I am trying to write a code to back out the structural shocks by myself. Any papers or sources I can to learn the methods to compute the smoothed shocks/variables from the data like in Dynare? I also want to learn how to do the variance decomposition. Any comments are appreciated. Thanks!

To give more information. I have a very non-linear DSGE model with heterogeneous agents. I have two exogenous shocks following AR(1). The problem is large. I have done the calibration by moment matching. I didn’t plan to do Bayesian estimation because it takes too much time for my model. With all the parameters, including the parameters of my shock processes, I’ve solved my problem using value function iteration. I also finished the code to simulate the model.

Now, I want to use data series to back out the seires of two shocks and conduct variance decomposition. I guess I also need to use the particle filter somewhere because of the non-linearity. But any recommendation to help me to understand the basic method is very welcome. Thank you in advance!

Thanks a lot for your reply, Prof. Pfeifer. I really appreciate it!

I think you are right. But I feel like I still want to know the algorithm. I found many materials online, but most of them focus on explaining Bayesian estimation for parameters. Do you have any recommendations of papers/materials for backing up shocks and variance decomposition? I guess my question is what’s the algorithm of Dynare doing these two parts.

Thanks a lot for your recommendation of papers, Prof. Pfeifer. That’s really helpful! I will start from them and see whether there is anything I can do.

I went through your recommended materials. I think the main difficulty is that my model has rich micro-foundations. And I don’t know how to write down the problem using the state-space representation.

I was wondering that maybe I can focus on the aggregate variables of my model’s simulation and use a state-space model to approximate it. And then I apply the technique of particle filters on the estimated state-space model to get the smoothed shocks.

I haven’t found other papers using a similar strategy, so I am afraid that my plan doesn’t make any sense. Could you please let me know how you think about it? That will be helpful.