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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 19-20: The Real Business Cycle Theory
(RBC)
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Lecture Outline:
- Introduction to economic fluctuations;
- Main ingredients of a real business cycle model;
- Critiques to RBC;

Essential reading:
This Lecture Note
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Among those shocks there are also changes in economic policy,
fiscal and monetary
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So if we use the IS-LM model to
explain output fluctuations we are assuming that all fluctuations are driven by the
aggregate demand
...
However, all the shocks
in the AD-AS model we have considered were temporary, meaning their effects
disappear after a while (the output goes back to the natural level, and the natural level
does not change because of those shocks)
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If no, we have to find something different
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F

F

The idea is the following: suppose that the real GDP series can be modelled using one
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Nelson C
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and C
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Plosser (1982) “Trends and random walks in macroeconomic time series:

Some evidence and implications”, Journal of Monetary Economics, vol
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139-162
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Equation 1) tells you that y t has a trend
and it differs from the trend in each period because of a random shock
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The trend line in equation 1) is captured by the term β t (that is a straight line),
any deviation from that line is due to ε t
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What is the main difference between model 1) and model 2)? In model 1) a shock at
time t ( ε t ) has an effect on the level of y at time t and that’s all
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In model 2) all the shocks are permanent, their effect will never disappear
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For time t-2 it must be true that: y t − 2 = α + y t − 3 + ε t − 2 etc
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If we substitute y t −1 = α + y t − 2 + ε t −1 into model 2) we have:

y t = α + α + y t − 2 + ε t + ε t −1
...
+ ε t −1 + ε t

3)

Shocks that happen many periods in the past (like ε 1 ) still have an effect on y at
time t
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Nelson and Plosser (1982) in looking at US time series data of the real GDP found
that model 2) is more appropriate in describing the behaviour of the real GDP in US
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This is the first step to understand Real Business Cycle (RBC) theory
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A shock that shifts the vertical aggregate supply changes the natural
level of output and so it affects the real GDP permanently
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How can it be that short-run movements of output are explained by movement
in what we call the long-run aggregate supply?
Remember that we have defined the short-run as a period of time in which the
aggregate price level is fixed
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We are back to the Say’s law that Keynes denied in his
General Theory
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While the results of Nelson and Plosser have been taken by RBC theorists as evidence
that permanent shocks are the main source of economic fluctuations, the fact that

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temporary shocks like aggregate demand shocks are irrelevant is more debatable
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Main ingredients of RBC theory

RBC theory tries to explain economic fluctuations using shock on the vertical
aggregate supply
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The real
GDP in the long run is given by the aggregate production function:

Y = A × F (K , L)

4)

Where Yt is the output produced according to the production function that depends on
the amount of capital (K), the amount of labour (L) and the level of technology
captured by the variable A
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So, shocks on the right hand side of 4) are shocks that will affect the natural level of
output
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Empirical evidence tells us that movements in
capital or labour (= movement in population) tend to be quite smooth, and so it is
difficult to think that shocks on those variables can create much of the fluctuations we
see every period in the real GDP
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Is that true empirically?
In the following graph we plot the growth rate of output year by year and growth rate
of the Total Factor Productivity (or Solow Residual)
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In equation 4)
this is equivalent to term A
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For example: in order to produce output you need labour and capital, but also
technological progress has an important role
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etc
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This may imply that indeed shocks on total factor productivity can drive changes in
real output
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A simple way to find total factor productivity is to estimate a production function
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Taking the logs in each
side you have: ln( Y ) = α ln( K ) + β ln( L ) , that now is a linear equation
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But if you estimate a linear regression you
have also a residual
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So, if you estimate ln( Y ) = α ln( K ) + β ln( L ) + ε you
have an estimate of the residual, and that residual can be considered a measure of
technical progress or what we have called total factor productivity (now it is clear
while total factor productivity is also called the Solow residual, because it is found as
a residual of an estimated regression)
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The first ingredient of RBC theory is that economic fluctuations are driven by
changes in the growth rate of total factor productivity that results from changes in

