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ijyliu / ECMA-31330-Project

Econometrics and Machine Learning Group Project
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Benchmarking Against an Instrument #13

Closed ijyliu closed 3 years ago

ijyliu commented 3 years ago

I think this is a good idea. We can simulate an instrument in the Monte Carlo, and also try to find one for the application and compare.

ijyliu commented 3 years ago

It's really hard to think of a good instrument for GDP @marionoro .

Exogenous technological progress comes to mind, but that's impossible to measure.

Macroeconomics is just the theory of everything affects everything.

ijyliu commented 3 years ago

Another point, which I had forgotten- you can instrument for one mismeasured variable with another measurement of the same thing and this estimator will do well if the error is just noise for both.

Ie you might not need an exclusion restriction, etc.

ijyliu commented 3 years ago

Another point, which I had forgotten- you can instrument for one mismeasured variable with another measurement of the same thing and this estimator will do well if the error is just noise for both. also in this case you might not need an exclusion restriction, etc.

@marionoro maybe you want to also try this for comparison?

ijyliu commented 3 years ago

Ugh, can't believe I forgot about this classic paper: https://www.jstor.org/stable/2117766?seq=7#metadata_info_tab_contents

See p.1163 where there are a couple tactics, including taking the mean of the mismeasured items and instrumenting one mismeasurement with the other.

ijyliu commented 3 years ago

@nicomarto I think we have been conceptualizing the usage of IV to deal with measurement error incorrectly- you don't need a totally new variable and an exclusion restriction.

Here's what I think are the paths forward

  1. Fix the theory section to describe the case where you instrument one mismeasurement with another. It should be fairly easy to find proofs for this in an intro econometrics text, and then paul and I will have to update our simulations and empirics
  2. Deprioritize IV (as paul I guess paul and I have been doing)

I don't think it's hard to either include or exclude IV so I don't have strong feelings

nicomarto commented 3 years ago

@nicomarto I think we have been conceptualizing the usage of IV to deal with measurement error incorrectly- you don't need a totally new variable and an exclusion restriction.

Here's what I think are the paths forward

  1. Fix the theory section to describe the case where you instrument one mismeasurement with another. It should be fairly easy to find proofs for this in an intro econometrics text, and then paul and I will have to update our simulations and empirics
  2. Deprioritize IV (as paul I guess paul and I have been doing)

I don't think it's hard to either include or exclude IV so I don't have strong feelings

I do not think we are doing that. By doing the "new variable", I am just generalizing the instrument that could be used: a new variable, or another missmeasure variable. The "other" miss-measures variable idea, it is a particular case in which \Pi=1.

What do you mean about not needing a exclusion restriction? We do need that. I literally took this from Shiakh's lecture notes.

nicomarto commented 3 years ago

We need also need the general case, since Bonhomme asked us to simulate the case with more than one missmeasured covariates.

ijyliu commented 3 years ago

Nevermind on that not needing the exclusion restriction point.

I guess the statement that's maybe not clear is

However, finding a reliable source of exogeneity is difficult, and it is impossible to conclusively prove a suitable exclusion restriction. The use of IV as a bias-correction method is thus often unfeasible.

I think you need to clarify what part of the exclusion restriction is difficult.

Let Y = XB + E with Z the other measurement, X = X* + U.

If you have the main model Y = XB + E correctly specified (no correlation between X and E) the it seems like you pretty clearly have no correlation between Z and E (since Z is just another measurement of X). No correlation between Z and U is probably the harder part. But when I see the word "exclusion restriction" or "exogeneity" in this case, my first instinct is that you are saying the Z and E correlation is hard.

Also if we are saying no correlation between Z and U is hard when we are using IV with another measurement, I don't see how PCA could do better since it also uses another measurement.

ijyliu commented 3 years ago

I kind of watered down claims about how hard IV is in d4f775d9e824f4bf766946e4bb28a0771a4fc583

if you click on that link you can see the changes so you can make adjustments on your own

ijyliu commented 3 years ago

I think we have moved on from this issue. We have identified a couple cases where IV does poorly and might want to develop those more.