Lecture 5: March 3, 2025

The Real Business Cycle Model (RBC)

Macroeconomics EC2B1

Eran Yashiv

London School of Economics, WT 2024/2025

February 26, 2025

Reminder: Business Cycles (from EC1B1 notes)

Business Cycles
• Recurrent but not periodic
• Last approximately from 2 to 10 years
• Phases:
– Expansion phase (trough to peak)
– Contraction phase (peak to trough)
• “Official” arbiter:
– Business Cycle Dating Committee of the National Bureau of Economic
Research in the US
– In the UK according to Office of National Statistics: recession is two
consecutive quarters of -ve GDP growth
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Reminder: Business Cycles (from EC1B1 notes)

Business Cycles
• Useful to de-trend output and focus on deviations of output
from trend
• We think of trend output as “potential output” or the “natural
rate of output”
• We define the output gap as percentage deviations of output
from potential output
𝑌 −𝑌 ത 𝑌𝑡
𝑌෨𝑡 = 𝑡 ത 𝑡 ≈ log
𝑌𝑡 𝑌ത𝑡

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Reminder: business cycles (from EC1B1 notes)

UK Deviations of Output from Trend

Percent Deviation of Output from Trend (light line is higher frequency estimate)
Source: Office of Budgetary Responsibility
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Plan (based on Ben Moll lecture notes)

1. Very brief history of business cycle macro modelling until the 1980s

2. A two-period real business cycle model = the model from lecture 4

3. The fully-fledged Real Business Cycle model

4. Criticisms of the RBC model

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Readings

1. EC1B1 lecture notes, in particular lecture 6

2. Kurlat, chapters 12 and 13

3. Jones, chapter 15 “DSGE Models: the Frontier of Business Cycle Research"

4. NPR Planet Money episode on Bob Lucas and Lucas critique

https://www.npr.org/2023/05/17/1176781995/the-man-who-busted-the-inflation-employment-myth

5. Ivan Werning (2023) “Lucas Miracles" https:

//economics.mit.edu/sites/default/files/inline-files/Translated%20Lucas%20Miracles%20by%20Ivan%20Werning.pdf

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A brief history of business cycle macro
modelling

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A brief history of business cycle macro until the 1980s
As with all attempts to fit complex history into simple narrative, won’t do justice

Some key models and ideas you should know:

• 1930s: Keynesian model (Keynesian cross, IS-LM or IS-MP-PC)

• 1970s
• Lucas critique and importance of microfoundations
• rational expectations

• 1980s: real business cycle (RBC) model

• (to be continued in later lectures)

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1930s: Keynesian model
• Macroeconomics becomes separate field in 1930s, starting with Keynes

• Keynes (1936) “The General Theory of Employment, Interest and Money"

• Keynesian cross and IS-LM model (or its modern incarnation = IS-MP-PC)

• One key policy prescription: countercyclical fiscal policy, i.e. provide fiscal stimulus
in recessions

• Most common methodology until 1970s: large-scale macroeconometric models

without microfoundations (i.e. no utility or profit maximization)
• write down big models with many equations like Keynesian consumption
function C = α + γ(Y − T ), Phillips curve, etc
• estimate these equations using time-series data
• conduct policy counterfactuals, e.g. monetary & fiscal policy
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Aside: Keynesian IS-LM is actually due to Hicks (1937)

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1970s: Lucas critique and importance of microfoundations
• Critique of 1970s-style macroecometric models without microfoundations
• Lucas (1976) “Econometric Policy Evaluation: A Critique". Idea:
• you cannot use these macroeconometric models for policy evaluation because
the parameters are not policy-invariant
• i.e. you’d expect these parameters to change when policy changes
• in a nutshell: behavior changes with the rules of the game. Models must allow
for this.

