Add replication code for first-order RBC + student T shocks

[jlperla]

@donskerclass can provide the jupyter notebook which does this and implements the model. The task will mostly be just taking it and "productionizing" it.

As this has non-gaussian shocks, the kalman filter won't work (and we don't need to do the 2nd order) so 1st order joint is enough.

What you will need to do is:

• Come up with the change in naming convention which will make copy/replace easy. I think that naming convention (i.e. replace rbc_ with rbc_student_t_ is probably the way to go?
• Replicate https://github.com/HighDimensionalEconLab/HMCExamples.jl/blob/main/src/estimate_rbc_1_joint.jl to estimate_rbc_student_t_1_joint.jl or something like that.
  • Add in any extra parameters if there are any.
  • Change the model in https://github.com/HighDimensionalEconLab/HMCExamples.jl/blob/main/src/estimate_rbc_1_joint.jl#L43-L62 to be whatever david had in the notebook. Most likely this just means changing the draw of shocks to be student-t there.
  • Add in the equivalent rbc_student_t_1_joint.txt default parameters
• Create simulation code for the student-t to generate datafiles for the estimatino following the RBC ones in https://github.com/HighDimensionalEconLab/HMCExamples.jl/blob/main/deps/generate_fake_data_rbc.jl. This may require slightly more manual steps because the LinearStateSpaceProblem might only support automatic simulation with gaussians right now. So I would create the noise vector directly yourself and then let it simulate it afterwards, etc. If the DifferenceEquations code isn't enough to make this happen then tell @jlperla and he will jump in to help.
• After you get that working, add in a placeholder for the replication. Maybe emulate something like we should make sure that we can generate some of the most basic plots of the results. But probably just basic summary statistics like https://github.com/HighDimensionalEconLab/HMCExamples.jl/blob/main/scripts/sgu_replication/sumstats_julia.py#L39-L58 and where we don't even compare to a dynare iimplementation, just the joint st order.

[donskerclass]

For reference, the notebook is available at

Student-t and stochastic volatility

This uses exactly the RBC model from the other experiments, but modify the Turing model applied around it.