A mathematical question about extracting the Phillips curve

General DSGE Modeling
1

Hi everyone
I have a mathematical question about extracting the Phillips curve.
I know how to extract a standard Philips curve. But based on an idea (from the subject of creative accounting in banking) I have made changes. Now I have a question about how to extract the Phillips curve in this situation. Thank you for your help. Sorry if the question level is low. I attach my questionm-philips.pdf (629.7 KB)
many thanks

2

I am not sure I understand the problem. You are solving the firm’s optimal pricing problem, i.e. the choice of the price today. All past decisions do not really matter. In the upload why should firms care about the past loan? They should take into account what will happen during the time the price set today is operative.

3

This is an idea that I have extracted based on the creative accounting and that equation is extracted based on 15 steps of the bank balance sheet . defaulted loans Instead of loan loss provisioning , are prorogated on the basis of creative accounting in banking . As a result, the firm’s debt to the bank becomes more and more. IC-A.pdf (723.9 KB) will attach a better description of the problem

4

i’m modeling the endogenous money creation

5

Again, in your document the relevant part of the constraint is completely irrelevant for the Phillips Curve. If you take the derivative with respect to P_t(i), it will drop out. Hence my question.

6

in the standard model, the loan is equal to the cost of labor and capital,L=wN+rK So there is no Pt(j) in the loan equation and If i take the derivative with respect to Pt(j) , it will drop out. But when I changed the loan equation, The loan equation became a function of the default rate ϕ; Loans of the previous period that have not been repaid and have been respited in this period, and etc. in this new loan equation, P(t-1)(j) , P(t-2)(i) , L(t-2)(j) and etc are seen. Now when I take the derivative with respect to Pt(j) in the objective function; it will not drop out (are seenP(t-1)(j) , P(t-2)(j) , L(t-2)(j) in the loan equation) .it may be said that P(t-1)(j) is not important in determining the price today. But in the phrase related to the menu cost, we have a P(t-1)(j) and we move time forward one period and then take the derivative with respect to Pt(j). .C-A.pdf (725.9 KB)