• Lucas aims critique at Phillips curve estimated with historical data & “the inference
that permanent inflation will induce a permanent economic high"
• ... but the point is much more general
• coffee-drinking example in NPR podcast
• Tom Sargent’s (1980) American football example
https://researchdatabase.minneapolisfed.org/downloads/kh04dp86z
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Lucas (1976) lays it out nicely

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Example: our models predict that MPCs not policy-invariant
• Recall microfounded consumption model from Lecture 3
• MPC out of transitory income shock
( )σ
1
∂c1 β (1+r )
(1 + r )
= ( )σ
∂y1 1+ 1
(1 + r )
β (1+r )

where r = interest rate, β = discount factor, σ = IES

• So can write a consumption function
( )σ
1
(1 + r )
β (1+r )
c1 = γy1 + ..., with γ= ( )σ
1 + β(11+r) (1 + r )
• Example of policy tool: interest rate r
• Clearly when r changes, MPC γ changes ⇒ when interest rates change drastically,
may no longer want to use historical MPC estimates
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Lucas’ solution = microfoundations
• Build models of individual behavior starting from policy-invariant primitives
• Which ones? Answer: primitives of classical microeconomics
• preferences
• technology
• resource constraints

• Preference and technological parameters are sometimes called “structural

parameters" where “structural" means “policy-invariant"
• examples: discount factor β, IES σ

• To think about: how satisfactory is proposed solution in practice?

• If a model is misspecified, can we treat primitives as policy-invariant?
• Is a model with a representative household really “microfounded"?
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Rational expectations

• Separate idea often mentioned together with Lucas critique, likely because pushed
by same economists (Lucas, Sargent & co) around same time
• People often use term “rational expectations revolution", often (not always) they
actually mean push for microfoundations
• Lucas critique and microfoundations are really the more fundamental & influential
ideas – “microfoundations revolution"?

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• Werning on Lucas: “Lucas was a visionary not for importing rational expectations into
[macro], but for understanding that GE theory was the basis for completely refounding
macroeconomics."
• Blanchard on Lucas:
https://www.tandfonline.com/doi/full/10.1080/09672567.2022.2137552
“[What Lucas did] was to define the rules of what a macro model had to be: It had to be
dynamic; it had to have general equilibrium; it had to have optimising agents; then it had to
have expectations, in that case rational expectations, but that was not essential."

“The widely accepted notion was that macro was different from micro because of
aggregation, because of complex behaviour, because of all that. You were inspired by theory,
but you surely didnt feel like you actually had to derive things from first principles. And
I was always struck by my revered colleague Paul Samuelson, who, when he did micro, did
it absolutely rigorously. And when he did macro he just wrote equations down which
sounded right, and that was thought to be the only way to go."

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Rational expectations

• While we’re at it, let’s also define “rational expectations" ... but first need some
language
• stochastic = there is uncertainty, i.e. something is a random variable
• rational = people and firms maximize some objective function

• Rational expectations = people know the correct probability distribution of

stochastic economic variables

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Rational expectations
• Example: throwing a fair coin
• rational expectations = people know that Pr(heads) = Pr(tails) = 0.5
• ... use this to compute expected utility 0.5 × U (heads) + 0.5 × U (tails)

• Rational expectations = same idea but applied to everything, e.g. you know correct
probability distribution of everything in entire economy
• clearly a very strong assumption
• but definitely does not say people always get it right or the like (which is
what’s sometimes stated in cheap criticisms of economics)
• “rational expectations" does not imply “rationality" or vice versa
• better word: “model-consistent expectations"
• much more controversial than Lucas critique which most economists agree
with (though not necessarily with the proposed solution)
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A Nobel prize for rational expectations & microfoundations

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https://www.nobelprize.org/prizes/economic-sciences/1995/summary/

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1980s: the Real Business Cycle (RBC) Model
• Developed in the 1980s, following the “rational expectations revolution"
• The first fully-fledged microfounded business cycle model
• Key paper by Kydland and Prescott (1982)

E C O N O M E T R I C A
VOLUME 50 NOVEMBER, 1982 NUMBER 6

TIME TO BUILD AND AGGREGATE FLUCTUATIONS

BY FINN E. KYDLAND AND EDWARD C. PRESCOTT1

The equilibrium growth model is modified and used to explain the cyclical variances of
a set of economic time series, the covariances between real output and the other series, and
the autocovariance of output. The model is fitted to quarterly data for the post-war U.S.
economy. Crucial features of the model are the assumption that more than one time period
is required for the construction of new productive capital, and the non-time-separable 20
Why Real Business Cycle Model?

Reminder: “nominal" and “real"

• Nominal: not adjusted for inflation, i.e. money values
• Real: adjusted for inflation, i.e. quantities valued such that they are comparable
over time – think “physical" quantities

Why real business cycle model?