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technological progress
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How can it be?
All technological changes eventually increase productivity growth
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The second ingredient is the assumptions that all markets are perfectly competitive
and prices are always flexible and agents in the economy have Rational Expectations
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The idea is
that we are in the “Classical case” all the time
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Moreover the Policy Ineffectiveness Proposition we discussed in the
previous lecture note about new classical macroeconomics will hold here
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The third ingredient is the use of microfoundations to derive the macroeconomic
behaviour of different variables
...
etc
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The problem faced by
consumers and firms is a problem of intertemporal optimization
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They use numerical methods
and an approach called “calibration”, to simulate numerically the models
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Summary:
1) Economic fluctuations are driven by changes in total factor productivity
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We normally assume that all consumers in the economy have the same preferences,
meaning they are all equal
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The same for firms
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This is for simplicity
since it avoids the problem of aggregation
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Assume that the
representative consumer lives forever (instead of a consumer you can think in terms
of a household)
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The
problem of a consumer at time 0 is to choose consumption and leisure in every period
in order to maximise his discounted expected life-time utility subject to some
constraints
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The production function used by the representative firm to produce is:

Y t = At F ( k t , h t )

6)

Where At denotes the level of technological progress at time t, kt is the level of capital
and ht denotes the level of labour (h for hours worked)
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The parameter ρ > 0 measures the persistence of
technology shocks
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Notice that the general price level (that would be the price of consumption and the
price of output) does not appear in the model, indeed it is like we have normalised to
1
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Representative consumer maximises its intertemporal utility subject to the
constraints 7), 8) and 9), while the representative firm maximises the present value of
profits
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The Propagation Mechanism: the Intertemporal Substitution of Labour Supply
All theories of the business cycle choose to interpret fluctuations in economic activity
as emanating from some hypothesized source called the impulse mechanism (like the

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demand and supply shocks in the AD-AS model), which is usually modelled as an
exogenous stochastic process
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In the RBC theory the impulse mechanism is given by shocks on Total Factor
Productivity (or equivalently shocks on technological progress), while the propagation
mechanism is given by the Intertemporal Substitution of Labour Supply
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People compared the return from working in the current period (given by the
current wage) and the expected return from working in a later period
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If your aim is to get a First in a
given module you should work hard almost all time
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The reason is that you may think that the return
from studying close to the exam is probably higher than the return from studying
when the exam is a long time away
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To
compare current wage with future expected wages we need to look at the present

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value of future expected wages
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Suppose
that the current real wage is £1 per hour
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06
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05, then working harder now and
less next year it is good, since you can get a higher real wage (1% higher)
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Then a £1 earned now will
worth £1
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If next year real wage is £1
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This example tells you the following: in deciding how much to work in every period
the workers look at the relative real wage in different periods (for example the real
wage today with the expected real wage tomorrow) and the real interest rate matters
in that decision
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A Graphical Representation of the RBC Mechanism
The RBC mechanism works as follow:

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1) First there is an exogenous (unexpected) shock on total factor productivity;
2) Since the marginal productivity of capital and labour changes, investment
demand and labour demand by firms will change;
3) Since the marginal productivity of labour changes, then the real wage offered
to workers will change
...
Those two effects will affect
the way workers will supply labour according to the intertemporal substitution
explained above;
4) Fact 3) magnifies the effect of the shock into the economy affecting the level
of real output;
Consider a negative technological shock
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Firms expect future profits
to fall and marginal productivity of labour to fall
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This creates a decrease in
the demand for capital (or demand for investment) and in the demand for labour
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What happens in the labour market?
This is shown in the following graph:

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LS1

Real wage

LS

w*
w1
LD
LD1
L*

L1

L

Labour demand decreases from LD to LD1
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The final effect is a big decrease in employment and also a decrease in real wage
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This is
consistent with the beliefs of RBC theorists
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Employment decreases, and so output will decreases
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LRS1

P

LRS0

P*
P1
AD0
AD1

Y1

Y*

Y

Before the shock we are at the equilibrium P*, Y*, where Y* is the natural level of

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output before the shock
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Real output produced decreases and the Long Run Aggregate Supply
shifts to the left to LRS1, However, also aggregate demand will decrease
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Therefore, aggregate demand shifts to AD1
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So now we have a
recession, the natural level of output is now lower than before and the aggregate price
level is also lower
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This means for example that a recession is just the optimal response of the economy
to a negative shock in technological progress
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Therefore, as you may expect
governments should not intervene in the economy to smooth fluctuations because if
they do it they will simply create inefficiencies
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Does RBC theory fits well the data?
The implications of RBC theory are quite strong
...

