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jmaih / RISE_toolbox

Solution and estimation of Markov Switching Rational Expectations / DSGE Models
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Question about irf #190

Open Zhanwenqing opened 1 month ago

Zhanwenqing commented 1 month ago

Hi professor, sorry to disturb you, I have some question about irf in RISE. In the examples of RISE, I saw there are two kinds of irfs,one type is irf, which is default, the other one is girf, what is the difference between the two kinds of irfs? Or could you please provide me some thesis about this question, Thanks in advance, best wishes!

jmaih commented 1 month ago

Hi, In linear models, simple IRFs and generalized IRFs (GIRFs) yield the same results because the principle of superposition holds. In linear models, the effect of a shock does not depend on the initial conditions or the history of the economy, so the response to a shock is straightforward and consistent across all points in time.

Impulse Response Functions (IRFs) are typically derived under the assumption of linearity, where a one-time shock to an endogenous variable generates a predictable and consistent path of responses in other variables, conditional on the system being at a steady state or at a specific point.

Generalized IRFs (GIRFs), however, are designed to handle nonlinear models. They take into account the fact that in a nonlinear or regime-switching context, the response of variables to a shock can depend on the state of the economy and other shocks. The GIRF calculates the expected response by averaging across different possible initial conditions and histories of the system. GIRFs allow us to capture the nonlinearity and state dependence in models where traditional IRFs cannot be applied.

Thus, GIRFs generalize the concept of IRFs to be applicable in models where linearity does not hold. In such cases, the IRFs cannot be applied, and GIRFs become necessary to handle the complexities of the model.

J.

On Mon, Oct 14, 2024 at 4:48 AM Zhanwenqing @.***> wrote:

Hi professor, sorry to disturb you, I have some question about irf in RISE. In the examples of RISE, I saw there are two kinds of irfs,one type is irf, which is default, the other one is girf, what is the difference between the two kinds of irfs? Or could you please provide me some thesis about this question, Thanks in advance, best wishes!

— Reply to this email directly, view it on GitHub https://github.com/jmaih/RISE_toolbox/issues/190, or unsubscribe https://github.com/notifications/unsubscribe-auth/AATKBT4ITUQCB7WII43EXYLZ3MWITAVCNFSM6AAAAABP4BW42SVHI2DSMVQWIX3LMV43ASLTON2WKOZSGU4DINJYHE2DCNA . You are receiving this because you are subscribed to this thread.Message ID: @.***>

Zhanwenqing commented 1 month ago

Thanks professors,I got it. I have anothor question about GIRFs. In linear DSGE models, the IRFs are deviation from the steady state, but when we compute GIRFs in regime-switching DSGE models, steady state varies, what the steady state is?

jmaih commented 1 month ago
  1. In linear models, the IRFs ARE NOT deviations from the steady state!!! If the model is linear, both IRFs and GIRFs give the same results irrespective of the initial conditions, irrespective of the size of the shocks, all of which would matter in a nonlinear model.
  2. Under regime switching, it is possible to calculate regime-specific impulse responses that will assume that the process remains in one regime throughout the simulation although the agents are aware that the system can switch at any moment going forward.
  3. Because the regime-switching model is inherently nonlinear, even in the presence of conditionally-linear regimes, it is possible to compute GIRFs and insist that they not be regime-specific. The result will then be the expected impact of some shock taking into account switches in the course of the simulation.

On Wed, Oct 16, 2024 at 9:51 AM Zhanwenqing @.***> wrote:

Thanks professors,I got it. I have anothor question about GIRFs. In linear DSGE models, the IRFs are deviation from the steady state, but when we compute GIRFs in regime-switching DSGE models, steady state varies, what the steady state is?

— Reply to this email directly, view it on GitHub https://github.com/jmaih/RISE_toolbox/issues/190#issuecomment-2415993296, or unsubscribe https://github.com/notifications/unsubscribe-auth/AATKBT67O7AVJDAJLHJOYQLZ3YLHRAVCNFSM6AAAAABP4BW42SVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDIMJVHE4TGMRZGY . You are receiving this because you commented.Message ID: @.***>

Zhanwenqing commented 1 month ago

Thanks, professor. So in RS-DSGE model, both IRFs and GIRFs calculated by RISE are not percentage of devation from ss ,right?

jmaih commented 1 month ago
  1. Constant-parameter models are written in such a way that in their stationarized form, they return to the steady state after a shock
  2. In nonlinear models, the impulse responses depend on initial conditions and on the size of the shocks. When you add the complexity of regime switching, you may have multiple steady states. Some or even all of those regimes might be unstable in the sense that if you are in one and you are pushed away by a shock, you may not return to that regime.
  3. Depending on the case and perhaps on the perturbation approach, some regime-switching models can have a unique steady state.

On Thu, Oct 17, 2024 at 3:53 AM Zhanwenqing @.***> wrote:

Thanks, professor. So in RS-DSGE model, both IRFs and GIRFs calculated by RISE are not percentage of devation from ss ,right?

— Reply to this email directly, view it on GitHub https://github.com/jmaih/RISE_toolbox/issues/190#issuecomment-2418326605, or unsubscribe https://github.com/notifications/unsubscribe-auth/AATKBT3HTIXU5U6F4U443DTZ34KARAVCNFSM6AAAAABP4BW42SVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDIMJYGMZDMNRQGU . You are receiving this because you commented.Message ID: @.***>