DSGE with public investment and debt

I want to implement a simple DSGE model that has government in it:

  1. Government spend on current spending (goods and services).
  2. Government spend on public capital investment.
  3. There is implementation delay on public capital investment.
  4. Both productive (public capital investment) and unproductive investment (goods and services) are financed through debt issuing.

I want to analyze output, labor supply, and aggregate capital stock.
I want to shock both current spending and public capital spending. I want both shocks to have the same persistence rho.

Do you know of any model out there that does this?

Thank you for your help,
Rodrigo

Leeper et al (2010) Government investment and fiscal stimulus seems quite close.

Thank you! This helps a lot.