If production function is of Cobb Douglas form, then it is a common practice to normalize labor to 1 and use Labor =1/3 in order to solve for other steady state variables (as @jpfeifer did on one of the replications) However, if Capital is assumed fixed as in some models, then is it okay to substitute its value as 1 since steady state values will be used as an arbitrary baseline (reference point) to which deviations is measured ?
If capital is fixed then is it still valid to impose it as 1 without normalizing labor ?
I am not sure I understand the approach. You can usually only normalize something if there is a parameter you can set to achieve that normalization. For labor, that is the labor disutility parameter. If you fix capital to be 1 at all points in time, then clearly that is the correct value to use. Labor is then a separate degree of freedom you can chose by adjusting the labor disutility parameter to be consistent with the desired value.
Sorry to bother you again Prof., I came across a paper (RBC model, two sector economy, No exchange rate) where Home produces Non tradable and Foreign produce tradables. Home country consume tradables through endowment and financing via debt.
In steady state the model is solved by setting P (relative price of nontradable to tradable) to 1 . What is the economic intuition to say price of tradables is the same as nontradables in the steady state ? The PPP conditions asserts that “tradables” prices in home and foreign must converge to 1 , but here what is the intuition to set relative prices to 1 in the SS.
If No capital evolution equation shows up in the FOC given capital is fixed .Namely the:
K = (1-\delta)K(-1) + I . Does not exist.
In this case: I can not use the relationship \delta=I/K in solving for steady state as the above capital evolution equation is not an FOC equation . True ? Or I can get K/Y and I/Y using national accounts and proceed as usual ?
In case capital equation is present but no data on K/Y exists, then is it sound to get data for I and Y and decompose them using HP filter to obtain their long term average (Steady state level) to obtain K/Y using \delta=(I/Y)/( K/Y) ?
If capital is fixed, you can use any value you like because it is exogenous determined. However, if capital is fixed, then usually investment also does not show up in the model.
Yes Sir, the issue I am facing that after imposing K=1 then when solving for steady state variables say
Y=AK^\alpha L^{1-\alpha}
Y/K=Ak^{1-\alpha}
In this case and although K is fixed and no capital evolution equation in the FOC as you mentioned, then can I determine K/Y values from national accounts as long term average of K and Y and use this ratio in solving the steady state values. ? Or because the model does not infer that K/Y is constant in the steady state then I cant do that.
Sorry , I was mistaken, let me rephrase my question if possible . If in the equation Y=AL^1-\alpha I want to solve for Y per say, then can I make use of the steady state K/Y ratio that can be determined from national accounts to determine Y given K is assigned ?
Likewise for other ratios (C/Y , etc) , can I make use of these steady state ratios or their corresponding equation must be present in my FOC .