I think one needs to take Keynes’ theory of sticky wages into account in this matter. Also, the indivisibility of labour argument goes a long way towards explaining employment changes. It also explains the unemployment and why labour share in GDP changes over productions cycle (in simple RBC with Cobb-Douglas production, it should be constant). Basically instead of adjusting the hours of work flexibly, people can either work or become unemployed. This makes the marginal utility of leisure constant, not variable over the cycle. Thus for representative agent, the marginal benefits and costs of employment are not equal at every period. People will have infinite elasticity of substitution for leisure, not diminishing and this will create all the anomalies.

Unemployment can also be incorporated by two other means to the RBC. Voluntary UE can be accounted for by the New Keynesian search cost argument, and involuntary by risk sharing employment contracts. However, I will not go into these in this essay.

Finally I have not talked about how RBC can explain the monetary variation. There are two ways of introducing money to RBC – by relying on Walrasian framework, or not. Although the latter approach seems more promising in real world, it is too difficult to go into depth at present and includes introducing nominal restrictions to the RBC model. In Walrasian framework one gets the necessary correlation by assuming that the financial services are produces lot more rapidly than the goods. Thus financial innovations will ensure that when productivity increases, before the investment can increase, the short-term interest will go up.

As seen, RBC can explain much of the facts of business cycle, without departing from Walras General Equilibrium system. That is very appealing to economists. However, it does so only after numerous post-mortem additions to the model to make it fit the facts. And RBC has got many criticisms, both methodological and ideological.

Main methodological snag is the aggregation issue. In real life macroeconomy behaves differently from micro, and just aggregating by using a representative agent will not do. There are also no evidence of periodic economic shocks over time.

On ideological side RBC does not explain the periodicity of cycles. There are no propagation mechanisms of cycles over time. Recessions can only occur with several technological shocks in a row, and there is no empirical evidence for that. And lastly, by using aggregation one can not take income distribution questions into account when analysing economies by RBC. Thus RBC theories can only be used as a complement for more fully developed endogenous growth and Keynesian macroeconomic models.


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