# Problems with irf analysis

Dear Professor Pfeifer,

I’ve got some confusing problems on irf analysis. Would you please take a look? Thank you!

(1) The results of my model display the irf figures as bellow. I wonder why some of them have steep rise and rapidly steep decline(as like the left figure), and some have very strange fluctuation(as like the right figure). Is it normal, or they just imply the mistake of model setting ?

(2) I set a policy parameter Z in the model, and I wanna compare irfs of different policies under a certain shock e.g. TFP shock. What’s the difference between: 1) just change the value of Z under TFP shock 2) give Z a permanent shock and get mixed irfs with TFP shock ?
Which one is the right case?

(3) If I wanna get the irfs when Z=1 change to Z=2 smoothly between 10 years, how should I realize this ?

(4) Concerning the first-order condition of consumption with habbit formation, I have read two types in the paper:
1){{\left( c_{t}^{{}}-{{a}^{{}}}c_{t-1}^{{}} \right)}^{-1}}-\beta a{{E}_{t}}{{\left( c_{t+1}^{{}}-ac_{t}^{{}} \right)}^{-1}}=\lambda _{t}^{{}}
2){{\left( c_{t}^{{}}-{{a}^{{}}}c_{t-1}^{{}} \right)}^{-1}}=\lambda _{t}^{{}}
What might be the difference of these two types?

1. That is hard to tell without knowing the model in detail. Sometimes timing errors can cause such a behavior, sometimes it’s a model feature.
2. I don’t really understand the question. What do you mean with "mixed IRFs"? And what is Z?
3. That depends on the information structure. Do agent’s know the full path or is there a surprise every period?
4. The first FOC comes from internal habits where agents take the evolution of the habit stock into account. The second FOC is for external habits. See e.g. the paper by Dennis (2008):

Dear Professor Pfeifer,

For Q1: I check the timing (especially the timing of capital variable) and find no apparent errors. Do you mean it is acceptable when you say model feature? And also, how should I interpret the decline in the first period?

For Q2: Sorry that I did not make myself clear. Z is a policy parameter which plays a role as cost coefficient. Z=2 changing to Z=1 represents the improvement of policy.
If I mean to compare irfs of different policies(different value of Z) under a TFP shock, what should I do?
(1) just change the value of Z under TFP shock
or
(2) make Z a variable and give it a permanent shock, and analyze the irfs under mixed shocks(TFP shock and this permanent shock)

For Q3:I prefer that agents actually know the full path of this policy reform. Then in this case, what should I do to the code?

1. It’s your model, you need to understand what is going on in it. You did not even tell us what YV` is. The picture looks like an incomplete price adjustment in the first period.