Hi all.
I introduced investment adjustment cost into my government capital accumulation function (line 154→line 155), but the irf under two different settings are exactly the same, can anyone explain why?
line 154 kg=ginv+(1-deltak)kg(-1); no adjustment cost
line 155 kg=(1-mu/2(((ginv/ginv(-1))-1)^2))*ginv+(1-deltak)*kg(-1); yes adjustment cost
rr2.mod (7.8 KB)
Quadratic adjustment costs in budget contraints etc are 0 up to first order. The derivative in steady state will contain phi*(ginv/ginv-1)=0 and drop out.
Thus, they only matter via other first order conditions where the first derivative above already appears and then the approximation takes another derivative. But in your model, government investment is exogenous and therefore adjustment costs do not affect any other condition. That explains why they drop out of the model.
Thank you for your reply, coudl you give me some suggestions how to correct the model so that the first order condition of public capital will not drop out of the model? The only thing I need to do is to endogenously determine government investment?
Yes, endogenizing it would help. Alternatively, you can simply make the exogenous process smoother.