Threshold for small/large T in quarterly panel data

[Abdan Syakura]

Dear all,

Sorry for basic question. I am estimating dynamic panel data model for 40 countries & 20-30 years at quarterly frequency. I am trying to decide whether I should use xtreg FE model or xtabond. From what I read, xtabond is for large N and small T, while xtreg FE can work (less dynamic panel bias) for large T. Since I have 20-30 years of data (depending on the country) at quarterly frequency, is that a small or large T? It is lower than 25 in terms of year, but of course more in terms of quarter. Thank you.


Best regards,

Abdan

[Joro Kolev]

Your question is not that basic.

If you have large N, small T, you have to use -xtabond-. In this scenario -xtreg, fe- will lead to inconsistent estimates.

In your case, because you can say that both N and T are large, both -xtabond- and -xtreg, fe- will lead to consistent estimates. The abstract condition for consistency of OLS (that is, the Least Squares Dummy Variable estimator), which in your case can be plausibly claimed, is that T must grow relative to N in such a way that N/T goes to come constant bigger or equal to 0 and smaller than infinity.

Alvarez, J., & Arellano, M. (2003). The time series and cross‐section asymptotics of dynamic panel data estimators. Econometrica, 71(4), 1121-1159.

[Abdan Syakura]

Many thanks Joro,,

[Joro Kolev]

You are welcome.

And one more thing: In asymptotics there are no thresholds. We cannot say that there is some real world/real dataset number P such that if N>P, then N is large.

The notion of T or N going to infinity is very abstract and in my view has no fixed/precise meaning in real life, for real datasets.

Once we have accepted this abstract notion of a quantity going to infinity, we can talk about relative rates of how other quantities go to infinity relative to the first quantity.

Many thanks Joro,,

[Jeff Wooldridge]

To add to Joro’s very helpful comments, you allow cross country correlation and Newey-West standard errors using the user-written xtscc. It also works with “large” T.

[Vasilis Papas]

Dear Joro Kolev i know this is an old thread but i have a relevant question to this topic. I have quarterly data, with 36 quorters from 2011 to 2019 and 32 banks, so it is a long panel. I am using the lagged value of the dependent variable Lending_ratio as an regressor, and i am also lagging all the other regressors one time period.

Since T>N, i understand that i cannot use xtabond is that correct? In this case can i use fixed effects with xtreg as you suggest above, or should i use xtregar?

Also if i want to include time fixed effects do i just have to include i.quorter ?

Also, if it is possible, could you tell me what are the tests for autocorrelation and heteroskedasticity in a dynamic panel with T>N?

Thank you very much in advance.

[Joro Kolev]

Hi Vasilis,

There is no such rule that if your T>N you cannot use -xtabond-. You can use -xtabond-, and because you have long T, you can also use -xtreg-, as the Nickell's bias vanishes as T grows.

We know what -xtregar- does, but I think we have not quite figured out yet in which conditions -xtregar- is appropriate, see this discussion between Professor Wooldridge and myself https://www.statalist.org/forums/for...ge-t-estimator

Yes, you can include time effects with i.quarter -- as your N can be assumed to be large, they will be estimated consistently, and even their standard errors will be correct.

In -xtabond- with short T, autocorrelation in the idiosyncratic error is a disaster which leads to inconsistency, I would think that if you apply -xtabond- it will automatically report autocorrelation test, because this is serious misspecification of the model.

If we take the view that both your N and T are large, and you go ahead with -xtreg, fe-, I would think that you could apply stanard test of autocorrelation and heteroskedasticity. There is one test of autocorrelation due to Wooldridge and programmed in Stata by Drukker. There must be also some pre-programmed hetero test, check out -xtreg postestimation- .

Dear Joro Kolev i know this is an old thread but i have a relevant question to this topic. I have quarterly data, with 36 quorters from 2011 to 2019 and 32 banks, so it is a long panel. I am using the lagged value of the dependent variable Lending_ratio as an regressor, and i am also lagging all the other regressors one time period.

Since T>N, i understand that i cannot use xtabond is that correct? In this case can i use fixed effects with xtreg as you suggest above, or should i use xtregar?

Also if i want to include time fixed effects do i just have to include i.quorter ?

Also, if it is possible, could you tell me what are the tests for autocorrelation and heteroskedasticity in a dynamic panel with T>N?

Thank you very much in advance.

[Vasilis Papas]

Dear Joro Kolev thank you very much for the immediate and detailed reply. I didn't know that i could use the xtreg command in dynamic panels even if T is large so that was really helpful. Regarding xtabond, when i read the description of the command it said that it is designed for datasets with many panels and few periods so i thought that it would not be the best choice for my case.

Regarding the tests i will check the things you pointed out. Thank you again very much for your help!