The Baseline New Keynesian DSGE model

Dear Professor Jpfeifer,
I am building a model based on the Baseline New Keynesian DSGE model described in Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez (2006) and I got very good help from your mod file. I have two questions. 1) in page 9 of the PDF we see: all intermediate goods prices are pti. But when the profit is calculated (F line 221 mod file) there is no price for the intermediate production. May I know why? 2) in calvo pricing (page 13) it is shown that Pi(inflation) is p/p(-1). but in mod file we have pi_ss=1.02. what is the intuition of this equation. Pi is a definition, or it is cleared endogenously within other equations?

Sincerely,
Leo

I don’t really understand the two questions.

  1. The profits are the aggregate profits, so you need to integrate over the intermediate goods. That’s why the aggregator ld shows up.
  2. Inflation is an endogenous variable, but it’s steady state value cannot be determined endogenously due to the Fisher equation. Thus, you need to fix a a value and then compute the corresponding nominal interest rate.

Dear Professor Jpfeifer,
Thank you for your reply and sorry for the vague questions. about the first question, we have final good (Y_d, with price P) and intermediary good (Y, with price P_i). It is my question that why in equation 22 of your mod file for the profit of intermediate producer, we see “Y_d” and not the aggregate of “Y=Y_d * v_p”, and we don’t see any price. and about the second question (is more basic), if the definition of inflation is pi=p/p(-1) why we cannot say the ss=1.
Sincerely,
Leo

  1. As I said, this is the real profits of the intermediate goods firms after aggregation. That is, you take the integral over firms. That is why yd shows up: the price dispersion term vp decreases aggregate output and thus profits.
  2. You can pick any number for pi_ss, which is the inflation target of the central bank. Only inflation rates are stationary in the model, not price level itself.

Great. Thank you for the clear answer.