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Suppose that I have a linear model with autocorrelated errors. Is there any results telling me that if I assume iid errors I overestimate or underestimate my standard errors ?

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There are no definite results (actually there are but it depends on the autocorrelation structure) for this and the reason is that if you know the correlation structure sufficiently, you can also correct for it and regain BLUE. So with the information you seek you no longer need to mitigate the error of regular SE, as you can use more appropriate measures to get a precise estimate.

The easiest option is just to use Newey/West estimates (in R, you can use the vcovHAC option of the sandwhich package). These are consistent (for large samples). This is the "easy way out".

If your sample is smaller or you can estimate a constant correlation structure, you can use (F)GLS estimation. Search for (iterative) Cochrane/Orcutt and Prais/Winston for two options on how to do this. Estimate iteratively with FGLS if you do know the structure, but not the parameter of the autocorrelation.
You can get some insight by using a Breusch-Godfrey test. This should give you some idea if there is a well defined autocorrelation structure.
Be aware though that FGLS still needs contemporary exogenity of the regressors!

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  • $\begingroup$ I agree with you and I usually perform the Breusch and Pagan test and use the Newey West estimates when necessary but I would like to have an intuition on how does a false assumption bias my standard error estimates. Is the bias similar when there is positive or negative autocorrelation ? Is the bias always in the same sense ? $\endgroup$ – PAC Jul 29 '13 at 10:06
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    $\begingroup$ ah okay got ya. Well you can write out analytically what happens with the SE if you have an AR(p) and then just try it out with a few parameters. I haven't done this but intuitively it depends on wether a) you have a structure such as AR(p) and b) how the parameters of this structure are (also in relationship to each other). I'd say that usually you would overestimate the variance of the errors because of those AR terms. But that's just guessing. $\endgroup$ – IMA Jul 29 '13 at 10:15

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