Hello,
I’m currently working with a DSGE model and what I would like to do is to make the variance of a measurement error change over time. I found this post Change in Measurement error variance that is closely related to mine. However, I’m not talking about a structural change, necessarily. Basically, I’m thinking more of a variance that can change several times along the path of the model or even change in every period. So I’m wondering if you could, for example, set the variance of a shock equal to an “auxiliary” observable shock/variable, thus making such variance time dependent. Is that at all posible or Dynare will demand me to specify a constant number instead?
Thanks!
What you have in mind is hardly possible. You don’t need to rely on Dynare’s built-in functionality for measurement errors, which relies on them being homoskedastic. Instead, you can define a normal shock for it. See 6.1 Measurement Errors as a Special Case of Exogenous variables of Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”
What you seem to suggest is having a measurement error with stochastic volatility. The problem is that this would turn your model solution/state-space representation nonlinear, making estimation unfeasible with Dynare as you would need to go to third order. Simulation would work, though.
First of all. thanks for your prompt response. Nevertheless I have a follow up question. You said that relying on Dynare’s built-in functionality to introduce measurement errors implies homoscedasticity. Suppose I’m no longer interested in having stochastic volatility, can I still have a heteroskedastic measurement error (but, strictly, still a deterministic variance) if I introduce such error in some kind of way?
Unfortunately, that is not so easy. What you have in mind amounts to a “structural break” in the Kalman filter. See my reply at Estimation With Structural Break In Shock Processes
Supporting this is still on our to-do-list, see http://www.dynare.org/DynareWiki/SubsamplesEstimation