I have been wondering for a long time if the papers on DSGE identification were already implemented somewhere. I am very happy to see dynare team implemented the local identification tools. Hope global identification tools such as Kocięcki, Kolasa 2023 and Z Qu, D Tkachenko (2017,2023) are implemented at some point. That would be wonderful
No this is not true. First of all we make the assumption that all Eigenvalues of inv(A0)*A1 lie within the unit circle, then there is the unique solution expressed by the infinite sum. We then make use that E_t eps_{t+j}=0 for j>0, then also E_t y_{t+1}=0 and the solution simplifies to y_t = inv(A0)*eps_t.
@@wmutschl Prof., why we assume that "E_t eps_{t+j}=0 for j>0, then also E_t y_{t+1}=0 "? And where is E_t y_{t+1} in =sum (A0^(-1)*A1)^j E_t eps_{t+j}? how we got rid of it?
Thank you, great video! @22:40 If I want to compare second moments from an estimated model with the data, what's the best way to do this in Dynare? Thanks.
Professor, thank you so much for sharing this! I notice all the identification analysis starts with a specific parameter combination either from calibration or conjecture. Is there a way to check identification before/while estimating the model (not after estimation, since with under-identification, the estimated result might not be "true")?
What do you mean by "estimated result might not be true"? Identification is a model property that can be checked before seeing any data. With simulated data we can also assess the strength of identification. So I don't understand your comment. Of course the identification tests are done at a certain parameter value. You can either draw these values from the prior or from the posterior or simply make them up to check identifiability. Usually, it is sufficient to check identification based on many draws from the prior, then fix any issues, then do Bayesian estimation and then check identification at the posterior mode and posterior mean again, or even at draws from the posterior. Or do you have global identification in mind?
@@wmutschl Thanks for your reply, let me make my point more clear. I was trying to consider when there is a `true' DGP that generated the data, would the Bayeisan estimated parameter (or equivalent identified set) be the true one under infinite sample if it is not point-identified? For example, in the OLS case, we know beta_0 cannot be identified if shocks are not mean zero before we evaluate a certain parameter value. Can we learn similar things to DSGE/state-space models? Basically its ``identification of the model'' vs ``identification at a certain point''.
@@kylekuang4057, in case of having partial identification in a frenquentist framework you would have a set of parameters that are observational equivalent (the identified set). In such case, if you obtain first an element of this identified set, then you can execute all the "identified test" proposed in the video. You do not need to use the population parameter of interest, this is so, of course, under some regularity conditions that most DSGE models we consider satisfy (the identified set is a regular manifold). I do not have too much knowledge about Bayesian methods. Yet, I guess something similar happens in a Byesian framework. The identified set I guess is a set of posterior distributions that are observational equivalent, and you only need to obtain an element of it, to perform the identification test.
Hi Professor, thank you so much for your lesson, it's really interesting. Now, I am building a simple model for my memory and I encounter some difficulties, please can I ask you some questions by mail? Thanks in advance Professor.
I have been wondering for a long time if the papers on DSGE identification were already implemented somewhere. I am very happy to see dynare team implemented the local identification tools.
Hope global identification tools such as Kocięcki, Kolasa 2023 and Z Qu, D Tkachenko (2017,2023) are implemented at some point. That would be wonderful
one question about 12:38, why sum of matrices is an identity matrix? sum A0^(-1)A1=I? thank you
No this is not true. First of all we make the assumption that all Eigenvalues of inv(A0)*A1 lie within the unit circle, then there is the unique solution expressed by the infinite sum. We then make use that E_t eps_{t+j}=0 for j>0, then also E_t y_{t+1}=0 and the solution simplifies to y_t = inv(A0)*eps_t.
@@wmutschl Prof., why we assume that "E_t eps_{t+j}=0 for j>0, then also E_t y_{t+1}=0 "? And where is E_t y_{t+1} in =sum (A0^(-1)*A1)^j E_t eps_{t+j}? how we got rid of it?
Thank you, great video! @22:40 If I want to compare second moments from an estimated model with the data, what's the best way to do this in Dynare? Thanks.
You should have a look at the method of moments which is an estimation technique specifically designed to do this.
Professor, thank you so much for sharing this! I notice all the identification analysis starts with a specific parameter combination either from calibration or conjecture. Is there a way to check identification before/while estimating the model (not after estimation, since with under-identification, the estimated result might not be "true")?
Especially in a bayesian framework...
What do you mean by "estimated result might not be true"? Identification is a model property that can be checked before seeing any data. With simulated data we can also assess the strength of identification. So I don't understand your comment. Of course the identification tests are done at a certain parameter value. You can either draw these values from the prior or from the posterior or simply make them up to check identifiability. Usually, it is sufficient to check identification based on many draws from the prior, then fix any issues, then do Bayesian estimation and then check identification at the posterior mode and posterior mean again, or even at draws from the posterior. Or do you have global identification in mind?
Bayesian or not does not matter.
@@wmutschl Thanks for your reply, let me make my point more clear. I was trying to consider when there is a `true' DGP that generated the data, would the Bayeisan estimated parameter (or equivalent identified set) be the true one under infinite sample if it is not point-identified? For example, in the OLS case, we know beta_0 cannot be identified if shocks are not mean zero before we evaluate a certain parameter value. Can we learn similar things to DSGE/state-space models? Basically its ``identification of the model'' vs ``identification at a certain point''.
@@kylekuang4057, in case of having partial identification in a frenquentist framework you would have a set of parameters that are observational equivalent (the identified set). In such case, if you obtain first an element of this identified set, then you can execute all the "identified test" proposed in the video. You do not need to use the population parameter of interest, this is so, of course, under some regularity conditions that most DSGE models we consider satisfy (the identified set is a regular manifold).
I do not have too much knowledge about Bayesian methods. Yet, I guess something similar happens in a Byesian framework. The identified set I guess is a set of posterior distributions that are observational equivalent, and you only need to obtain an element of it, to perform the identification test.
Hi Professor, thank you so much for your lesson, it's really interesting. Now, I am building a simple model for my memory and I encounter some difficulties, please can I ask you some questions by mail? Thanks in advance Professor.
You may ask your question in the dynare forum
Thank you so much :)
Very welcome!
Hi !
Watching the video long time after the summer school, but that's super useful! Thanks for the toolbox and the very clear video! Merci beaucoup!!
Glad it helps!