Dynamic GMM vs local projection vs Time-varying parameters (TVP) model selection

[Mario Ferri]

I am having a macro panel where I assume some sort of political ideology indicators (left -right) and other political variables are affecting standard macro variables.

I would like to consider that coefficients are time varying. and determined over time. That means political variables affect macro variables over time. So I am looking for the proper model among Dynamic panel (GMM) , local projection methods and Time-varying parameters (TVP) with stochastic volatility going bayesian for the latest(I am having a code for this)
Occam's razor is the best way to go.But which one is it in this case? Previous literature is ambiguous.

Thanks