Is it possible to have only firm effects or simply do a plug-in estimation with Krueger-Summers style correction?

[Alalalalaki]

I recently learned Patrick Kline's AEA lecture and want to do an empirical practice on some data I have. It gets me here.

The problem is that the data I want try has no worker identifiers and thus only firm effects and worker characteristics. Is it still possible to do the estimation using this pkg? I read the document and find "first_id_effects: includes first id effects. At this version it is required to include the firstideffects. (default = true)", so I guess it's no?

The second question is that is it possible to use some functions of this pkg to do the simple plug-in estimation with Krueger-Summers style correction or the homoscedasticity unbiased estimates in Andrews et al 2008? These methods seem not to be as complicated as Kline et al 2020 but the problem I encounter is that they seems to require inverting the matrix of the regressors. I have no idea how to do this because all high-dimensional FE packages using methods like LSMR does not produce the std errors for absorbed effects. I guess this could be done by the JLA approximation but I am not sure how to do it. Thanks in advance for any suggestions.

[rsaggio87]

Hi! Thanks for stopping by! These are good questions...

About the first one: This is not fully tested by what I would do is create "worker identifiers" by considering unique combination of your set of observable characteristics. Suppose you have (gender,education,birth,etc), you then create an identifier for each possible combo of these observables and let that be the "first_id".

About the second question. This is fairly simple to do. Inside the code, you can see that a key quantity that is being computed is the heteroskedastic unbiased estimates \sigma_{i}^{2}. You should simply replace each value of the vector with the corresponding MSE estimate: \sigma^{2} (a scalar). Changing the KSS routine in this way will then return you the Andrews et al. 2008 correction.

I hope this helps.
Best,
Raffaele.

[Alalalalaki]

@rsaggio87 Thanks for comment!

In terms of the first problem, you mean I can make all unique combination of the observed characteristics (which would be the controls in the original case) as some imaginary worker identifier and then do a KSS without controls? But in the document of the executable it says "The user should specify the most "granular" id here (first ID)." The unique combination of the observed characteristics are surely far less granular than firm effects in my data. Does it matter? And as far as I know the KSS algorithm , like all other methods under AKM framework with both worker and firm effects, identify the connected set and estimate through the movers. My data don't have any movers at all but only repetitive cross-sectional workers. Wouldn't it have then many observations with same worker_id moving to different firms if I make all unique combination of the observed characteristics as worker identifier? (Sorry if I am terribly wrong)

About the second question. To be clear, do you mean that to do Andrews et al. 2008 correction I should do first Bii_cov, y, X, sigma_i = leave_out_estimation(y,first_id,second_id,controls,settings) and then use the observation-specific errors \sigma_i to calculate DoF adjusted \sigma^{2} and replace all \sigma_i, and finally do lincom_KSS(y, X, Z, Transform, sigma_i; lincom_labels) ?

Btw, I have some precompling issues on the julia package. I will open an individual issue about this.

[rsaggio87]

First question: In this case identifaction (and the associated connected set) will be form by looking at workers with same, say, combination of (gender birth race education location) but who are working in different firms. So it's perfectly ok if you only have a cross-section. Having said this, I can't guarantee you that this would work or more importantly whether this makes sense for your paper but you can give this a spin and see what happens :)

Second question: Yes, exactly. But no need to run the lincom_KSS thing, that's for something else.

About compiling: yes, please, post your problem. I'll have someone look at it.

[Alalalalaki]

@rsaggio87 I am sorry but I tried the way you said, i.e. "create worker identifiers by considering unique combination of your set of observable characteristics" and it returns ArgumentError: reducing over an empty collection is not allowed. I think this is the problem that the worker_id is less granular than firm_id, because when I set some less granular random worker_id to the example in the document of VarianceComponentsHDFE, it shows exactly the same error.

[rsaggio87]

ok, good to know. Will try to give this a spin and see whether the code can be adapted for something along these lines and get back to you. You also said that you had compilation issues. Make sure to open a seperate issue on this so we can take a look. thanks! R

[Alalalalaki]

I have opened the issue about the compilation and @Alim-faraji has already fixed it. Looking forward to the future version of the pkg that could apply to the one FE case.

[Alim-faraji]

@Alalalalaki I tried to create a dataset with less granular worker_ids. I got the same error and it arises because the code couldn't find a leave-one-out connected set within its largest cluster. I don't think there is an easy way to get around it if it's inherent to your data. One idea is to utilize also other characteristics of the workers to create more granular worker identifiers if your dataset allows for it. Or even make it less granular, it will work if the largest connected set has a leave-one-out connected subset.

@rsaggio87 on our side, maybe we can also change the code in a way to check other connected sets if there wasn't any leave-one-out set in the largest connected set.

[Alalalalaki]

@Alim-faraji Thanks for comment. I dont think I can make it more or less granular given the data. How difficult would it be if I try to the learn the pkg code and borrow some part to make an ad-hoc solution? I think what I want to do is only a simpler version of the algorithm here (actually I think it is just the first example in section 2 of the original paper). (Btw, I am quite new to julia.)

[rsaggio87]

Hi! The real bottleneck of the code is computing what we define in KSS as (Bii,Pii). If you don't have a particularly large dataset it might be possible to exactly compute these quantities. If that is the case, then running the correction is very simple, particularly when looking at a simple one-way model like in that example. Let us know if you need any help!