Can first difference estimator alleviates serial correlation in panel data?

[Will Hayes]

Hi Statalist,

I am working on a state-level panel. Using -xtserial- tests for serial correlation and result is positive for serial correlation. I hope to use first differencing. If serial correlation exists in the panel, can I say the FD is more reliable than fixed effects? And why? Many thanks for your advice!

Will

[Justin Niakamal]

I don't think there's enough information here for sound advice. Some additional context would help, but if T is not large then serial correlation isn't necessarily a major issue and you can generally use robust standard errors to deal with the problem. Take a look at the community-contributed xtscc (from SSC) and see if it suits your setup.

[Jeff Wooldridge]

If there is strong positive serial correlation then FD can be more efficient than FE, but it's not guaranteed. If you use FD you should still compute cluster-robust standard errors because there is likely still serial correlation (and heteroskedasticity is always possible).

Unfortunately, the xtserial command isn't as informative as it could be. Here's a version that is more informative, where you get an estimate of pho, the parameter in the AR(1) model:

xtset id year
reg D.(y x1 ... xK year2 .. yearT), nocons vce(cluster id)
predict ehat, resid
reg ehat L.ehat, vce(cluster id)
lincom 1 + 2*L1.ehat

The last lincom command gives an estimate of rho and also a 95% CI. The xtserial command gives an F-type statistic (which is the square of the t statistic) but no estimate of rho.