Closing Small Open Economy with Debt elastic interest rate

[Philipp]

Hi there,

I want to replicate the paper by Schmitt-Grohé and Uribe 2003 "Closing Small open Economy models". I was able to compute the Models 1 and 1a for the endogenous discount factor. Then I tried to compute the Model 2 for the debt elastic interest rate and thats where the struggling began... Actually, I have no clue anymore how to proceed. I would like to have a model in exp() rather than levels to capture the %-age deviations from steady state.

I would appreciate it if someone had a hint on where to start with the corrections.

Thanks for your comments,

Philipp

[Philipp]

I figured out (with the great help from my professor F.Collard) how to do it.

For the ones who are interested in solving SOE models some hints:

1. If you have a model with %age deviations from Steady State, i.e. in exp(), then make sure that foreign assets (usually d_t, sometimes b_t) can be negative and hence logs cannot be taken. So this variable should not be written as exp(d) rather just d. This also holds for the trade balance and the current account!

2. Make sure you get the right initial values. If you have exp(k)... in your equation, then the initial value should be k = log(kss) or something similar. This is the substitution you were making when substituting k by log(k) (from unit deviation to %age deviation).

3. Make also sure that the lambda (marginal utility of wealth) is expressed in exp().

I hope I could help some of you, students mainly, who encountered some similar problems as I did when starting with dynare.

Sincerely, Philipp

[monad]

Hi Philipp,

I also work with the SOE model which I expressed in exp() in Dyanre. As yourself, I also figured out that NFAs must be in levels. Therfore, I agree with all your points and remarks. However, I would like to double check with you if my thinking is correct on implementing an exponential function to 'close' the model. In particular, if the function is of the form:

psi*[exp(d-dbar)];

1) I need to assume that the ss of d (i.e., dbar)=0
2) And then, do I want to take another exponent because the model is in exp(), ie., exp(psi*[exp(d-dbar)])
or - simply have psi*[exp(d-dbar)-1]

What is your opinion?

Thanks a lot,
Monika

[Philipp]

Dear Monika,

I'm truly sorry that I haven't answered before, I hope you were able to figure out how to do it anyways.

Actually, there is a really elegant way how to deal with the problem:

First, in an open economy the level of debt can be negative so you cannot take logs, this is yet not true for the other variables. Thus it is possible to write the model in %-age deviations from Steady State.

Second, I told dynare to compute the risk premium:

risk = psi*(exp(d-d_bar)-1);

and then the interest rate follows:

exp(r) = r_w+risk;

This gives the euler equation of the form:

// FOC wrt d (Euler Equation)
exp(lambda) = beta*(1+exp(r))*exp(lambda(+1));

I hope I could help you with that.

I'll send you the complete model anyways.

Sincerely

Philipp

[singer]

Hi Phillip,

I am a student who is trying to replicate the SGU models as well. I was able to replicate the debt elastic interest rate and portfolio adjustment costs but not the endogenous discount factor ( 1, 1a) and the complete markets model. In your earlier post you said that you were able to figure out the two versions of the endogenous discount factor and I was wondering if you could post the file for me.


Thank you

[singer]

Here is my file for the endogenous discount factor model. The first one is model 1 and the second is model 1A.

Thanks!

[jpfeifer]

Some of the above files contained errors. A (hopefully correct) replication file for Schmitt-Grohe/Uribe (2003): "Closing small open economy models", Journal of International Economics, 61, pp. 163-185 is available on my homepage at https://sites.google.com/site/pfeiferecon/dynare.