Smet and Wolter DSGE for EU

[phuong.macro]

Hallo Leute

I am now replicating the Smet and Wolter's paper (2003) (DSGE of Euro area). Then I would like to ask you some questions about dynare code

1. According to Bayesian method, when I want to estimate a parameter, I have to declare prior mean, prior standard error, and prior shape as well. These prior values are reported by Smet and Wolter (2003). However, in Dynare, it is necessary to declare a starting value. So in this case, how we can give a starting value. It is fine if I can assign any value as a starting point? In particular, the persistent parameter for productiviy shock is declared by Smets and Wolter as 0.85 for prior mean, 0.1 for prior S.E, and Beta distribution as prior shape. Then I follow the dynare syntax

// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE

Accordingly, how can I assign the initial value. It is fine if I can assign any value for the initial point. If I am not sure about the intial value that I assign, then I will increase number of draws.

2. For Bayesian econometrics, how we assign number of draws (mh_replic) to make sure that the estimated mean and variance will be very close to true values?

[jpfeifer]

1. In case of replications, it is often best to initially start at the reported posterior mode, e.g. using the

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estimated_params_init(use_calibration);

block. You can also leave the inital value empty so that Dynare will start at the prior mean, i.e. having something like

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betta, beta_pdf, 0.993, 0.002;

2. You need to check convergence. If that is not the case, use more draws. A good starting point is the number of draws in the original paper. But given recent computer power, I would go for more draws than in the original paper.

[phuong.macro]

I got it. Thank you so much for your usefull answer

I have 2 more questions:

1. Accordinging to Bayesian econometric, posterior is proportional to likehood times prior. Thus, I think that assigning a starting value will not impact our final estimated parameters. Then, I do not need to declare a starting point into my syntax in Dynare for my future research?

2. How I can check whether my estiamted mean and variance are close to true value in Dynare? order how I can check convergence in Dynare?
Is this ok if I only compare prior shape to posterior shape. Then if these two shapes look like the same, so that I can conlucde my estimated mean and variance is good.
Otherwise, I have to change my prior mean and prior S.E order I have to increase number of draws. So my understanding is correct?

Vielen dank

[jpfeifer]

1. In theory it does not matter, but in practice it does. The further you start away from the posterior mode, the harder will it be to achieve convergence. However, if you don't have any information, the prior mean/mode is by definition your best guess for the starting value.

2. If

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mh_replic>2000

Dynare will display convergence diagnostics (either Brooks/Gelman or Geweke, depending on mh_nblocks)

Regarding prior/posterior comparison, you are mistaken. See http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=8201

[phuong.macro]

Thank you so much indeed for your very detailed explanation

As your explanation, the further I start away from the posterior mode, the harder will it be to achieve convergence. So if I am not sure about a starting value, I can consider prior mean/mode as a starting point.
On the other hand,according to Monte Carlo theorem,if the number of draws (or replications) goes to infinity, then the estimated values will converge to the true values. Thus, in practice, to make sure that the estimated value will be close to the true values, then I should use the number of draw as large as possible. For example, in the case of Smets and Wolters (2003) they take 100000 replications. My understanding is correct?

[jpfeifer]

Yes, starting from the prior mean is ok, although you should typically check robustness by using different starting values.

Often a million draws is a good starting point.

[phuong.macro]

Vielen dank für die Helfen

I habe ganz verstenhen