First Difference vs Fixed Effects Serial Correlation

[Darcy Hill]

Hi,

I am running the following regression:

xtreg recycling loginc logpopden md11 md12 md13 md14 md15 md16 md17 md18 md19 md20 md21 md22 md23 md24 md25 md26 md27 md28 md29 md291 wasteavg dryavg quarter2 quarter3 quarter4 year2 year3 year4 year5, fe vce(cluster acode)

I check for serial correlation using

xtserial recycling loginc logpopden md11 md12 md13 md14 md15 md16 md17 md18 md19 md20 md21 md22 md23 md24 md25 md26 md27 md28 md29 md291 wasteavg dryavg quarter2 quarter3 quarter4 year2 year3 year4 year5, output

This gives me output

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
F( 1, 310) = 69.989
Prob > F = 0.0000

So I then do

reg D.(recycling loginc logpopden md11 md12 md13 md14 md15 md16 md17 md18 md19 md20 md21 md22 md23 md24 md25 md26 md27 md28 md29 md291 wasteavg dryavg quarter2 quarter3 quarter4 year2 year3 year4 year5)
predict u,resid
regress u l.u
Below is my output.

Source | SS df MS Number of obs = 5,174
-------------+---------------------------------- F(1, 5172) = 703.69
Model | 4128.47295 1 4128.47295 Prob > F = 0.0000
Residual | 30343.7093 5,172 5.86691981 R-squared = 0.1198
-------------+---------------------------------- Adj R-squared = 0.1196
Total | 34472.1822 5,173 6.66386666 Root MSE = 2.4222

------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
u |
L1. | -.3368239 .0126974 -26.53 0.000 -.3617161 -.3119317
|
_cons | -.048475 .0336738 -1.44 0.150 -.1144898 .0175399
------------------------------------------------------------------------------


Am I correct in thinking my results indicate I am inbetween a First difference and Fixed effects estimator?

What commands do I need to run this as a first difference calculation? I have never done first difference in Stata before.

[Carlo Lazzaro]

Darcy:
if you detected autocorrelation of the idiosyncratic error, why not simply sticking with -vce(cluster panelid)- standard errrors, that will acount for ir?

[Darcy Hill]

Hi Carlo, I have already clustered by panelid- acode? Is this sufficient to overcome the serial correlation and use a fixed effects model? Thank you

[Carlo Lazzaro]

Darcy:
yes, it is.

[Darcy Hill]

I am still a little confused, how does Clustering account for autocorrelation? What are the values from my regression
regress u l.u

need to be in order for me to consider first difference rather than fixed effects?

[Carlo Lazzaro]

Darcy:
-you ran an -xtreg,fe- panel data regression;
-you detected serial correlation via the community-contributed command -xtserial-;
-you received the advice to invoke cluster-robust standard errors instead of default standard errors to take serial correlation into account.
I would say that there's nothing else you can do to deal with serial correlation in panel data setting.

If you want to learn more details about the way cluster-robust standard errror relaxes the assumption of no correlation among the idiosyncratic errors within the same panel, see [ U ] 20 Estimation and postestimation commands, section 20.22, Stata .pfd manual.

[Paul Pelzl]

Interesting discussion. Carlo Lazzaro, wouldn't your argument then render the entire discussion on first difference versus fixed effects obsolete? See e.g. page 5 onwards here: http://fmwww.bc.edu/ec-c/S2007/327/EC327.S2007.nn3.pdf Specifically, if one can account for serial correlation in the error term anyway by simply clustering at the treatment unit, when would it ever be wise to use the first difference model rather than the fixed effect model?

[Carlo Lazzaro]

Paul:
personally, I've never used FD models, which are possibly useful when you have two time spells only.