Simple NK Model


I am trying to run a simple Non-linear New-Keynesian model, but it doesn’t satisfy to BK conditions. However it does and displays IRFs correctly when I remove the budget constraint. Can anyone help with this problem?
Simple.mod (1020 Bytes)

What determines B in your model? Usually, people impose that bonds are 0 in equilibrium

B is determined as the equilibrium level of net saving, that arises because of mismatches between the income and expenditures of the consumer. It can be zero if epsilon goes to infinity or marginal costs go to one in limit.

But where is the FOC for it?

In my model D stands for the Bonds, and the Euler equation is its FOC. As far as I understand, problem with BK arises because D(-1) is predetermined and in case it isn’t, IRF-s are identical to the standard simple models

The Euler equation only makes the household indifferent between consuming and investing into bonds. That is in every model. But there must be some market clearing assumption or endogenous mechanism that determines pins down the quantity of bonds. Do a thought experiment: if bonds are above steady state what makes them go back?

Ok, I got your point, but why there isn’t such a condition in other models, say in Gali and Monacelli (2005) or the models in Gali (2008) ?

Gali 2008 has that net debt is 0. Gali/Monacelli also assumes that domestic debt is in zero net supply

Ok, thanks for explanation. Then do I have to remove the budget constraint and variable D, or do something different?

Simply impose that D=0 in the budget constraint by dropping all terms related to D.
Note that I did not understand you logic where bonds come from. It sounded like you are tying to account for firm profits in equilibrium because of decreasing marginal returns. In that case, you need to be careful in distinguishing profits and bonds.

Thanks a lot Dr. Pfeifer. The logic was the same as the model Chapter 3 of Gali (2008) with only difference of non-linearity and Rotemberg pricing.

Dear Johannes,

You mentioned above, that in order to have non-zero net bonds in steady state, there should be a “some market clearing assumption or endogenous mechanism that determines pins down the quantity of bonds”.

Could you please refer me to one of the papers where this mechanism/assumption is present? Am working on a model with non-zero households’ deposits in steady state (because deposits is on liability side of banks’ balance sheet, who invest in loans), but I have not seen any examples in the literature with such a mechanism so far. Hence, I have problems with running the code of the model.

Thank you in advance.

A classical example is Schmitt-Grohe/Uribe’s (2003) paper on closing small open economy models. There is a unit root in the net foreign asset position if interest rates are constant/do not react to asset positions. Solutions in their case were to have a debt elastic interest premium or an endogenous discount factor. In closed economy models you can generate something similar by having a borrowing constraint where the Lagrange multiplier on the constraint increases in debt and therefore creates a “utility premium”.