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I've estimated a dynamic linear model to capture time varying parameters in an Okun's law type of model:

Model in levels and DLM

I set the starting values for the state vector all equal to zero and estimate the system variances via ML before running the filter.

An encouraging sign is that my model can replicate the results presented in table 1 of the paper (the paper cited can be sourced here : https://www.rba.gov.au/publications/rdp/2015/pdf/rdp2015-14.pdf )

Other important information: I am using the DLM package in R

My questions:

To uncover the estimate of mu_t, I divide the fourth element of the filtered state by the second? Is there anything wrong with this?

Is there another / better way of specifying this system?

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