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Advanced Macroeconomics
University Lille 1
M2 EITEI
Thomas Weitzenblum
Organization of the course
• My name: Thomas Weitzenblum
• To join me: [email protected]
• To get the PPT presentations:
http://weitzenblum.free.fr
What will the course look like?
• If we can stick to the original plan, each 2
hours course will be devoted to a
theory/economic question,
• I will take care of the introduction,
• The rest of the course will consist in studying a
document that you will have previously read
Advanced Macro II: what’s in it??
• Prof. Ragot has focused on the economic
analysis of the long run dynamics,
• Therefore, we will analyse the short-medium
run implications of macroeconomic dynamics,
for the Advanced Macro course to be a
complete survey of modern macro.
(expected) plan of the course
1.
2.
3.
4.
An introduction to Real Business Cycle Theory
A 2-country RBC
Endogenous cycles,
Keynesian views of macroeconomic fluctuations:
fixed or staggered prices
5. The labor market: job creation and job
destruction
6. Monetary policy in a multi-country model
Remarks:
• Only 2 hours for each subject is a binding
constraint…
• Especially with the first topic, which is not a
particular application, but a whole field in
macro, with numerous applications…
• So, more likely than not, one of the previous 6
subject might be sacrificed… on the altar of
the total inelasticity of time supply…
Subject 1: RBC theory:
the modern view of competitive
equilibria in a fluctuating world
I. Introduction
• Attention to economic cycles has arisen quite
early: Clément Juglar, as early as 1860,
• The beginning of the analysis of cycles (as
opposed to the simple enumeration of crises):
– Descriptive: different types of cycles: Juglar, Kitchin
and Kondratieff,
– First attempts to understand the propagation of
shocks over time and sectors: Mitchell (1927),
– First attempts to tackle the statistical issue: how to be
sure that what we see as a cycle is really one?
Cycles or not cycles??
In 1927, Slutzky shows that what may appear,
visually, and statistically, as cycles –to be
defined…- may be the result of pure
randomness, deprived of any mean-reverting
mechanism:
A simple mobile average of a period-by-period
white noise does the job…
A simulated example
Frisch’s rocking horse
Ragnar Frisch (1933) proposes a new distinction
regarding the analysis of economic fluctuations:
• Fluctuations are due to shocks affecting the
economy,
• Consequently, an obvious distinction must be
made between the impulse of the shock (its
origin, its magnitude, its own temporal and
statistical characteristics) and its propagation
onto the economy,
• Very much like we distinguish between the stick
that hits a rocking horse (its intensity, etc…) and
the subsequent movement of the horse.
Frisch claims that this distinction originally belongs
to Wicksell.
What is the meaning/ the extent of this view?
• stochastic shocks are regarded as an essential source
of fluctuations,
• but, while shocks are exogenous, the response of the
economy, over time, over sectors, over types of agents,
will be endogenous: the structure of the economy
determines the nature of the propagation
 This suggests a clear departure from the
point of view that cycles may be fully
endogenous (they solely depend on the
structure of the economy)
 But it also clearly departs from the other
extreme view: that shocks are fully exogenous,
so that the whole macrodynamics is itself
exogenous
Simply because here, part of the story is
exogenous, and part is endogenous.
A simulated example:
Assume a type of Samuelson’s oscillator
(Investment depends on expected demand, and
the production function is linear in K):
I t  I 0   Yt 1  Yt 2 
Also assume that current consumption depends
on past income (1-period lag):
Ct  C0  cYt 1
This implies that the GDP dynamics is
characterized by the following second-order
difference equation:
Yt  C0  I 0  c   Yt 1  Yt 2
With a plausible parameterization, this gives rise
to damped fluctuations:
Yt
time
If additional stochastic shocks were to affect,
say, investment:
I t  I 0   Yt 1  Yt 2    t
with t being a white noise, that is a random
variable such that:
 its mean (rather, its expected value) is equal to
zero,
 its current realization t is independent from any
past one t-i,
 its has a Gaussian distribution, that is, its variance
is constant throughout the time
The response of the economy to this repeated
shocks might well look like the time series of
GDP in France, or the US.
What we have seen so far:
 The impulse-propagation view tends to be
prefered to the endogenous cycle one,
 It suggests to describe with as much precision
as one can the propagation mechanisms,
 But it of course requires too, and even
beforehand, to correctly model the exogenous
shock : as a random variable, it may be
characterized by persistence (or not), multilags (or not), etc…
• The RBC framework is very much the heir of
Frisch’s rocking horse,
• However, a word needs be said about the real
aspect of business cycles, which, of course,
opposes to nominal aspects of the business
cycle.
Real vs. Nominal cycles??
If RBC are named this way, it owes a lot to their initial
developments, and to Long and Plosser’s (1983) initiative;
However, the impulse propagation mechanisms can be
relevant with monetary disturbances as well as real ones.
Historically, the first « fluctuations at the equilibrium »
models were rooted in monetary policy, and…
Modern RBC models do take money and financial
considerations into account.
So that these models are not all focused on real sources
of fluctuations.
II. Facts on macroeconomic fluctuations
The various dimensions along which temporal
fluctuations do matter:
 The standard deviation of the variable, of course in
percentage points, dives an insight on how volatile the
variable is,
 Its auto-correlation, with respect to various lags and leads,
gives valuable information on the degree of persistence of
the variable,
 Its correlation with any other variable may be of interest.
Of course, its correlation with GDP comes first: it makes
the variable either procyclical, or countercyclical
But, even before all these considerations, how
can we obtain time series in such a format that
they are suited for revealing business cycle
properties?
The answer is: detrending time series first, and,
once detrended, fluctuations around the trend
may be analyzed.
Trend and fluctuations around the trend in the US
U.S. business cycle characteristics
III. RBC: a basic framework
1) Uncertainty and intertemporel choices
We assume the absence of government, and a
closed economy.
Same assumptions as the Ramsey model.
In particular, no market imperfection (no
externality, or imperfect information).
This implies that the equilibrium is Paretoefficient in a Ramsey model. The exogenous shifts
in the productivity parameter will not change
anything in terms of efficiency
 The dynamic equilibrium of the economy,
subject to aggregate shocks, is optimal.
This does not mean that agents like fluctuations,
but that, given that there are fluctuations, the
decentralized equilibrium cannot be
outperformed.
This has another essential implication:
The resolution of the central planner’s program, or
that of the decentralized equilibrium, will lead to
the same results:
We can choose whether we explicitly describe the
behavior of individuals, facing prices, or the optimal
allocation of the planner.
Caution:
this is not true for all RBCs, since many, of course,
are going further and do introduce government
spendings, distorsive taxation, externalities, etc…
The setting
A 2-period economy.
The uncertainty takes the form of 2 possible
states of nature for date 2.
Agents can by claim to 1 unit of date 2consumption depending on the state of nature
(high h or low l). To each state is associated a
probability: l and h =1- l
Markets are said to be complete.
Agents are all alike, and there is a continuum, of
measure 1, of such agents.
Each is endowed with an endowment : w1 at
date 1, and produces according to the function:
y2  ei f (k )
Where ei is the productivity shock (el < eh) and k
is the individual date 1 investment.
The aggregate endowment is identical to the
individual one (agents’ measure equals 1).
Agent’s preferences (no leisure):
Agents live for 2 periods, and the utility is
separable with respect to time:
U  u c1   E u c2   u c1    l u c2l  hu c2h 
Agent’s program:
 