To fit data about business cycles we need to start by saying what are the main stylized
facts about business cycles we get from data
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In terms of volatility, during a fluctuation (a recession or a boom) we have that:
1) Consumption is less volatile than Real GDP;
2) Investment are around 3 times more volatile than Real GDP;
3) Employment has the same volatility as Real GDP;
4) The real wage is less volatile then Real GDP;
In terms of co movement we have:
1) Consumption is procyclical;
2) Investment are procyclical;
3) Employment is procyclical;
4) Real Wage is procyclical;

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We would like RBC theory to fit those stylised facts
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Therefore RBC theorists came
out with the idea of simulating the models using numerical methods
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We then have a bunch of dynamic
equations that we would like to solve to find the equilibrium values of the endogenous
variables as a function of the exogenous variables
...
etc
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For example suppose the following dynamic
equation:
y t = α + β y t −1 + ε t
Suppose that you know that from real data α = 1 and β = 0
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Then you need a
random generator number (available in many software) to draw the value of ε in
each period
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5 y 0 + ε 1
Suppose that y 0 = 1 , that is the starting point and that ε 1 = 1
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5 (1) + 1 = 2
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Then you can find the value of y in
the second period as well since:
Suppose that ε 2

y 2 = 1 + 0
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5 , then:
y 2 = 1 + 0
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5 ) − 0
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And so on
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Once you have such a series of data you can calculate the volatility
of that series (you just need to calculate the standard deviation of the series) and
performing any other calculations
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For example suppose that one of the first order conditions of the model tells you:
w×h
1−α =
y
where α is a parameter of the model and w × h is the real wage multiplied by the
hours worked (so it is labour income) and y is real GDP
...
6 is the share of labour income on total income
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4
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So RBC theorists can find artificial data for real output, consumption, investment,

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employment, etc
...
from the model and then look if those artificial data do fit the
behaviour of the real data
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81

1
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74

0
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93

2
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99

0
...
38

0
...
16

0
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σ C / σ Y is the relative standard deviation of consumption compared to real GDP
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In terms of co-movements the RBC theory is consistent with pretty much all the
stylised facts outlined above
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This result creates the famous statement by Prescott that: “aggregate
fluctuations are not just consistent with a competitive neoclassical model, but are
predicted by such a model”
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For example, the main driving force of business cycles is changes in
technological progress
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However we do not observe large productivity shocks in every period
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For example a problem in measuring technological changes using the Solow Residual
is the phenomenon of Labour Hoarding
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This implies that labour input is overestimated during

2

Kydland and Prescott introduced the idea of Real Business Cycle
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recessions simply because workers do not work as hard as usual
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Moreover, the intertemporal substitution of labour supply should be big to magnify
the effects of a shock
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Critics claim that:
2) According to data the elasticity of labour supply is normally less than 1,
meaning that decision to supply labour is not very sensitive to changes in
wages;
Another implication of the model is that unemployment can be only voluntary
...
However:
3) high unemployment observed in recessions is mainly involuntary;
In RBC theory money supply has no role in affecting real variables (from this the
name of Real Business Cycle)
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Critics claim that in the data we see that:
4) reductions in money growth and inflation are almost always associated with
periods of high unemployment and low output
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RBC proponents argue that the degree of price stickiness occurring in the real world is
not important for understanding economic fluctuations
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Critics claim that:
5) wage and price stickiness explains involuntary unemployment and the nonneutrality of money
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Moreover, RBC theory
is a theory that explains business cycles in a way that is consistent with economic
growth (a change in the natural level of output over time)
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Moreover, methodologically the RBC theory by introducing Dynamic Stochastic
General Equilibrium 3 model based on microfoundations has become the standard way
of performing modern macroeconomic analysis
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