Picking Simulations

[ijyliu]

Here's what I suggest. Pick two tables to put in the main text:

1. Simulation that most matches our empirical application (we already have this run. It is probably one of the rho tables in the paper at the moment)
2. Simulation under which PCA performs best relative to other estimators (we have some options for this but I will try one last crack with N roughly equal to p. Specifically: me_cov = 0, p table, N roughly equal to p, exp. Exp will hurt the mean estimator, p and N will ensure curse of dimensionality hurts the IV estimator, me_cov doesn't really do much). I think the thing to use here is parallel_p_apes_N_100_exp.tex

I don't think the beta tables show much so maybe we should completely toss those out.

[paul-opheim]

I agree that we should throw the beta tables out.

That leaves these as characteristics that we can vary (along with the purpose that they serve in the paper):

• rho (matches up with our metric theory)
• p and N (these show that when N/p is low that PCA does better than IV and all measurements)
• exponential transformation y/n (this shows that PCA does better than avg when transformation = yes)
• me_cov (we know that this being nonzero makes IV worse but still better than the other options; maybe we shouldn't vary this anymore?)

[paul-opheim]

So basically the sim section should go like:

1. Here is the table varying by rho that matches with our application. We see how PCA does relative to other options and talk about how it matches with our theory
2. Talk about how we then investigated under what circumstances PCA does well
3. Reference tables in the appendix showing that this is when N/p is low and when we exponentially transform the data
4. Then show a table that has both low N/p and with exponential transformation of data (parallel_p_apes_N_100_exp.tex) that shows how PCA does the best in that circumstance

Does that seem like the plan? Maybe I should swap 3 and 4?

[ijyliu]

That would work. Though I would say you maybe don't need 3. Especially if we can add like a quick theoretical note on the exponential transform and/or curse of too many instruments

[paul-opheim]

Okay, let me write that up now.

[paul-opheim]

I just pushed the changes. I ended up putting just the p-charts in the appendix (for every N value and for both exp and no exp). Could someone read through my section to make sure it all seems reasonable?

[ijyliu]

I am reading and editing now

On Fri, Jun 4, 2021 at 4:18 PM marionoro @.***> wrote:

I just pushed the changes. I ended up putting just the p-charts in the appendix (for every N value and for both exp and no exp). Could someone read through my section to make sure it all seems reasonable?

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[ijyliu]

I think we will want to clean up this paragraph as it seems a little long and rambly:

but other than that the sim section now looks pretty good

[ijyliu]

I ended up putting just the p-charts in the appendix (for every N value and for both exp and no exp).

So you didn't think the rho charts added anything really? I guess that seems plausible.

I know that like the beta charts didn't show much at all of course. And probably no need to mention the me_cov stuff.

[paul-opheim]

I made some changes:

Yeah, I figured that 10 charts would be too many in the Appendix, so I didn't include the rho charts. I'm open to being persuaded otherwise though.

[ijyliu]

Yeah, I figured that 10 charts would be too many in the Appendix, so I didn't include the rho charts. I'm open to being persuaded otherwise though.

Ok yeah the rho chart we have in the main text is pretty good.

[ijyliu]

Let me read over that new paragraph, in the mean time I guess you should proofread everything else

[ijyliu]

Alright, made some revisions. But overall I think this issue is closed. I feel pretty good about the sim section, just need to work on everything else now.