• because money and nominal variables play no role in it
• in contrast to Keynesian theories – see next lecture and your EC1B1 and EC1P1
notes

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A Nobel prize for the RBC model

https://www.nobelprize.org/prizes/economic-sciences/2004/summary/

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Reading suggestions for those who like old papers and drama (not
examinable)
• Lucas and Sargent (1979) “After Keynesian Macroeconomics"
https://www.bostonfed.org/-/media/Documents/conference/19/conf19d.pdf

• don’t miss discussion by Ben Friedman, Lucas & Sargent response

• 1978 Boston Fed conference “After The Phillips Curve" for which paper was
written https://www.bostonfed.org/news-and-events/events/economic-research-conference-series/
after-the-phillips-curve-persistence-of-high-inflation-and-high-unemployment.aspx

• ... and Sargent’s recollection of conference here

http://www.liuyanecon.com/wp-content/uploads/Sargent-2022.pdf

• Summers (1991) “The Scientific Illusion in Empirical Macroeconomics"

https://www.jstor.org/stable/3440321

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A Two-Period RBC Model

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Model from lecture 4 = baby RBC model

• Key idea of RBC model: (random) variations in productivity (TFP) as source of

business cycles
• changes in productivity drive output, investment, consumption, ...

• Solow model emphasized TFP as source of growth

• .... now emphasize variations in TFP as source of business cycles

• The model of lecture 4 had exactly these features

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Recall: primitives of baby RBC model
• Preferences: households have utility function

C 1− σ − 1
1

U (C1 ) + βU (C2 ) with U (C ) =

1 − σ1
• Technology: firms have production function

Yt = At Kt , t = 1, 2

and capital accumulates according to K2 = I1 + (1 − d)K1 with d = 1, i.e.

K2 = I1
• Resource constraints (feasibility):

goods in period 1: C1 + I1 = Y1
goods in period 2: C2 = Y2

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Recall: competitive equilibrium allocation
( )σ
1
βA2 A2
C1 = ( )σ A 1 K1
1
1 + βA 2
A 2

A2
C2 = ( )σ A 1 K1
1
1+ βA2 A2
1
K2 = I1 = ( )σ A 1 K1
1
1+ βA2 A2
Y1 = A1 K1
A2
Y2 = ( )σ A 1 K1
1
1+ βA2 A2
1 + r1 = A2

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Recall: a recession due to a drop in A1 and/or A2

1. When A1 falls, all of (C1 , C2 , I1 , Y1 , Y2 ) fall unambigously

• C1 and I1 both fall because C1 + I1 = Y1 and Y1 = A1 K1 falls

2. When A2 falls and σ < 1, (C1 , C2 , Y1 , Y2 ) fall and I1 rises

• C1 + I1 = Y1 and Y1 unaffected, σ < 1 ⇒ income effect dominates

3. When both A1 and A2 fall (e.g. log A2 = ρ log A1 + ε 2 ), economic effect is

combination of effects in cases 1 and 2

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REMINDER: Oil shocks as productivity shocks (or gas shocks)
• What on earth is a drop in productivity?
• do we think people forget how to make stuff? Not really
• hard to come up with sensible justifications

• One possible justification: oil shocks or energy (gas etc) shocks

• Technology: firms use oil to produce
Ỹt = Ãt Ktα Ot1−α .
• Firms maximize output net of oil expenditure
Yt = max Ãt Ktα Ot1−α − pt Ot where pt = oil price
Ot
( )(1−α)/α
1−α
⇒ Yt = At Kt where At = effective productivity = α Ã1/α
t
pt
so an increase in pt causes a drop in effective productivity
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Room for policy in the baby RBC model?
• Suppose we introduce government spending into this model

goods in period 1: C1 + I1 + G1 = Y1
goods in period 2: C2 = Y2

• Should the government engage in countercyclical fiscal stimulus, i.e. increase G1 if

there is a recession (due to a fall in A2 )?

• Why or why not?

• How does this compare with policy prescriptions of the Keynesian model?

• What about other policies, e.g. investment subsidies, income taxes, ...?

• What about monetary policy?

