Why is IV doing so well now?

[ijyliu]

It seems like IV is now beating everything else by a ton in the sims. This is true in both the non-transformed and the half-transformed case.

This seems to have happened after the run Paul uploaded yesterday. You can see where the tables changed here: https://github.com/ijyliu/ECMA-31330-Project/commit/27c837e75e953764bbe076aab79b7a74ed5703b0

So I think this is the result of including an intercept in the simulations and the IV first stage, or switching from 2SLS by hand to the statsmodels package.

[ijyliu]

Notes:

IV collapses when you bump p up to like 100 or 500, but at this point averaging does well again. So, the ideal environment for PCA is to do the transformation and a large p.

[ijyliu]

Notes:

Estimator probably does better with p roughly equal to N

Ideal empirical setting might be more p and more principal components

With more time, could try to use an optimizer to find precisely ideal conditions for the estimator

[paul-opheim]

I think we've resolved this.

[ijyliu]

Note for isaac to maybe note in like the conclusion:

Ideal empirical setting might be more p and more principal components

With more time, could try to use an optimizer to find precisely ideal conditions for the estimator

[ijyliu]

@marionoro added this to conlusion

probably can close this issue now

[paul-opheim]

Hmm I don't think that we should add that. I don't think we need/should mention the ways in which what we did was incomplete.

[ijyliu]

ok I want to hear @nicomarto 's opinion tho

[nicomarto]

Hmm, I would say that instead of that we could say "an interesting extension of this project could be an empirical case where p is large and n small"?

[paul-opheim]

I think that makes sense.

[ijyliu]

ok let me draft something

[nicomarto]

good!

[ijyliu]

[paul-opheim]

Looks good to me.

[nicomarto]

Good job Isaac!