Endogenous elasticity of substitution

Good morning everyone,

I was wondering if it was complicated to render the elasticity of substitution endogenous in a DSGE model since the ratio K/L and relative factor remuneration may change in the long run. That would make my elasticity non-constant.

Thank you.

Best regards

  1. What exactly did you have in mind?
  2. And are you thinking about stochastic or perfect foresight simulations?

I have an economy which is going to be more capital intensive in the long run because of the energy transition policies. I wanted to know if it was possible to make the elasticity of substitution between capital and energy depending on time. Meaning that the substitution elasticity will vary through time according to the relative price of energy or something like that.

I reckon that this is feasible for distribution parameters as they are calibrated on ratios and relative prices. But for elasticities of substitution, I’m not sure as they rely on estimation techniques and can’t be calibrated manually.

I’m in a perfect foresight model. If it is complicated to do so, I’ll just drop the idea.

Thank you @jpfeifer

I guess this should be doable, but you need to come up with a function that allows for this. The usual CES function obviously has constant elasticities.

@jpfeifer pfeifer I saw this variable elasticity substitution (VES) function but the elasticity does not appear to depend on the time. But, aren’t those functions complicated to handle manually when computing FOC’s ?

Note that my production functions have several imbrications.