Heteroskedasticity and Serial Correlation in Two Way Panel FE models

[Prateek Bedi]

Hi,

I have an unbalanced panel dataset with 1696 cross-sectional units and 16 years. I am using FE model (as suggested by Hausman test) with cross-sectional fixed effects and year dummies. I have the following questions:

1. Do I need to check and correct for heteroskedasticity and autocorrelation as I have already eliminated the firm-fixed effects through within group transformation and I have also introduced time dummies to treat each year separately.

2. If I need to check for heteroskedasticity and autocorrelation, how do I do it? Which are the relevant tests in STATA for large N and small T?

3. If both heteroskedasticity and autocorrelation are present in my model, how do I correct for them?

4. Does presence of heteroskedasticity and autocorrelation affect sign and significance of coefficients?

Thanks a lot!

[Andrew Musau]

If you cluster your standard errors at the cross-sectional level, they will be robust to heteroskedasticity and arbitrary forms of autocorrelation given the dimensions of your data.

*id is the cross-sectional identifier in your xtset command
xtreg depvar indepvars i.year, fe cluster(id)

Regarding 4, heteroskedasticity and autocorrelation affect your inference, not the point estimates.

[Prateek Bedi]

Thanks a lot Andrew Musau! Any idea about Point 2?

[Andrew Musau]

#2 implies that testing is not needed, but if you must, see

https://www.stata.com/support/faqs/s...tocorrelation/


ADDED IN EDIT: Note that the link uses xtgls to run a likelihood ratio test to test for heteroskedasticity. The equivalent xtgls command for the two-way fixed effects model estimated using xtreg is the following

*xtset id year
xtreg depvar indvars i.year, fe
xtgls depvar indvars i.id i.year, nmk

[Prateek Bedi]

Alright. I actually used Modified Wald test for examining group-wise heteroskedasticity in fixed-effects model (xttest3). Please guide as to which test is recommended: Wald Test or LR Test and what is the difference between the two.

[Andrew Musau]

The help file of xttest3 addresses the difference

Greene's discussion of Lagrange multiplier, likelihood ratio and standard Wald
test statistics points out that these statistics are sensitive to the
assumption of normality of the errors. The modified Wald statistic computed
[by xttest3] is workable when the assumption of normality is violated, at least in
asymptotic terms. In terms of small sample properties, simulations of the test
statistic have shown that its power is very low in the context of fixed effects
with "large N, small T" panels. In that circumstance, the test should be used
with caution.

Because you have a large N, small T panel, you should prefer the LR test. But as stated again and again, you do not need to run any tests if you just run your regressions with robust standard errors. Because of this, I will bail out from further discussion of testing since it is a purely theoretical exercise.

[Prateek Bedi]

Alright Andrew Musau. Thanks a lot for your very helpful inputs and guidance. Really appreciate.