Implement Bianchi overborrowing model

[jstac]

Implement the model in Overborrowing and Systemic Externalities in the Business Cycle

On http://www.javierbianchi.com/research.html there is Matlab code.

Can anyone reproduce Fig 1 of the paper in Python or Julia? I've had a go but couldn't get the same output. If you run main.m in the Matlab zip file you'll see that the code seems to roughly reproduce Fig 1.

It would be enough just to replicate the decentralized equilibrium, which is up to line 162 in main.m

CC @Smit-create @chien-y @Flintro @natashawatkins @cc7768 @shlff --- in case anyone feels like a small coding challenge :-)

[jstac]

Here's my not very successful attempt: https://gist.github.com/jstac/0b0fbe7a3afcdd14c9286154235138b2

[jstac]

CC @crondonm

[shlff]

Thanks @jstac and @Flintro. It is a very interesting paper.

Just in case when you read. There is a small typo in their definition 1 on page 3406 that the second $\hat c^N (b, B, y)$ should be $\hat c^T (b, B, y)$. Please find the circle in the following screenshot:

[jstac]

Thanks @shlff , nice pick up.

I agree it's an interesting line of work, and potentially very useful.

[jstac]

@Flintro, did you find time to take a look? @shlff please keep me posted if you make progress.

CC @zejinshi, in case you have time + interest.
CC @Shunsuke-Hori in case you have time + interest, and a Julia version would be fine.

[Flintro]

@jstac I think I've fixed the issue for the decentralised but the planner is still a bit buggy. I'll email the ipynb to you.

[jstac]

Huge thanks to @Flintro for finding the typos in my code that were messing up the equations!

Closing this in favor of QuantEcon/cbc_workshops#3

[shlff]

@jstac sorry a bit late but I reckon I also find the typo. I'll email mine to you too.