Elasticity of substitution

General DSGE Modeling
1

hi everybody
If I am right when we linearized CES function the elasticity of substitution between inputs will wipe out. But I want to have elasticity of substitution in linearized form of my equation. in the other words because I want to have sensitivity analysis on this parameter so I must have it on final equation that inputed in dynare. based on this which functional form should I chose to reach this goal?
thanks a lot

2

It indeed cancels out in the CES function itself, but it should show up in the optimal demand functions, i.e. in the demand for labor and capital if it is a production function with labor and capital as inputs.

3

Thanks for your answer
But I think I could not been able to describe the problem accurately
In this case I am trying to integrate two variable buy specific rate of substitution and its not production function so when we linearizing this substitution rate will cancel out
In fact I using it as a integrator and I am seeking other functional form to have substitution rate in final linear form

4

I am not really able to follow. As @Romero pointed out, the elasticity of substitution should still show up in the FOCs.

5

As I said we want to integrate two variable( not necessary input of production function) and use it in model. In this case we need to do sensitivity analysis on elasticity of substitution between this two variable. So when we linearizing this integrator we lose this parameter in linear form. Based on this what is your suggestion for the shape and functional form of this integrator??

6

From what you describe, the parameter has no effect at first order. So you cannot work with a first order approximation to study sensitivity.