# Philips curve for a country with high inflation

my question is about the modeling of an economy with steady state positive inflation rate (net rate is 15% and gross rate is 1.15)
I have three ways
1- standard approach: linearization of the philips curve around the gross 1 and net zero steady stae inflation rate and ignore the positive rate. This method seems to be wrong.

2- the price indexation method

3- linearization of the philips curve around the gross non-one and net non zero steady state inflation rate.

Which approach is more correct?

Hi mmmoney,

Approach 1 is not suitable for your case.

Under Approach 2 indexation to trend inflation is used as a modeling device to muffle the very relevance of positive steady-state inflation. The theoretical and empirical grounds for this approach have been contested (in this respect, see primarily the criticism by Ascari and Sbordone (2014), section 3.6.1 at https://www.aeaweb.org/articles?id=10.1257/jel.52.3.679, previously discussed in Ascari (2004) https://www.sciencedirect.com/science/article/abs/pii/S1094202504000158)

Approach 3 is economically inconsistent. See section 2.2.2 in Ascari and Sbordone (2014). The correct approach is therein explained.

For example code, see @jpfeifer’s https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Ascari_Sbordone_2014

Dear. cmarch
hi

No, indexation is not the correct approach to deal with trend inflation, as documented in the sources referenced above.
I would suggest you follow the example code and read the paper by Ascari and Sbordone (2014) and the sections highlighted in my previous reply.

To qualify @cmarch’s answer: evidence from most developed economies rejects the presence of indexing in micro-data. So it’s not a micro-founded approach to deal with trend inflation. Maybe your country is different.

My modeling is for Iran.The long-run(steady stae) inflation rate in Iran is about 15%. Based on your answers, I need to check whether the microdata confirms the existence of indexation in iran or not.
I will also read the mentioned papers.
many thanks

I have another question. I would be very grateful if you answer it:
in linearization of the Philips (in presence of the price indexation), is gross inflation in stedy state considered one(Pi=one?)? I am attaching my linearization file. If possible, take a look at it and help me. Did I do it right?
Many thanksmaxPtit.pdf (437.1 KB)

No, it’s not necessarily equal to one. Is there a reason you linearize by hand?

is there another way? We usually do the linearization by hand

many thanks

You can work with a nonlinear model. See e.g. https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_3_nonlinear.mod

Yes, the nonlinear method can also be used. But in this case, solving the model becomes difficult.And it is generally recommended to use the linear method .is it not?

No, I think what @jpfeifer means is that you do not have to carry the burden of linearizing the model by hand.
Instead dynare can do this job for you.

Does dynare do this job?!! I didn’t know. What I have seen so far is that we either enter the non-linear model into the dynare or we linearize the nonlinear equations by hand and then enter the linear equations into the dynare

Yes, stoch_simul computes a Taylor approximation of the model around the deterministic
steady state and solves for the decision and transition functions for the approximated model.

You can manage the order of approximation with the option `order` which is 2 by default.

What do you think happens internally in Dynare if you enter the nonlinear model equations? It solve the model using linearization if you use `stoch_simul(order=1)`. The mod-file linked above produces exactly the same output as the linearized version at https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_3.mod

in the case that we enter the nonlinear model equations, we have to calculate and enter the steady state values of the variables and this makes it more difficult for us. But in the case that we enter the linear model equations, we consider the steady state values of the variables to be zero.it makes it easy for us

Now, if we use the indexation method, the steady state of inflation is non-zero for us. In this case, should we use the method of entering nonlinear model?

When linearizing, you linearize around the steady state. Except in very simple models without capital where the steady state drops out, the steady state values of the levels will be needed to set the parameters of the model. Thus, linearization does not make your life easier, it just shifts the problem.

If you have no idea about the steady state, then dynare can try to solve the static equations of the model for you. In this case it is typically a best practice to offer reasonable initial guesses for the steady state values. This can be done via an `initval` block.