Advanced Macroeconomics

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Advanced Macroeconomics

• University Lille 1
• M2 EITEI
• Thomas Weitzenblum

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Organization of the course

• My name Thomas Weitzenblum
• To join me thomas.weitzenblum_at_univ-lille2.fr
• To get the PPT presentations
• http//weitzenblum.free.fr

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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

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Advanced Macro II whats 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.

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(expected) plan of the course

1. An introduction to Real Business Cycle Theory
2. A 2-country RBC
3. Endogenous cycles,
4. 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

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• 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

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Subject 1 RBC theory the modern view of
competitive equilibria in a fluctuating world
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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?

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• 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

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A simulated example
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Frischs 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.

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• 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

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• 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.

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• A simulated example
• Assume a type of Samuelsons oscillator
  (Investment depends on expected demand, and the
  production function is linear in K)
• Also assume that current consumption depends on
  past income (1-period lag)

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• This implies that the GDP dynamics is
  characterized by the following second-order
  difference equation
• With a plausible parameterization, this gives
  rise to damped fluctuations

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• If additional stochastic shocks were to affect,
  say, investment
• 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

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• The response of the economy to this repeated
  shocks might well look like the time series of
  GDP in France, or the US.

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• 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), multi-lags
  (or not), etc

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• The RBC framework is very much the heir of
  Frischs 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.

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• Real vs. Nominal cycles??
• If RBC are named this way, it owes a lot to their
  initial developments, and to Long and Plossers
  (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.

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• 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

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• 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.

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Trend and fluctuations around the trend in the US
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U.S. business cycle characteristics
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• III. RBC a basic framework
• 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).

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• This implies that the equilibrium is
  Pareto-efficient 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.

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• This has another essential implication
• The resolution of the central planners 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

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• 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
  2-consumption 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.

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• 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
• Where ei is the productivity shock (el lt eh) and
  k is the individual date 1 investment.
• The aggregate endowment is identical to the
  individual one (agents measure equals 1).

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• Agents preferences (no leisure)
• Agents live for 2 periods, and the utility is
  separable with respect to time
• Agents program

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• The intertemporal budget constraint writes
• Standard program (with 3 goods)
• Optimality condition
• agents equate the marginal rate of substitution
  with the relative price

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• Agents can individually perfectly insure
  themselves against the uncertain future

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• 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.

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• 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

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• 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.

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• 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).

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• 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

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• 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.

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• 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.

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• 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

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• 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.

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• And the intertemporal budget constraint
• The optimality condition writes
• Another optimality condition

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• In the presence of uncertainty, one obtains the
  same equation as one put forward previously
• 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.

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• 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.

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• It is now your turn to work a bit
• Here are the following questions, that await
  answers from you all
• What is the general principles for solving
  numerically more complex RBC models?
• How are the coefficient of the log-linearized
  version of the model found?
• What is an impulse response function?
• What is the impact of a 1 productivity shock on
  the dynamics of the various variables of interest?

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• 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.

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