Following the papers of Cantore and Levine (2009) and Klump et al. (2012) regarding dimensionless parameters, I wondered if the reparametrization or normalization of functions is also needed in CES where inputs have the same measurement units. If it does not, the distribution parameters can be considered as budget share parameters, while they are not in a CES functions that does not verify the dimension homogeneity (and need to be reparametrized in that case).
I believe that the point of the authors apply to CES where the inputs are not of the same units, such as capital and labor.
The point of these papers is that you need should carefully parameterize these models and need to be extra careful when doing comparative statics that may affect the steady state. The problem persists even with the same measurement units. You can see this in Cantore/Levine (2012), equations (6-7). The parameters change also in the exponent.
Ok just read De Jong’s paper. I think the normalization is easier to implement to have a dimensionless system.
But if I normalize the CES production and consumption functions, I should also normalize all the budget equations by dividing variables by their SS value, right @jpfeifer ? (government and households’ budget constraints)
If I follow Klump et al. (2012)'s normalized function, in the production funtion, Y(t), K(t) and L(t) are dived by their steady state values Y0, K0, L0. I just wondered if I had to do the same thing to every variable in the module or occurence of Y, K and L, even in the budget constraints: in the budget constraint of households the rental rate rK(t) becomes rK(t)/K0.
I’ll stick to just normalizing the CES functions only in the model, following your paper.