Arellano 2008 max question

Lectures
1

Hi everyone,

I’m going over the Julia notebook on Arellano (2008) and I’m struggling to understand something.

In the inner for-loop of the one_step_update! function, it seems like optimal bond choice is solved by taking the maximum over consumption. However, I would’ve thought that the max should be taken over the value function for continuing/commitment, instead.

Is there a particular reason why this is done/why this is okay?

Cheers!

2

Thanks for your question @NuancedPaul .

When you said

it seems like optimal bond choice is solved by taking the maximum over consumption.

were you referring to the following two lines of code?

The function max here is just to ensure positive consumption.

And this if condition reflects B \geq -Z to rule out Ponzi schemes.

The whole method one_step_update! is to update the value functions and their relevant policy.

Hope this answers your question. Feel free to let me know if you have further questions.

Best - Shu

2 Likes
3

Hi Shu,

thanks alot for your response!

I understand most of it except for one small bit - I agree that v_c(B^\prime, y^\prime) is a constant term w.r.t. B, but since we’re maximizing w.r.t. B^\prime, wouldn’t we need v_c(B^\prime, y^\prime) to be constant w.r.t. B^\prime for it to be okay to take the max operator inside u()?

Cheers!

4

Thanks @NuancedPaul . Please find a modified answer above.

Hope it answers your question. Let me know if you have further question.

Best - Shu