# Rounding to zero too quickly

Hi! I took the example file (basic RBC model) and added the variable “test=(k-k(-1))^4”. When simulating, this term didn’t show up and then I figured this “test” variable is too small and therefore it’s not showing up. But here’s the problem, even when I multiply this term with 1000000000000000000000000000000000000000 it’s still not showing up. Sometimes in models I have this problem even when raising to 2 “test=(k-k(-1))^2”. Since it’s quite popular in the literature to use quadratic adjustment cost functions, for prices, capital e.t.c. this problem could mean that these terms are irrelevant. It seems like Dynare round this term to zero no matter what you do. Is this a bug in Dynare?

It’s not a bug. You are approximating a parabola up to first order at its vertex (i.e. in steady state where k=k(-1)). At this point, the slope is 0. Hence, up to first order, there is no change in test. Regarding quadratic adjustment costs, the first order conditions contain linear terms which do not evaluate to 0.

Yes you’re right . Thank you very much for your help!

I was puzzled when finding out that investment adjustment costs as used, e.g., in Gertler/Karadi (2011) have a zero variance. But I think I’m given the answer right here.

You are approximating a parabola up to first order at its vertex (i.e. in steady state where k=k(-1)). At this point, the slope is 0. Hence, up to first order, there is no change in test.

However, what still puzzles me is that when I use the aggregate ressource constraint (from FA.mod from Peter Karadi’s homepage): exp(Y) = exp( C )+exp(G)+exp(I)+eta_i/2*((In+I_ss)/(In(-1)+I_ss)-1)^2*(In+I_ss) and define
investcost = exp(Y) - (exp( C )+exp(G)+exp(I));

Dynare still gives me a zero variance for investcost, however, it provides me with a variance decomposition for investcost. How can a zero variance be decomposed?

You are right for the first part. For the second one, that is indeed strange. I would need to see the codes.

Thanks for the quick reply. Here is the code (taken from Peter Karadi’s homepage, I only added investcost).
FA_investcost.mod (7.6 KB)

Which version of Dynare are you using? In Dynare 4.5.7 the variance decomposition correctly shows NaN.