Firm and Year Fixed Effects Panel Data Quantile Regression

[Taruntej Singh]

Hi

I wish to apply quantile regression to a panel dataset of 281 firms over a 5 year period.

I have come across the following commands but am confused on which one to go for:

1. qreg
2. qreg2
3. qregpd
4. xtqreg

Please help me in this regard.

[Joao Santos Silva]

Dear Taruntej Singh,

With T = 5, I am afraid none of the methods is reliable. It is true that qregpd will work, but it will not estimate a model with fixed effects as you probably have in mind.

Best wishes,

Joao

[Taruntej Singh]

Dear Joao Santos Silva

Thank you for your reply.

If not with fixed effects, can I still run quantile regression on my dataset? If yes, then which command should I be using: qreg or qreg2?

Dear Taruntej Singh,

With T = 5, I am afraid none of the methods is reliable. It is true that qregpd will work, but it will not estimate a model with fixed effects as you probably have in mind.

Also, can you please suggest any readings that I could cite with respect to your reply above in which case I would consider dropping the fixed effects from the model.

Regards
Taruntej

[Joao Santos Silva]

Without fixed effects, you can use qreg2 and cluster the standard errors. You can also use qreg2 to estimate a model with "correlated random effects".

Best wishes,

Joao

[Taruntej Singh]

Dear Joao Santos Silva

I just saw this comment on a different post:

Dear Chan Lim

Strictly speaking, in the paper we did not prove any results for that case. Having said that, my guess is that including also time dummies will be OK; we will work on that case as soon as we have time to do it. Finally, note that qregpd allows you to control for the two types of fixed effects, but does not really include them.

Best wishes,

Joao

I actually just need to control for firm and year fixed effects and not really include them. In that case, can I use 'qregpd' given my panel of 281 firms and 5 years? (And, Is 5 years of 'N' enough of a time period to carry out quantile regression reliably in case I use qregpd?)

Regards
Taruntej

[Joao Santos Silva]

In what sense do you want to control for FE without including them?

Joao

[Taruntej Singh]

Dear Joao Santos Silva

I meant I don't really need the coefficients for the firm and year effects; just need to control for those effects.

Did I interpret you wrongly?
What did you mean when you said qregpd controls for those effects but does not really include the?

Regards
Taruntej

[Joao Santos Silva]

Dear Taruntej Singh,

The estimator implemented in qregpd uses the fixed effects in the moment conditions used to estimate the parameters, but the model does not include the fixed effects. This is just like when we use instrumental variables estimators: the instruments are used in the moment condition but they are excluded from the model.

Best wishes,

Joao

[Nishant Kathuria]

Hi Joao,

I am a bit confused by the conversation above. If firms in a sample across multiple years remain in the same industry, do I need to control for the industry effects if I use xtqreg?

Thanks,
Nishant

[Joao Santos Silva]

Dear Nishant Kathuria,

It depends on what you are doing and on how you are defining your panel. If you define your panel at the firm level and firms do not change sector, the sector effects is captures by the firm fixed effect and you do not need to add industry controls.

Best wishes,

Joao

[Nishant Kathuria]

Dear Joao Santos Silva,

Thank you so much for the reply. Yes, I meant the analysis by firm-year. Have a good day!


Nishant

[Travis A. Smith]

Dear Taruntej Singh,

The estimator implemented in qregpd uses the fixed effects in the moment conditions used to estimate the parameters, but the model does not include the fixed effects. This is just like when we use instrumental variables estimators: the instruments are used in the moment condition but they are excluded from the model.

Best wishes,

Joao

I want to point out that the time fixed effects are estimated in qregpd. They can be accessed post estimation

mat list e(gamma)

I suppose the word "model" in Joao's quote is specifically referring the equation of interest. I would say an IV is in the model, although it is not specified in the equation of interest. It enters the model through a separate moment condition.

I think a better comparison of what qrepd does is to compare it to the demeaning method of estimating an OLS fixed effects regression: here, you don't estimate the actual individual fixed effects in OLS, but you control for them.

qregpd uses demeaned X's (and/or Z's) as instruments in one set of moment conditions. The second set of moment conditions is the standard qreg moment condition.

Also, qregpd is consistent for T=2. I'm not sure what Joao meant by it being unreliable at T=5.

[Joao Santos Silva]

Dear Travis A. Smith,

You are right in saying that I used the word model to mean the equation; I believe this is in line with standard use as we say things like valid instruments are excluded form the model (meaning the equation). In this context, I would say the instruments are observable and are in the information set, but are not part of the model.

You are also right in that my comment about T = 5 was not very precise: the correct statement would be that no quantile regression estimator of a model that includes additive fixed effects will be reliable for T = 5. As I noted, the estimator implemented by qregpd will be valid, but it does not estimate the equation most people have in mind.

However, I think it is very misleading to compare what qrepd does with the demeaning method of estimating an OLS fixed effects regression. In the OLS approach you estimate an equation with additive fixed effects, although you do not need to explicitly estimate the fixed effects. The method implemented in qrepd estimates an equation that does not contain the fized effects, and that is a fundamentally different approach.

Do not get me wrong, the estimator implemented in qregpd is beautiful, but users should be aware of what exactly they are estimating, and that is not what most peolpe have in mind when they think of models with fixed effects.

Joao
PS: Good to hear from you!

[Jessica Thacker]

Dear @Joao Santos Silva,

I want to run pooled quantile regression for firms that belong to two different industries and I have unbalanced panel data for the same. I am not able to figure out the difference between qreg command with robust standard errors and qreg2 command.

Also, I read that using qreg2 command with the option of cluster helps in taking into consideration the serial correlation that may be present in the firm data, and the standard errors will be heteroskedasticity as well as serial correlation robust. In this context, I wanted to ask if the cluster should be firm or industry as each firm in the data remain in the same industry for the entire data period.


I would be of great help if you help in clarifying the same. I would also like to ask what tests are needed to be performed before and after using these commands.

[Joao Santos Silva]

Dear Jessica Thacker,

The difference is that, as far as I recall, qreg does not allow the use of clusteres standard errors, and qreg2 does (they also use different versions of the robust standard errors). In your case, I would cluster by firm.

Best wishes,

Joao