 
max U  u c1   E  u c2    l u c2l   h u c2h
 c1 ,c1

c1  pl d 2l  ph d 2h  k  w1


 l
l
s
.
c
.
c

d

 2
2  el f ( k )

 h
h
c

d

2  eh f ( k )
 2

The intertemporal budget constraint writes:
c1  pl c2l  ph c2h  k  w1  pl el f (k )  ph eh f (k )
Standard program (with 3 goods):
Optimality condition:
agents equate the marginal rate of substitution
with the relative price…
 
l
2
TMS1/ 2l
u' c
  l
 pl
u ' c1 
TMS1/ 2 h
u ' c2h
  h
 ph
u ' c1 
TMS 2l / 2 h
 
 h u ' c2h  ph


l
 l u ' c2  pl
 pl el  ph eh  f ' (k )  1
• Agents can individually perfectly insure
themselves against the uncertain future
However, if all agents are alike, they will all try to
perfectly insure, raising the relative value of the
good they want to buy (low) and lowering that
of the other (high).
In the end, we know that perfect insure is
impossible, because the global endowment at
date 2 depends on the state of nature.
Agents will all behave similarly, and similarly to a
representative agent whose consumption is the
average of the agents’.
This representative agent behaves like Robinson
Crusoe on his island: he is alone, so cannot
exchange with anyone.
He simply consumes, at each date, his
endowment (he would probably invests, if he
was allowed to…).
The Euler Equation of the agent writes:
 
