Evolution of substitution elasticities

Good afternoon,

I am running my model while making the substitution elasticity of a CES nest evolve during 25 years (to reflect structural changes). I do not change the distribution parameters (those are computed at steady state from the value of substitution elasticity and volumes). This causes a lot of instabilities and sometimes it fails to find a perfect foresight solution.

I’ve never come across papers making substitution elasticities evolve through time. I’m guessing that them being deep parameters will inevitably cause numerical instabilities in a dynamic general equilibrium model. For now, because making these parameters evolve dynamically through time makes the model unstable, I mainly run scenarios with different (static) values of this elasticity.

I wondered if the problem I am bumping into is what should be expected or not. Thank you for the help.