Short Panel data + fixed effect model, questions about time dummy and unit root

[Angelina Hwang]

Hi dear Statalist, I’m exploring how the bank specific characteristics and macro variables (liquidity of loan secondary market) affect the banks’ loan origination decision.
In my story, liquidity of loan secondary market plays important role, because the banks’ behaviour will show difference upon different market liquidity trend.
I meet some problem when I’m working with my panel data so I’m asking for your kind help.

Here is some information about my data and model
1) Short balanced panel data:
N=370 banks
T=22 quarters
2) choose between Pooled regression/FE/RE: result is FE
3) data suffer from heteroskedasticity, autocorrelation/serial correlation, cross-sectional dependence problems

My questions are:
Q1.I test the time-effect by running
-xtreg y x i.quarter,fe-
-test quarter1=quarter2=…=quarter22=0
I find that there is time-effect. It seems that I should do the two-way-fixed effect.
But since my “liquidity of loan secondary market” is a macro variable which takes on the same values for all banks in any given time period, it will be colinear with the year dummy. It should be dropped. I’ve tried the two-way-fixed effect model, and the coefficient of liquidity became really strange.
So is it OK if I do not include time-fixed effect? Or are there any other ways to fix time-effect problem without dropping my liquidity variable?

Q2. Is the unit root test necessary to do here? My T is 22 quarters, only about 5 years. And should we judge whether to do the unit root test based on absolute time length, or just number of T?

Q3.It -xtscc- the right way to solve my data problem?

Thanks so much for your help!
Best,
Angelina

[Angelina Hwang]

Some people suggest that i don't need to consider the time effect then. But i still feel uncertain since the liquidity cannot represent every thing.
Dear Statalists, do you have any suggestion?

[Phil Bromiley]

You might consider xthybrid or the Mundlak estimators.

22 observations doesn't seem short by most standards. If you're using quarterly observations, then 22 is the right number.

In general, you can estimate xtreg with clustered robust standard errors and i.quarter as a control for year. There is a trade off with serial correlation - xtregar doesn't handle heterskedasticity but does give you better estimates of the betas, but xtreg handles the error problems better at the cost of less good estimates of the betas.

[Angelina Hwang]

You might consider xthybrid or the Mundlak estimators.

22 observations doesn't seem short by most standards. If you're using quarterly observations, then 22 is the right number.

In general, you can estimate xtreg with clustered robust standard errors and i.quarter as a control for year. There is a trade off with serial correlation - xtregar doesn't handle heterskedasticity but does give you better estimates of the betas, but xtreg handles the error problems better at the cost of less good estimates of the betas.

Thanks sooo much Sir!