I am running a time-series regression. The Durbin-Watson statistics is very close to 2. In such a situation, would it still be better to use Newey-West standard errors, or is it ok to use OLS standard errors?
First, I would recommend to use a software package that not only reports the Durbin-Watson test statistics but also a p-value. That might give you more of an indication how close or far from 2 the statistic actually is. Furthermore, you may consider other tests for autocorrelation, e.g., Breusch-Godfrey etc. And if there is no evidence for autocorrelation (or heteroscedasticity) then the OLS standard errors are probably fine.
A pragmatic approach could also be to simply try whether using Newey-West standard errors makes a relevant difference. If the autocorrelations in the residuals are small, then Newey-West should lead to very similar results anyway.