Dynare Toolbox 4 Matlab Introduction

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Dynare Toolbox 4 MatlabIntroduction

• Alon Binyamini
• 26 MAY, 2008

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Roadmap

• 1st / 2nd order Taylor approximation
• Technical intuition
• Economic intuition
• Dynare
• Background.
• Hands on.
• Procedural issues.

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Taylor Approximation

• Intuition
• 1st order linearization.
• 2nd order
• In 1st order we employ the derivative at a.
• Better to employ f a0.5(x-a).
• So, lets linearize the function f .

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2nd order technical intuition
Begin with 1st order
But, instead of f (a), take
Substituting instead of f (a), we get
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2nd order economic intuition

• Non-linear utility
• Diminishing marginal-utility
• gtgt The direction also matters (not only the size)
• gtgt Risk aversion
• gtgt Second moments of shocks also matter
• The more we can deviate, the lower is
  E(u).
• Non-linear technology
• Diminishing marginal-productivity
• gtgt Likewise

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1st or 2nd order approximation?

• 1st order
• Only first moment matters (0)
• Certainty equivalence
• 2nd order
• With risk aversion or concave technology
• Second moment also matters
• No certainty equivalence
• Questions regarding welfare evaluation risk
  premium in stochastic environment.

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Dynare background

• Collection of Matlab files.
• Solves and estimates nonlinear-dynamic models
  with RE.
• By several people from CEPREMAP

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Dynare background 2

• Steady state
• Alternative optimization algorithm (not only
  fsolve)
• Stability analysis (Blanchard Khan, 1980)
• Deterministic simulation
• Earlier version Fair and Taylor (1983).
• Now Newton-type algorithm (Collard and Juillard
  2001) all equations simultaneously.

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Dynare background 3

• Stochastic simulations
• 1st and 2nd approximation
• An eigenvalue method of undetermined
  coefficients.
• State space representation (policy)
• Impulse responses
• Moments
• Estimation
• Maximum likelihood
• Bayesian estimation
• Kalman filter

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Hands on RBC problem

• Simple RBC model (two shocks)

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Hands on RBC FOCs

• The first is a standard Euler-condition (FW
  looking)
• Note on the time-impatient shock.
• The second is the standard labor-supply
• Note on income and substitution effects

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Hands onwhat Dynare needs 2 know

• The three constraints.
• The two FOCs.
• All together
• 5 equations (fw looking).
• 5 variables.
• Note on the capital time-index.

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Hands onthe model in Dynare syntax

• c(-sigmaC) zb(1)/zb beta c(1)(-sigmaC)
  (alpha y(1)/k 1 - delta) // Euler
• psi lsigmaL csigmaC (1-alpha)y/l //
  Labor supply
• y zy k(-1)alpha l(1-alpha)
  // Technology
• k i (1 - delta) k(-1)
  // Investment
• y c i
  // Sources
• zb zb(-1)rhoB exp(zbe)
  // Impatient-shock process
• zy zy(-1)rhoY exp(zye)
  // Tech-shock process

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Hands onJust do it!

• Dynare
• Download the Dynare toolbox (version 3.065)
• Save it in the Matlab-work directory
• Set path to dynare_v3/matlab
• Our model
• Download RBC.mod from the course website.
• Save it in a new directory
• In the command window dynare RBC

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Hands on

• Example

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Procedural issues

• Set path
• Web site
• Courses and Conferences

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The End!

• 10 Q