Marco%20Del%20Negro,%20Frank%20Schorfheide,%20Frank%20Smets,%20and%20Raf%20Wouters%20(DSSW)%20%20On%20the%20Fit%20of%20New-Keynesian%20Models - PowerPoint PPT Presentation

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Marco%20Del%20Negro,%20Frank%20Schorfheide,%20Frank%20Smets,%20and%20Raf%20Wouters%20(DSSW)%20%20On%20the%20Fit%20of%20New-Keynesian%20Models

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Although the marginal likelihood is a sensible way to assess fit in principle... Out of Sample Root Mean Square Errors. Most likely ... – PowerPoint PPT presentation

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Title: Marco%20Del%20Negro,%20Frank%20Schorfheide,%20Frank%20Smets,%20and%20Raf%20Wouters%20(DSSW)%20%20On%20the%20Fit%20of%20New-Keynesian%20Models


1
Marco Del Negro, Frank Schorfheide, Frank Smets,
and Raf Wouters (DSSW) On the Fit of
New-Keynesian Models
  • Discussion by
  • Lawrence Christiano

2
Objective
  • Provide a scalar measure of the fit of a Dynamic,
    Stochastic, General Equilibrium Model (DSGE).
  • Apply measure of fit to an empirically important
    example.

3
  • Consider a vector autoregression (VAR)
  • Least squares estimation

4
  • DSGE model implication for VAR
  • DSGE model parameters ?
  • Hybrid model

5
  • Models
  • Marginal likelihood

6
Questions
  • Although the marginal likelihood is a sensible
    way to assess fit in principle
  • Compromises are required for tractability
  • How compelling are the assumptions about
    likelihood function, priors
  • How severe is the evidence against the model when
  • Even if DSGE model were true, unrestricted VAR
    might fit better in a small sample
  • Is the Hybrid model useful?

7
DSSW Assume the Likelihood of the Data is Gaussian
  • Fit a four-lag, 7 variable VAR using US data,
    1955Q4-2006Q1.
  • Compute skewness and kurtosis statistics for each
    of 7 VAR disturbances

8
  • There is strong evidence against normality
    assumption

9
Prior on VAR Parameters
  • Gaussian Likelihood is a function only of VAR
    parameters
  • How do DSGE model parameters enter?
  • They control the priors on VAR parameters

10
Prior on VAR Parameters
Density In case DSGE model Is true
Density in case DSGE model is false
11
Prior on VAR Parameters
  • Do DSSW priors fairly capture notion that DSGE
    model might be false?
  • Another possibility
  • If preferred DSGE model is false, some other DSGE
    model is true.
  • Must specify a prior over alternative DSGE
    models. Induced priors over VAR parameters likely
    to be different from Normal/Wishart assumption of
    DSSW
  • Problem Most likely, could not even describe
    alternative DSGE models, much less assign priors
    to them! Presumably, this would lead us even
    further away from DSSW.
  • These concerns about the DSSW priors would be
    mere quibbles if their approach were the only one
    to assessing model fit.
  • But, there are other approaches
  • More on this later

12
And DSGE Model Fit
  • Priors for DSGE
  • Marginal likelihood

13
Questions
  • How severe is the evidence against the model when
  • To answer this, studied multiple artificial data
    samples generated from a simple DSGE model

14
Simple (Long-Plosser) Model
  • Setup
  • Experiment

15
Results
  • Doing DSSW calculations on artificial data
  • Implications
  • DSSW evidence of misspecification occurs 1/3 of
    the time, even though DSGE model is true.
  • Misspecification of likelihood seems not to
    matter.

16
Interpretation of Results
  • Why do DSSW find evidence against DSGE model,
    even when the model is true?
  • One answer In finite samples, unrestricted VAR
    often fits substantially better than true VAR
    implied by DSGE.

17
Interpretation of Results
  • Interior typically occur in samples where
    VAR fits substantially better than true model

18
Conclusion
  • DSSW rule
  • We have evidence of misspecification whenever
    the peak of the marginal likelihood function
    is attained at a finite value.
  • with high probability, this rule leads to overly
    pessimistic assesment of models.
  • What can we learn from about fit of DSGE
    models?
  • Requires doing simulation experiments in more
    elaborate models.
  • Poses significant computational challenges.

19
Conclusion.
  • Marginal likelihood provides a sensible measure
    of fit in principle, however
  • Assumptions required for tractability render
    marginal likelihood hard to interpret.
  • The hybrid model is selected by marginal
    likelihood criterion why should it be taken
    seriously?
  • A less sophisticated, but more transparent and
    easy to interpret measure of fit
  • Out of Sample Root Mean Square Errors.

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Prior on model 1 P(M1 )
Most likely Model,
Prior on model 2 P(M2 )
Other model
27
Prior on VAR Parameters
  • The alternative priors would presumably be very
    different (e.g., multimodal).
  • In practice, we dont know what other model might
    be true (this is a basic fact about research!)
  • How would we even think of priors in this case?
  • Robust control?
  • Placing priors on VAR parameters conditional on
    model being false seems very difficult.
  • Is the DSSW approach the right one?
  • If DSSW approach were the only way to assess
    model fit, concerns about plausibility of prior
    would have less force
  • But, there are other approaches
  • More on this later
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