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The Fully-Fledged RBC Model

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Primitives of the RBC model
• Relative to baby RBC model: infinite horizon, uncertainty, labor supply
• a “dynamic stochastic general equilibrium (DSGE) model"
• Preferences: households have utility function
∞
U (C0 , N0 ) + βE [U (C1 , N1 )] + β2 E [U (C2 , N2 )] + ... = E ∑ βt U (Ct , Nt )
t =0

Note: expectation E [·] because Ct and Nt are stochastic (because At is)

• Technology: firms have production function
Yt = At F (Kt , Nt ), t = 1, 2, ...
where At is stochastic (see next slide), capital accumulates according to
Kt+1 = It + (1 − d)Kt , 0<d<1
• Resource constraints (feasibility):
goods in period t: Ct + It = Yt , t = 1, 2, ...
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Evolution of the Technology
• At changes randomly over time
• ignore growth and just think of fluctuations around a trend

• Assume At follows the process:

log At = ρ log At−1 + ε t , ε t ∼ N (0, σ2 )

where ε t ∼ N (0, σ2 ) means ε t is normally distributed w mean 0, var σ2

• This process is called AR(1) process: “autoregressive of order 1"

• The parameter ρ governs persistence of changes in TFP

• if ρ = 1 they are permanent
• if 0 < ρ < 1 they are persistent but eventually die out
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 Economics 311 7

Examples of TFP Processes

Examples of TFP Processes
4

−2

−4

−6

ρ=0
ρ=0.7
ρ=0.99
−8
0 50 100 150 200 250 300 350 400 450 500

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Logic of RBC model: response to positive TFP shock
• Static effects of positive TFP shock:
• implies higher labor productivity, increasing wages
• substitution effect leads to higher labor supply, thus increasing output
• Dynamic effects of positive TFP shock:
• part of increased output is consumed, but part is saved
• the more persistent the shock, the more is saved
• return to capital ↑⇒ investment ↑⇒ capital stock ↑
• So for extended period: greater output due to labor, capital ↑ (plus TFP ↑)
• effects of single shock eventually die out, but they may be long-lived
• new shocks continually arrive
• Two key features of RBC model
1. amplification: small shocks generate large cycles
2. persistence: transitory shocks generate persistent cycles
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 Figure 10.03 Small shocks and large cycles
Small, transitory shocks generate large, persistent cycles

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Room for policy in the RBC model?
• No, because 1st welfare theorem holds

• Same logic as in baby RBC model

• In RBC model, business cycles are efficient

• the optimal response to a changing environment
• when productivity falls, it’s a bad time to produce, so households should work
and invest less
• government intervention can only worsen the allocation

• For more discussion, see Kurlat, chapter 13.5, section “Policy Implications"

• Come back to this at end of lecture

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Criticims of the RBC Model

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Criticisms of the RBC model
See the good discussion in Kurlat, chapter 13.5, section “Criticisms"

1. Mechanism for generating recessions not plausible (see next slides)

2. Need implausible parameter values, in particular implausibly high labor supply

elasticity

3. Model fits cyclical behavior of quantitities but not of prices

4. Model does not feature any unemployment

5. Inappropriate to treat measured TFP (Solow residuals) as productivity shocks, e.g.

due to mismeasured capacity utilization

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A hostile description of the RBC model (part 1)

Source: http://bactra.org/notebooks/dsges.html by Cosma Shalizi (statistician)

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A hostile description of the RBC model (part 2)

Source: http://bactra.org/notebooks/dsges.html by Cosma Shalizi (statistician)

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A hostile description of the RBC model: brief discussion
• To be clear: this description is basically correct
• But it is a bit unfair in that it somewhat misunderstands how economists think
about models – see “Modeling in (Macro)economics" in Lecture 1
• “descriptive realism is not the objective"
• idea of “crucial" or “critical" assumptions
• “Do not criticize an economists model because of its assumptions; ask how the
results would be changed if the assumptions that seem problematic were more
realistic."
• We teach this hostile description because
• it’s pretty funny
• some of these assumptions do turn out to be “crucial" assumptions
• ... i.e. when assumptions are made more realistic, results change, in particular
policy implications
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Key takeaways from RBC model

1. RBC model makes one pretty deep point: Just because something fluctuates doesn’t
mean it’s necessarily inefficient
• forces us to ask harder questions
• any argument for trying to stabilize the business cycle must first make the case
of why such stabilization is desirable
• an application of what we said in Lecture 2: 1st welfare theorem forces us to
think about rationale for policy intervention – what market failures, frictions,
externalities are there?

2. Methodologically, RBC model shows how a simple model can generate

amplification and persistence

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