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Discussion by: Lawrence Christiano

Marco Del Negro, Frank Schorfheide, Frank Smets, and Raf Wouters (DSSW) On the Fit of New-Keynesian Models. Discussion by: Lawrence Christiano. Objective:. Provide a scalar measure of the fit of a Dynamic, Stochastic, General Equilibrium Model (DSGE).

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Discussion by: Lawrence Christiano

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  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 – θ • Hybrid model

  5. Models: • Marginal likelihood: • Best fit: • Finding: • Conclusion: ‘Evidence of model misspecification’

  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.

  20. Prior on model 1: P(M1 ) Most likely Model, Prior on model 2: P(M2 ) Other model

  21. Prior on VAR Parameters… • The alternative priors would presumably be very different (e.g., multimodal). • In practice, we don’t 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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