 


u ' c2l
u ' c2h
  l
el   h
eh  f ' (k )  1
u ' c1 
u ' c1  

 u ' c1     l el f ' (k )u ' c2l   h eh f ' (k )u ' c2h

 
 u ' c   E e f ' (k )u ' c 
1
i
i
2
 
1  r  ei f ' ( k )
i
2

  
E u ' c   cov1  r , u ' c 
 u ' c1    E 1  r2i u ' c2i

u ' c1    E 1  r2i
i
2
i
2
This is the Euler equation (or the Keynes-Ramsey
condition) for the discrete-time uncertainty
augmented Ramsey model.
The new term is the covariance: when the
productivity shock is high, so is the interest rate,
consumption is high too, but then its marginal
utility is low
 The covariance is negative.
i
2
What can be understood from these calculations?
In an uncertain world, expected value do matter,
but they are not the whole story: the covariance
must not be forgotten.
The Euler equation has a similar form here, to that
in deterministic models.
And, very important, we know that we can resort to
the representative agent (rigorously, the marginal
rate of substitution needs be homogeneous of
degree 0 with respect to consumption at different
dates).
The next step: adding leisure.
Absolutely necessary: otherwise, the
fluctuations of output would be only caused by:
 The productivity shock, which is exogenous,
 The investment behavior of the agents, who take
advantage of a positive productivity shock,
whenever it occurs.
However, we may notice that this simple model
already contains, qualitatively, if not
quantitatively, the mechanisms pertaining to the
rocking horse…
The productivity shock may hit the economy only
once, but…
…agents’ reaction will be to save/invest more at the
time productivity is high.
Otherwise, if they did not save more, they would
simply increase their current consumption.
This would break the smoothness of the
consumption path.
 Agents decide to save part of the increase in
productivity, to take advantage of a higher
consumption during several time periods.
Since investing increases the capital stock, this
means that future capital levels will be higher
than their long-run target
 Future GDP will also be higher, even if the
productivity shock is gone
 This model, however simple, manages, at least
qualitatively, to create some form of persistence
in the dynamics of output and capital.
This is precisely what is intended: data show a
considerable amount of persistence, so the
model has to contain the mechanisms creating it,
otherwise the persistence would be solely due to
the exogenous shock.
As was already noted, the next step consists in
adding leisure (cf. Romer, chapter 4):
A 2-period model, without uncertainty (to start
with…).
The intertemporal utility function is:
U  u c1 , l1   u c2 , l2  
ln c1   b ln 1  l1    ln c2   b ln 1  l2 
The productive sector: a large number of
identical firms, with a Cobb-Douglas production
function:
A constant rate of capital depreciation .
Factors earn their marginal productivity.
And the intertemporal budget constraint:
1
1
c1 
c2  w1l1 
w2l2
1 r
1 r
The optimality condition writes:
1  l1
1
w2

1  l2  1  r  w1
Another optimality condition:
w1 1  l1   bc1
In the presence of uncertainty, one obtains the
same equation as one put forward previously:

1
1 

 E  1  rt 1 
ct
ct 1 

In the case of total capital depreciation between
2 consecutive periods, the saving rate can be
proved to be constant, as well as the labor
supply.
Advantage of the simplifying assumptions:
Enabling for a closed-form solution.
Great inconvenient: labor supply does not
depend on the current wage: no intertemporal
substitution of labor.
This model will not generate enough volatility,
and not enough persistence.
It is now your turn to work a bit…
Here are the following questions, that await
answers from you all:
1) What is the general principles for solving
numerically more complex RBC models?
2) How are the coefficient of the log-linearized
version of the model found?
3) What is an impulse response function?
4) What is the impact of a 1% productivity shock
on the dynamics of the various variables of
interest?
5) What were the possible reasons of the
success of RBC models among economists
(compare with potential explanations from
another paradigm)?
6) What does it mean, to consider that per
capita output has a random walk component?
What does an RBC model endowed with such
a property tell us, in terms of short-run
dynamics?
7) With a standard RBC model, what variables
have their dynamics correctly mimicked by the
model? Which ones do not? Explain.