Normalization to 1 of several variables

Dear Dynare community,

I have a medium scale model with many variables, hence the steady-state of the model is tricky to find. I wanted to normalize some variables, such as aggregate labor, capital and material used by my different sectors, to 1. Of course, I’m being careful in the calibration procedure by taking into account this normalization to 1 of aggregate inputs. I just wanted to be sure that this does not pose any problems on the conceptual part and it does not constrain the evolution of inputs through time. I know that normalizing total labor to 1 is standard, but I wondered if I could do it for other inputs.

Thank you.

Best regards

Typically, linear homogeneity means you can introduce normalizing constants into many places of your model. The tricky part is computing these constants. However, in many cases that computation actually facilitates steady state computations as you can start from the normalized variable and then work towards the constants. I don’t know whether that is feasible for your model.

thank you @jpfeifer

But Do I really need normalization constants for total inputs ? Usually there is no normalization constant parameter for total labor, that is just assumed equal to 1.

This normalization would only impact these equations :

  • Labor: 1 = sum labor in each sector
  • Capital : 1 = sum capital in each sector
  • Materials: 1 = sum materials in each sector

Thanks for your help

Sometimes things have no natural units and you normalize. For hours that is possible because time is an endowment.
Sidenote: even when normalizing total labor, there is often still a parameter providing the relative weights of consumption and leisure in utility that you need to determine.

For capital and materials things are more tricky. They are usually endogenously produced from TFP and hours. Why would you be able to fix their value in steady state without, e.g., appropriately setting TFP.

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