Hello, I am trying to estimate a DSGE model and have a general question about the steady state values of variables in a log-linearised model. For example the equation:
Yt=λCt+(1-λ)Dt
has the following log-linearised representation:
yt=(λCct+(1-λ)Ddt )/(λC+(1-λ)D)
where C and D are the steady state values and yt, ct and dt are the deviations from the steady state. So what can I use for these steady state values? Should I estimate them, too? Or is there any other way to find out the steady state values and set them as fixed parameter in the second step?
When you move from a nonlinear to a linearized model, the steady state values of the nonlinear model become parameters that typically depend on the deep parameters of the model. They are not free parameters you can estimate. What you usually need to do is compute the steady state of the nonlinear model and assign these values to the parameters. Please take a look at Pfeifer(2013): A Guide to Specifying Observation Equations for the Estimation of DSGE Models, particularly Listing 3
Thank you very much for your paper, “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”. I found it very useful.
I have a question with reference to the question by Gildenberg and your answer above. I have looked into listing 3 as you have advised, and there the steady state values of the non-linear model have been derived analytically. However, in my model I cannot derive them analytically and I use fsolve in Matlab to find the steady state values. Afterwards, I import the numerical values of the non-linear steady states as parameters into the mod file, where the equations are log-linearised. So, my understanding is that if I estimate deep parameters in this model as it is, the estimated parameters would not be correct as the parameters depending on non-linear steady states are not updated during Bayesian estimation steps.
Can I please ask whether my understanding is correct, and if so whether there is any work-around to estimate deep parameters of the model using log-linearised model? I believe, I can use the non-linear model itself and use an external steady state file so that this issue is not there anymore, but want to know whether there is any other method please.
As in nonlinear models, you can also use a steady state file to update parameters in linear models. That adds a computational burden as now the steady state file needs to be executed, but it takes parameter dependence into account.