# Response to Shocks Instantly Go to Steady State

Hello all,

I have been working on a deterministic model and I would like to document the response to a permanent shock. Dynare solves for steady state just fine and the Blanchard-Khan conditions are satisfied. However, after implementing the shock, all variables adjust instantaneously to the new steady state values, so there is effectively no adjustment, just one jump.

I was wondering what possible model features could cause something like this in general. I have looked at other deterministic models with permanent shocks and they seem to have curvature rather than the sharp kink I am experiencing, which indicates to me that it is not simply an artifact of a deterministic setting.

I guess a better question may be what causes the curvature for deterministic models? For models with auto-regressive processes, I totally understand why there would be a smooth adjustment to the new steady state. It is also intuitive to me why curvature exists for models that have outcomes that are probabilistic and depend on expectations. But why wouldn’t deterministic models with a permanent shock always instantly adjust to the new steady state? I have not been able to find a resource that explains this, so if there is an obvious one, just let me know and I will go read it!

Ben

Do you have predetermined variables in your model?

If your model is purely forward the absence of transition is not surprising. If your model is c_t = \beta c_{t+1}+x_t, a permanent shift on x from 0 to 1 in period one will cause a jump of c in period one, from 0 to (1-\beta)^{-1}. The endogenous variable c jumps to the new steady state in period one, and there is no transition. This would be also true if the model was non linear.

If you consider a model where x is a stationary AR, and do the permanent shock on its innovation \varepsilon, you will observe a transition only because it takes time have the full effect of \varepsilon on x. You will obtain a more interesting transition if you have predetermined endogenous variables, e.g. the physical capital stock in a growth model.

The absence of transition is not a consequence of the perfect foresight assumption. For instance, in a purely forward stochastic linear(ized) NK model (Phillips curve, IS curve and Taylor rule) you would observe that the IRFs converge to the steady state in one period (i.e. no transition). Which makes sense since the reduced form solution of the model is a white noise.

Best,
Stéphane.

There are two predetermined variables in the model. I have tried looking at dynamics with greatly simplified versions of the model, and there is a more interesting adjustment for some but not all variables.

Based on your answer, I suspect there is either a mistake in the code or it is just a weak transmission mechanism for the predetermined variables in my model. I will investigate further. But your answer really helped clarify the role of predetermined variables in the dynamics, so thank you!